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t=C.charCodeAt(w.pos+=e);if(w.pos=g.digit0&&e<=g.digit9?Se(!0):e===g.dot&&C.charCodeAt(w.pos+2)===g.dot?(w.pos+=3,ve(k.ellipsis)):(++w.pos,ve(k.dot))}();case g.leftParenthesis:return++w.pos,void ve(k.parenL);case g.rightParenthesis:return++w.pos,void ve(k.parenR);case g.semicolon:return++w.pos,void ve(k.semi);case g.comma:return++w.pos,void ve(k.comma);case g.leftSquareBracket:return++w.pos,void ve(k.bracketL);case g.rightSquareBracket:return++w.pos,void ve(k.bracketR);case g.leftCurlyBrace:return void(I&&C.charCodeAt(w.pos+1)===g.verticalBar?Ae(k.braceBarL,2):(++w.pos,ve(k.braceL)));case g.rightCurlyBrace:return++w.pos,void ve(k.braceR);case g.colon:return void(C.charCodeAt(w.pos+1)===g.colon?Ae(k.doubleColon,2):(++w.pos,ve(k.colon)));case g.questionMark:return void function(){const 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function(e){for(w.pos++;;){if(w.pos>=C.length)return void U("Unterminated string constant");const t=C.charCodeAt(w.pos);if(t===g.backslash)w.pos++;else if(t===e)break;w.pos++}w.pos++,ve(k.string)}(e);case g.slash:return void(C.charCodeAt(w.pos+1)===g.equalsTo?Ae(k.assign,2):Ae(k.slash,1));case g.percentSign:case g.asterisk:return void function(e){let t=e===g.asterisk?k.star:k.modulo,n=1,s=C.charCodeAt(w.pos+1);e===g.asterisk&&s===g.asterisk&&(n++,s=C.charCodeAt(w.pos+2),t=k.exponent),s===g.equalsTo&&C.charCodeAt(w.pos+2)!==g.greaterThan&&(n++,t=k.assign),Ae(t,n)}(e);case g.verticalBar:case g.ampersand:return void function(e){const t=C.charCodeAt(w.pos+1);if(t!==e){if(e===g.verticalBar){if(t===g.greaterThan)return void Ae(k.pipeline,2);if(t===g.rightCurlyBrace&&I)return void Ae(k.braceBarR,2)}t!==g.equalsTo?Ae(e===g.verticalBar?k.bitwiseOR:k.bitwiseAND,1):Ae(k.assign,2)}else C.charCodeAt(w.pos+2)===g.equalsTo?Ae(k.assign,3):Ae(e===g.verticalBar?k.logicalOR:k.logicalAND,2)}(e);case g.caret:return void(C.charCodeAt(w.pos+1)===g.equalsTo?Ae(k.assign,2):Ae(k.bitwiseXOR,1));case g.plusSign:case g.dash:return void function(e){const t=C.charCodeAt(w.pos+1);t!==e?t===g.equalsTo?Ae(k.assign,2):e===g.plusSign?Ae(k.plus,1):Ae(k.minus,1):Ae(k.preIncDec,2)}(e);case g.lessThan:return void function(){const e=C.charCodeAt(w.pos+1);if(e===g.lessThan)return C.charCodeAt(w.pos+2)===g.equalsTo?void Ae(k.assign,3):void(w.isType?Ae(k.lessThan,1):Ae(k.bitShiftL,2));e===g.equalsTo?Ae(k.relationalOrEqual,2):Ae(k.lessThan,1)}();case g.greaterThan:return void Ie();case g.equalsTo:case g.exclamationMark:return void function(e){const t=C.charCodeAt(w.pos+1);if(t!==g.equalsTo)return e===g.equalsTo&&t===g.greaterThan?(w.pos+=2,void ve(k.arrow)):void Ae(e===g.equalsTo?k.eq:k.bang,1);Ae(k.equality,C.charCodeAt(w.pos+2)===g.equalsTo?3:2)}(e);case g.tilde:return void Ae(k.tilde,1)}U(`Unexpected character '${String.fromCharCode(e)}'`,w.pos)}function Ae(e,t){w.pos+=t,ve(e)}function 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Le(e){const[t,n]=Oe(e.jsxPragma||"React.createElement"),[s,o]=Oe(e.jsxFragmentPragma||"React.Fragment");return{base:t,suffix:n,fragmentBase:s,fragmentSuffix:o}}function Oe(e){let t=e.indexOf(".");return-1===t&&(t=e.length),[e.slice(0,t),e.slice(t)]}class De{getPrefixCode(){return""}getHoistedCode(){return""}getSuffixCode(){return""}}class Pe extends De{__init(){this.lastLineNumber=1}__init2(){this.lastIndex=0}__init3(){this.filenameVarName=null}__init4(){this.esmAutomaticImportNameResolutions={}}__init5(){this.cjsAutomaticModuleNameResolutions={}}constructor(e,t,n,s,o){super(),this.rootTransformer=e,this.tokens=t,this.importProcessor=n,this.nameManager=s,this.options=o,Pe.prototype.__init.call(this),Pe.prototype.__init2.call(this),Pe.prototype.__init3.call(this),Pe.prototype.__init4.call(this),Pe.prototype.__init5.call(this),this.jsxPragmaInfo=Le(o),this.isAutomaticRuntime="automatic"===o.jsxRuntime,this.jsxImportSource=o.jsxImportSource||"react"}process(){return!!this.tokens.matches1(k.jsxTagStart)&&(this.processJSXTag(),!0)}getPrefixCode(){let e="";if(this.filenameVarName&&(e+=`const ${this.filenameVarName} = ${JSON.stringify(this.options.filePath||"")};`),this.isAutomaticRuntime)if(this.importProcessor)for(const[t,n]of Object.entries(this.cjsAutomaticModuleNameResolutions))e+=`var ${n} = require("${t}");`;else{const{createElement:t,...n}=this.esmAutomaticImportNameResolutions;t&&(e+=`import {createElement as ${t}} from "${this.jsxImportSource}";`);const s=Object.entries(n).map((([e,t])=>`${e} as ${t}`)).join(", ");if(s){e+=`import {${s}} from "${this.jsxImportSource+(this.options.production?"/jsx-runtime":"/jsx-dev-runtime")}";`}}return e}processJSXTag(){const{jsxRole:e,start:t}=this.tokens.currentToken(),n=this.options.production?null:this.getElementLocationCode(t);this.isAutomaticRuntime&&e!==Y.KeyAfterPropSpread?this.transformTagToJSXFunc(n,e):this.transformTagToCreateElement(n)}getElementLocationCode(e){return`lineNumber: ${this.getLineNumberForIndex(e)}`}getLineNumberForIndex(e){const t=this.tokens.code;for(;this.lastIndex or > at the end of the tag.");this.tokens.removeToken(),this.processAutomaticChildrenAndEndProps(t)}s&&this.tokens.appendCode(`, ${s}`)}for(this.options.production||(null===s&&this.tokens.appendCode(", void 0"),this.tokens.appendCode(`, ${n}, ${this.getDevSource(e)}, this`)),this.tokens.removeInitialToken();!this.tokens.matches1(k.jsxTagEnd);)this.tokens.removeToken();this.tokens.replaceToken(")")}transformTagToCreateElement(e){if(this.tokens.replaceToken(this.getCreateElementInvocationCode()),this.tokens.matches1(k.jsxTagEnd))this.tokens.replaceToken(`${this.getFragmentCode()}, null`),this.processChildren(!0);else if(this.processTagIntro(),this.processPropsObjectWithDevInfo(e),this.tokens.matches2(k.slash,k.jsxTagEnd));else{if(!this.tokens.matches1(k.jsxTagEnd))throw new Error("Expected either /> or > at the end of the tag.");this.tokens.removeToken(),this.processChildren(!0)}for(this.tokens.removeInitialToken();!this.tokens.matches1(k.jsxTagEnd);)this.tokens.removeToken();this.tokens.replaceToken(")")}getJSXFuncInvocationCode(e){return this.options.production?e?this.claimAutoImportedFuncInvocation("jsxs","/jsx-runtime"):this.claimAutoImportedFuncInvocation("jsx","/jsx-runtime"):this.claimAutoImportedFuncInvocation("jsxDEV","/jsx-dev-runtime")}getCreateElementInvocationCode(){if(this.isAutomaticRuntime)return this.claimAutoImportedFuncInvocation("createElement","");{const{jsxPragmaInfo:e}=this;return`${this.importProcessor&&this.importProcessor.getIdentifierReplacement(e.base)||e.base}${e.suffix}(`}}getFragmentCode(){if(this.isAutomaticRuntime)return this.claimAutoImportedName("Fragment",this.options.production?"/jsx-runtime":"/jsx-dev-runtime");{const{jsxPragmaInfo:e}=this;return(this.importProcessor&&this.importProcessor.getIdentifierReplacement(e.fragmentBase)||e.fragmentBase)+e.fragmentSuffix}}claimAutoImportedFuncInvocation(e,t){const n=this.claimAutoImportedName(e,t);return this.importProcessor?`${n}.call(void 0, `:`${n}(`}claimAutoImportedName(e,t){if(this.importProcessor){const n=this.jsxImportSource+t;return this.cjsAutomaticModuleNameResolutions[n]||(this.cjsAutomaticModuleNameResolutions[n]=this.importProcessor.getFreeIdentifierForPath(n)),`${this.cjsAutomaticModuleNameResolutions[n]}.${e}`}return this.esmAutomaticImportNameResolutions[e]||(this.esmAutomaticImportNameResolutions[e]=this.nameManager.claimFreeName(`_${e}`)),this.esmAutomaticImportNameResolutions[e]}processTagIntro(){let e=this.tokens.currentIndex()+1;for(;this.tokens.tokens[e].isType||!this.tokens.matches2AtIndex(e-1,k.jsxName,k.jsxName)&&!this.tokens.matches2AtIndex(e-1,k.greaterThan,k.jsxName)&&!this.tokens.matches1AtIndex(e,k.braceL)&&!this.tokens.matches1AtIndex(e,k.jsxTagEnd)&&!this.tokens.matches2AtIndex(e,k.slash,k.jsxTagEnd);)e++;if(e===this.tokens.currentIndex()+1){const e=this.tokens.identifierName();Be(e)&&this.tokens.replaceToken(`'${e}'`)}for(;this.tokens.currentIndex()=g.lowercaseA&&t<=g.lowercaseZ}function qe(e){let t=0,n=0;for(const s of e)"\n"===s?(t++,n=0):" "===s&&n++;return"\n".repeat(t)+" ".repeat(n)}function Me(e,t){let n,s="",o=0,r=t;if("#"===e[r]){let t,s=10;if(r++,"x"===e[r])for(s=16,r++,t=r;r=g.digit0&&i<=g.digit9||i>=g.lowercaseA&&i<=g.lowercaseF||i>=g.uppercaseA&&i<=g.uppercaseF);)r++;else for(t=r;r=g.digit0&&e<=g.digit9}function $e(e,t){const n=Le(t),s=new Set;for(let o=0;o0||t.namedExports.length>0)continue;[...t.defaultNames,...t.wildcardNames,...t.namedImports.map((({localName:e})=>e))].every((e=>this.shouldAutomaticallyElideImportedName(e)))&&this.importsToReplace.set(e,"")}}shouldAutomaticallyElideImportedName(e){return this.isTypeScriptTransformEnabled&&!this.keepUnusedImports&&!this.nonTypeIdentifiers.has(e)}generateImportReplacements(){for(const[e,t]of this.importInfoByPath.entries()){const{defaultNames:n,wildcardNames:s,namedImports:o,namedExports:r,exportStarNames:i,hasStarExport:a}=t;if(0===n.length&&0===s.length&&0===o.length&&0===r.length&&0===i.length&&!a){this.importsToReplace.set(e,`require('${e}');`);continue}const c=this.getFreeIdentifierForPath(e);let l;l=this.enableLegacyTypeScriptModuleInterop?c:s.length>0?s[0]:this.getFreeIdentifierForPath(e);let u=`var ${c} = require('${e}');`;if(s.length>0)for(const e of s){u+=` var ${e} = ${this.enableLegacyTypeScriptModuleInterop?c:`${this.helperManager.getHelperName("interopRequireWildcard")}(${c})`};`}else i.length>0&&l!==c?u+=` var ${l} = ${this.helperManager.getHelperName("interopRequireWildcard")}(${c});`:n.length>0&&l!==c&&(u+=` var ${l} = ${this.helperManager.getHelperName("interopRequireDefault")}(${c});`);for(const{importedName:e,localName:t}of r)u+=` ${this.helperManager.getHelperName("createNamedExportFrom")}(${c}, '${t}', '${e}');`;for(const e of i)u+=` exports.${e} = ${l};`;a&&(u+=` ${this.helperManager.getHelperName("createStarExport")}(${c});`),this.importsToReplace.set(e,u);for(const e of n)this.identifierReplacements.set(e,`${l}.default`);for(const{importedName:e,localName:t}of o)this.identifierReplacements.set(t,`${c}.${e}`)}}getFreeIdentifierForPath(e){const t=e.split("/"),n=t[t.length-1].replace(/\W/g,"");return this.nameManager.claimFreeName(`_${n}`)}preprocessImportAtIndex(e){const t=[],n=[],s=[];if(e++,(this.tokens.matchesContextualAtIndex(e,m._type)||this.tokens.matches1AtIndex(e,k._typeof))&&!this.tokens.matches1AtIndex(e+1,k.comma)&&!this.tokens.matchesContextualAtIndex(e+1,m._from))return;if(this.tokens.matches1AtIndex(e,k.parenL))return;if(this.tokens.matches1AtIndex(e,k.name)&&(t.push(this.tokens.identifierNameAtIndex(e)),e++,this.tokens.matches1AtIndex(e,k.comma)&&e++),this.tokens.matches1AtIndex(e,k.star)&&(e+=2,n.push(this.tokens.identifierNameAtIndex(e)),e++),this.tokens.matches1AtIndex(e,k.braceL)){const n=this.getNamedImports(e+1);e=n.newIndex;for(const e of n.namedImports)"default"===e.importedName?t.push(e.localName):s.push(e)}if(this.tokens.matchesContextualAtIndex(e,m._from)&&e++,!this.tokens.matches1AtIndex(e,k.string))throw new Error("Expected string token at the end of import statement.");const o=this.tokens.stringValueAtIndex(e),r=this.getImportInfo(o);r.defaultNames.push(...t),r.wildcardNames.push(...n),r.namedImports.push(...s),0===t.length&&0===n.length&&0===s.length&&(r.hasBareImport=!0)}preprocessExportAtIndex(e){if(this.tokens.matches2AtIndex(e,k._export,k._var)||this.tokens.matches2AtIndex(e,k._export,k._let)||this.tokens.matches2AtIndex(e,k._export,k._const))this.preprocessVarExportAtIndex(e);else if(this.tokens.matches2AtIndex(e,k._export,k._function)||this.tokens.matches2AtIndex(e,k._export,k._class)){const t=this.tokens.identifierNameAtIndex(e+2);this.addExportBinding(t,t)}else if(this.tokens.matches3AtIndex(e,k._export,k.name,k._function)){const t=this.tokens.identifierNameAtIndex(e+3);this.addExportBinding(t,t)}else 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vo extends De{constructor(e){super(),this.tokens=e}process(){if(this.tokens.matches1(k.num)){const e=this.tokens.currentTokenCode();if(e.includes("_"))return this.tokens.replaceToken(e.replace(/_/g,"")),!0}return!1}}class Io extends De{constructor(e,t){super(),this.tokens=e,this.nameManager=t}process(){return!!this.tokens.matches2(k._catch,k.braceL)&&(this.tokens.copyToken(),this.tokens.appendCode(` (${this.nameManager.claimFreeName("e")})`),!0)}}class wo extends De{constructor(e,t){super(),this.tokens=e,this.nameManager=t}process(){if(this.tokens.matches1(k.nullishCoalescing)){const e=this.tokens.currentToken();return this.tokens.tokens[e.nullishStartIndex].isAsyncOperation?this.tokens.replaceTokenTrimmingLeftWhitespace(", async () => ("):this.tokens.replaceTokenTrimmingLeftWhitespace(", () => ("),!0}if(this.tokens.matches1(k._delete)){if(this.tokens.tokenAtRelativeIndex(1).isOptionalChainStart)return this.tokens.removeInitialToken(),!0}const 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dist2).sum() / 2\n"})}),"\n",(0,n.jsxs)(e.admonition,{title:"note",type:"info",children:[(0,n.jsxs)(e.p,{children:[(0,n.jsx)(e.strong,{children:"3 Ways of Manually Computing TVD:"})," \ud83e\uddee"]}),(0,n.jsx)(e.p,{children:(0,n.jsxs)(e.em,{children:["Assume ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"P"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"P"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.13889em"},children:"P"})]})})]})," is the first distribution and ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"Q"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"Q"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.8778em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"Q"})]})})]})," is the second distribution, and the categories appear in the same order."]})}),(0,n.jsxs)(e.ol,{children:["\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:[(0,n.jsx)(e.strong,{children:"Follow the Definition:"})," Calculate the sum of the absolute differences of the proportions of the two distributions ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"P"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"P"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.13889em"},children:"P"})]})})]})," and ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"Q"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"Q"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.8778em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"Q"})]})})]}),", all divided by 2."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:[(0,n.jsx)(e.strong,{children:"Sum of Positive Differences:"})," Add only the values where the first distribution ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"P"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"P"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.13889em"},children:"P"})]})})]})," is greater than the second distribution ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"Q"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"Q"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.8778em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"Q"})]})})]}),". This essentially sums the excessive probabilities in one distribution over the other."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:[(0,n.jsx)(e.strong,{children:"Sum of Negative Differences:"})," Add only the absolute values where the first distribution ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"P"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"P"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.13889em"},children:"P"})]})})]})," is less than the second distribution ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"Q"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"Q"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.8778em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"Q"})]})})]}),". This can also be interpreted as adding only the values where the second distribution ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"Q"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"Q"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.8778em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"Q"})]})})]})," is greater than the first distribution ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"P"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"P"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.13889em"},children:"P"})]})})]}),"."]}),"\n"]}),"\n"]}),(0,n.jsx)(e.p,{children:(0,n.jsx)(e.strong,{children:"Any of the three methods can be the optimal choice depending on specific distributions."})}),(0,n.jsxs)(e.admonition,{title:"Example \ud83c\udf1f",type:"note",children:[(0,n.jsx)(e.p,{children:"Let's use an example to show how TVD can be computed in three ways."}),(0,n.jsxs)(e.p,{children:["In the ",(0,n.jsx)(e.code,{children:"full_pets"})," DataFrame, we found that the color distribution of dogs seems different from that of all pets. 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dist2).sum() / 2\n"})}),"\n",(0,n.jsxs)(e.admonition,{title:"note",type:"info",children:[(0,n.jsxs)(e.p,{children:[(0,n.jsx)(e.strong,{children:"3 Ways of Manually Computing TVD:"})," \ud83e\uddee"]}),(0,n.jsx)(e.p,{children:(0,n.jsxs)(e.em,{children:["Assume ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"P"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"P"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.13889em"},children:"P"})]})})]})," is the first distribution and ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"Q"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"Q"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.8778em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"Q"})]})})]})," is the second distribution, and the categories appear in the same order."]})}),(0,n.jsxs)(e.ol,{children:["\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:[(0,n.jsx)(e.strong,{children:"Follow the Definition:"})," Calculate the sum of the absolute differences of the proportions of the two distributions ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"P"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"P"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.13889em"},children:"P"})]})})]})," and ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"Q"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"Q"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.8778em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"Q"})]})})]}),", all divided by 2."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:[(0,n.jsx)(e.strong,{children:"Sum of Positive Differences:"})," Add only the values where the first distribution ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"P"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"P"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.13889em"},children:"P"})]})})]})," is greater than the second distribution ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"Q"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"Q"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.8778em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"Q"})]})})]}),". This essentially sums the excessive probabilities in one distribution over the other."]}),"\n"]}),"\n",(0,n.jsxs)(e.li,{children:["\n",(0,n.jsxs)(e.p,{children:[(0,n.jsx)(e.strong,{children:"Sum of Negative Differences:"})," Add only the absolute values where the first distribution ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"P"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"P"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.13889em"},children:"P"})]})})]})," is less than the second distribution ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"Q"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"Q"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.8778em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"Q"})]})})]}),". This can also be interpreted as adding only the values where the second distribution ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"Q"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"Q"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.8778em",verticalAlign:"-0.1944em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",children:"Q"})]})})]})," is greater than the first distribution ",(0,n.jsxs)(e.span,{className:"katex",children:[(0,n.jsx)(e.span,{className:"katex-mathml",children:(0,n.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(e.semantics,{children:[(0,n.jsx)(e.mrow,{children:(0,n.jsx)(e.mi,{children:"P"})}),(0,n.jsx)(e.annotation,{encoding:"application/x-tex",children:"P"})]})})}),(0,n.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(e.span,{className:"base",children:[(0,n.jsx)(e.span,{className:"strut",style:{height:"0.6833em"}}),(0,n.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.13889em"},children:"P"})]})})]}),"."]}),"\n"]}),"\n"]}),(0,n.jsx)(e.p,{children:(0,n.jsx)(e.strong,{children:"Any of the three methods can be the optimal choice depending on specific distributions."})}),(0,n.jsxs)(e.admonition,{title:"Example \ud83c\udf1f",type:"note",children:[(0,n.jsx)(e.p,{children:"Let's use an example to show how TVD can be computed in three ways."}),(0,n.jsxs)(e.p,{children:["In the ",(0,n.jsx)(e.code,{children:"full_pets"})," DataFrame, we found that the color distribution of dogs seems different from that of all pets. 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t}processPropName(e){e.includes("-")?this.tokens.replaceToken(`'${e}'`):this.tokens.copyToken()}processPropValue(){this.tokens.matches1(k.braceL)?(this.tokens.replaceToken(""),this.rootTransformer.processBalancedCode(),this.tokens.replaceToken("")):this.tokens.matches1(k.jsxTagStart)?this.processJSXTag():this.processStringPropValue()}processStringPropValue(){const e=this.tokens.currentToken(),t=this.tokens.code.slice(e.start+1,e.end-1),n=qe(t),s=function(e){let t="";for(let n=0;n<e.length;n++){const s=e[n];if("\n"===s)if(/\s/.test(e[n+1]))for(t+=" ";n<e.length&&/\s/.test(e[n+1]);)n++;else t+="\n";else if("&"===s){const{entity:s,newI:o}=Me(e,n+1);t+=s,n=o-1}else t+=s}return JSON.stringify(t)}(t);this.tokens.replaceToken(s+n)}processAutomaticChildrenAndEndProps(e){e===Y.StaticChildren?(this.tokens.appendCode(" children: ["),this.processChildren(!1),this.tokens.appendCode("]}")):(e===Y.OneChild&&this.tokens.appendCode(" children: "),this.processChildren(!1),this.tokens.appendCode("}"))}processChildren(e){let t=e;for(;;){if(this.tokens.matches2(k.jsxTagStart,k.slash))return;let e=!1;if(this.tokens.matches1(k.braceL))this.tokens.matches2(k.braceL,k.braceR)?(this.tokens.replaceToken(""),this.tokens.replaceToken("")):(this.tokens.replaceToken(t?", ":""),this.rootTransformer.processBalancedCode(),this.tokens.replaceToken(""),e=!0);else if(this.tokens.matches1(k.jsxTagStart))this.tokens.appendCode(t?", ":""),this.processJSXTag(),e=!0;else{if(!this.tokens.matches1(k.jsxText)&&!this.tokens.matches1(k.jsxEmptyText))throw new Error("Unexpected token when processing JSX children.");e=this.processChildTextElement(t)}e&&(t=!0)}}processChildTextElement(e){const t=this.tokens.currentToken(),n=this.tokens.code.slice(t.start,t.end),s=qe(n),o=function(e){let t="",n="",s=!1,o=!1;for(let r=0;r<e.length;r++){const i=e[r];if(" "===i||"\t"===i||"\r"===i)s||(n+=i);else if("\n"===i)n="",s=!0;else{if(o&&s&&(t+=" "),t+=n,n="","&"===i){const{entity:n,newI:s}=Me(e,r+1);r=s-1,t+=n}else t+=i;o=!0,s=!1}}s||(t+=n);return JSON.stringify(t)}(n);return'""'===o?(this.tokens.replaceToken(s),!1):(this.tokens.replaceToken(`${e?", ":""}${o}${s}`),!0)}getDevSource(e){return`{fileName: ${this.getFilenameVarName()}, ${e}}`}getFilenameVarName(){return this.filenameVarName||(this.filenameVarName=this.nameManager.claimFreeName("_jsxFileName")),this.filenameVarName}}function Be(e){const t=e.charCodeAt(0);return t>=g.lowercaseA&&t<=g.lowercaseZ}function qe(e){let t=0,n=0;for(const s of e)"\n"===s?(t++,n=0):" "===s&&n++;return"\n".repeat(t)+" ".repeat(n)}function Me(e,t){let n,s="",o=0,r=t;if("#"===e[r]){let t,s=10;if(r++,"x"===e[r])for(s=16,r++,t=r;r<e.length&&((i=e.charCodeAt(r))>=g.digit0&&i<=g.digit9||i>=g.lowercaseA&&i<=g.lowercaseF||i>=g.uppercaseA&&i<=g.uppercaseF);)r++;else for(t=r;r<e.length&&Fe(e.charCodeAt(r));)r++;if(";"===e[r]){const o=e.slice(t,r);o&&(r++,n=String.fromCodePoint(parseInt(o,s)))}}else for(;r<e.length&&o++<10;){const t=e[r];if(r++,";"===t){n=Re.get(s);break}s+=t}var i;return n?{entity:n,newI:r}:{entity:"&",newI:t}}function Fe(e){return e>=g.digit0&&e<=g.digit9}function $e(e,t){const n=Le(t),s=new Set;for(let o=0;o<e.tokens.length;o++){const t=e.tokens[o];if(t.type!==k.name||t.isType||t.identifierRole!==J.Access&&t.identifierRole!==J.ObjectShorthand&&t.identifierRole!==J.ExportAccess||t.shadowsGlobal||s.add(e.identifierNameForToken(t)),t.type===k.jsxTagStart&&s.add(n.base),t.type===k.jsxTagStart&&o+1<e.tokens.length&&e.tokens[o+1].type===k.jsxTagEnd&&(s.add(n.base),s.add(n.fragmentBase)),t.type===k.jsxName&&t.identifierRole===J.Access){Be(e.identifierNameForToken(t))&&e.tokens[o+1].type!==k.dot||s.add(e.identifierNameForToken(t))}}return s}class Ue{__init(){this.nonTypeIdentifiers=new Set}__init2(){this.importInfoByPath=new Map}__init3(){this.importsToReplace=new Map}__init4(){this.identifierReplacements=new Map}__init5(){this.exportBindingsByLocalName=new Map}constructor(e,t,n,s,o,r,i){this.nameManager=e,this.tokens=t,this.enableLegacyTypeScriptModuleInterop=n,this.options=s,this.isTypeScriptTransformEnabled=o,this.keepUnusedImports=r,this.helperManager=i,Ue.prototype.__init.call(this),Ue.prototype.__init2.call(this),Ue.prototype.__init3.call(this),Ue.prototype.__init4.call(this),Ue.prototype.__init5.call(this)}preprocessTokens(){for(let e=0;e<this.tokens.tokens.length;e++)this.tokens.matches1AtIndex(e,k._import)&&!this.tokens.matches3AtIndex(e,k._import,k.name,k.eq)&&this.preprocessImportAtIndex(e),this.tokens.matches1AtIndex(e,k._export)&&!this.tokens.matches2AtIndex(e,k._export,k.eq)&&this.preprocessExportAtIndex(e);this.generateImportReplacements()}pruneTypeOnlyImports(){this.nonTypeIdentifiers=$e(this.tokens,this.options);for(const[e,t]of this.importInfoByPath.entries()){if(t.hasBareImport||t.hasStarExport||t.exportStarNames.length>0||t.namedExports.length>0)continue;[...t.defaultNames,...t.wildcardNames,...t.namedImports.map((({localName:e})=>e))].every((e=>this.shouldAutomaticallyElideImportedName(e)))&&this.importsToReplace.set(e,"")}}shouldAutomaticallyElideImportedName(e){return this.isTypeScriptTransformEnabled&&!this.keepUnusedImports&&!this.nonTypeIdentifiers.has(e)}generateImportReplacements(){for(const[e,t]of this.importInfoByPath.entries()){const{defaultNames:n,wildcardNames:s,namedImports:o,namedExports:r,exportStarNames:i,hasStarExport:a}=t;if(0===n.length&&0===s.length&&0===o.length&&0===r.length&&0===i.length&&!a){this.importsToReplace.set(e,`require('${e}');`);continue}const c=this.getFreeIdentifierForPath(e);let l;l=this.enableLegacyTypeScriptModuleInterop?c:s.length>0?s[0]:this.getFreeIdentifierForPath(e);let u=`var ${c} = require('${e}');`;if(s.length>0)for(const e of s){u+=` var ${e} = ${this.enableLegacyTypeScriptModuleInterop?c:`${this.helperManager.getHelperName("interopRequireWildcard")}(${c})`};`}else i.length>0&&l!==c?u+=` var ${l} = ${this.helperManager.getHelperName("interopRequireWildcard")}(${c});`:n.length>0&&l!==c&&(u+=` var ${l} = ${this.helperManager.getHelperName("interopRequireDefault")}(${c});`);for(const{importedName:e,localName:t}of r)u+=` ${this.helperManager.getHelperName("createNamedExportFrom")}(${c}, '${t}', '${e}');`;for(const e of i)u+=` exports.${e} = ${l};`;a&&(u+=` ${this.helperManager.getHelperName("createStarExport")}(${c});`),this.importsToReplace.set(e,u);for(const e of n)this.identifierReplacements.set(e,`${l}.default`);for(const{importedName:e,localName:t}of o)this.identifierReplacements.set(t,`${c}.${e}`)}}getFreeIdentifierForPath(e){const t=e.split("/"),n=t[t.length-1].replace(/\W/g,"");return this.nameManager.claimFreeName(`_${n}`)}preprocessImportAtIndex(e){const t=[],n=[],s=[];if(e++,(this.tokens.matchesContextualAtIndex(e,m._type)||this.tokens.matches1AtIndex(e,k._typeof))&&!this.tokens.matches1AtIndex(e+1,k.comma)&&!this.tokens.matchesContextualAtIndex(e+1,m._from))return;if(this.tokens.matches1AtIndex(e,k.parenL))return;if(this.tokens.matches1AtIndex(e,k.name)&&(t.push(this.tokens.identifierNameAtIndex(e)),e++,this.tokens.matches1AtIndex(e,k.comma)&&e++),this.tokens.matches1AtIndex(e,k.star)&&(e+=2,n.push(this.tokens.identifierNameAtIndex(e)),e++),this.tokens.matches1AtIndex(e,k.braceL)){const n=this.getNamedImports(e+1);e=n.newIndex;for(const e of n.namedImports)"default"===e.importedName?t.push(e.localName):s.push(e)}if(this.tokens.matchesContextualAtIndex(e,m._from)&&e++,!this.tokens.matches1AtIndex(e,k.string))throw new Error("Expected string token at the end of import statement.");const o=this.tokens.stringValueAtIndex(e),r=this.getImportInfo(o);r.defaultNames.push(...t),r.wildcardNames.push(...n),r.namedImports.push(...s),0===t.length&&0===n.length&&0===s.length&&(r.hasBareImport=!0)}preprocessExportAtIndex(e){if(this.tokens.matches2AtIndex(e,k._export,k._var)||this.tokens.matches2AtIndex(e,k._export,k._let)||this.tokens.matches2AtIndex(e,k._export,k._const))this.preprocessVarExportAtIndex(e);else if(this.tokens.matches2AtIndex(e,k._export,k._function)||this.tokens.matches2AtIndex(e,k._export,k._class)){const t=this.tokens.identifierNameAtIndex(e+2);this.addExportBinding(t,t)}else if(this.tokens.matches3AtIndex(e,k._export,k.name,k._function)){const t=this.tokens.identifierNameAtIndex(e+3);this.addExportBinding(t,t)}else this.tokens.matches2AtIndex(e,k._export,k.braceL)?this.preprocessNamedExportAtIndex(e):this.tokens.matches2AtIndex(e,k._export,k.star)&&this.preprocessExportStarAtIndex(e)}preprocessVarExportAtIndex(e){let t=0;for(let n=e+2;;n++)if(this.tokens.matches1AtIndex(n,k.braceL)||this.tokens.matches1AtIndex(n,k.dollarBraceL)||this.tokens.matches1AtIndex(n,k.bracketL))t++;else if(this.tokens.matches1AtIndex(n,k.braceR)||this.tokens.matches1AtIndex(n,k.bracketR))t--;else{if(0===t&&!this.tokens.matches1AtIndex(n,k.name))break;if(this.tokens.matches1AtIndex(1,k.eq)){const e=this.tokens.currentToken().rhsEndIndex;if(null==e)throw new Error("Expected = token with an end index.");n=e-1}else{if(Q(this.tokens.tokens[n])){const e=this.tokens.identifierNameAtIndex(n);this.identifierReplacements.set(e,`exports.${e}`)}}}}preprocessNamedExportAtIndex(e){e+=2;const{newIndex:t,namedImports:n}=this.getNamedImports(e);if(e=t,!this.tokens.matchesContextualAtIndex(e,m._from)){for(const{importedName:e,localName:t}of n)this.addExportBinding(e,t);return}if(e++,!this.tokens.matches1AtIndex(e,k.string))throw new Error("Expected string token at the end of import statement.");const s=this.tokens.stringValueAtIndex(e);this.getImportInfo(s).namedExports.push(...n)}preprocessExportStarAtIndex(e){let t=null;if(this.tokens.matches3AtIndex(e,k._export,k.star,k._as)?(e+=3,t=this.tokens.identifierNameAtIndex(e),e+=2):e+=3,!this.tokens.matches1AtIndex(e,k.string))throw new Error("Expected string token at the end of star export statement.");const n=this.tokens.stringValueAtIndex(e),s=this.getImportInfo(n);null!==t?s.exportStarNames.push(t):s.hasStarExport=!0}getNamedImports(e){const t=[];for(;;){if(this.tokens.matches1AtIndex(e,k.braceR)){e++;break}const n=Ne(this.tokens,e);if(e=n.endIndex,n.isType||t.push({importedName:n.leftName,localName:n.rightName}),this.tokens.matches2AtIndex(e,k.comma,k.braceR)){e+=2;break}if(this.tokens.matches1AtIndex(e,k.braceR)){e++;break}if(!this.tokens.matches1AtIndex(e,k.comma))throw new Error(`Unexpected token: ${JSON.stringify(this.tokens.tokens[e])}`);e++}return{newIndex:e,namedImports:t}}getImportInfo(e){const t=this.importInfoByPath.get(e);if(t)return t;const n={defaultNames:[],wildcardNames:[],namedImports:[],namedExports:[],hasBareImport:!1,exportStarNames:[],hasStarExport:!1};return this.importInfoByPath.set(e,n),n}addExportBinding(e,t){this.exportBindingsByLocalName.has(e)||this.exportBindingsByLocalName.set(e,[]),this.exportBindingsByLocalName.get(e).push(t)}claimImportCode(e){const t=this.importsToReplace.get(e);return this.importsToReplace.set(e,""),t||""}getIdentifierReplacement(e){return this.identifierReplacements.get(e)||null}resolveExportBinding(e){const t=this.exportBindingsByLocalName.get(e);return t&&0!==t.length?t.map((e=>`exports.${e}`)).join(" = "):null}getGlobalNames(){return new Set([...this.identifierReplacements.keys(),...this.exportBindingsByLocalName.keys()])}}var Ke=n(9320);function He({code:e,mappings:t},n,s,o,r){const i=function(e,t){const n=new Array(t.length);let s=0,o=t[s].start,r=0;for(let i=0;i<e.length;i++)i===o&&(n[s]=o-r,s++,o=t[s].start),e.charCodeAt(i)===g.lineFeed&&(r=i+1);return n}(o,r),a=new Ke.GenMapping({file:s.compiledFilename});let c=0,l=t[0];for(;void 0===l&&c<t.length-1;)c++,l=t[c];let u=0,h=0;l!==h&&(0,Ke.maybeAddSegment)(a,u,0,n,u,0);for(let m=0;m<e.length;m++){if(m===l){const e=l-h,s=i[c];for((0,Ke.maybeAddSegment)(a,u,e,n,u,s);(l===m||void 0===l)&&c<t.length-1;)c++,l=t[c]}e.charCodeAt(m)===g.lineFeed&&(u++,h=m+1,l!==h&&(0,Ke.maybeAddSegment)(a,u,0,n,u,0))}const{sourceRoot:p,sourcesContent:d,...f}=(0,Ke.toEncodedMap)(a);return f}const Ve={require:'\n import {createRequire as CREATE_REQUIRE_NAME} from "module";\n const require = CREATE_REQUIRE_NAME(import.meta.url);\n ',interopRequireWildcard:"\n function interopRequireWildcard(obj) {\n if (obj && obj.__esModule) {\n return obj;\n } else {\n var newObj = {};\n if (obj != null) {\n for (var key in obj) {\n if (Object.prototype.hasOwnProperty.call(obj, key)) {\n newObj[key] = obj[key];\n }\n }\n }\n newObj.default = obj;\n return newObj;\n }\n }\n ",interopRequireDefault:"\n function interopRequireDefault(obj) {\n return obj && obj.__esModule ? obj : { default: obj };\n }\n ",createNamedExportFrom:"\n function createNamedExportFrom(obj, localName, importedName) {\n Object.defineProperty(exports, localName, {enumerable: true, configurable: true, get: () => obj[importedName]});\n }\n ",createStarExport:'\n function createStarExport(obj) {\n Object.keys(obj)\n .filter((key) => key !== "default" && key !== "__esModule")\n .forEach((key) => {\n if (exports.hasOwnProperty(key)) {\n return;\n }\n Object.defineProperty(exports, key, {enumerable: true, configurable: true, get: () => obj[key]});\n });\n }\n ',nullishCoalesce:"\n function nullishCoalesce(lhs, rhsFn) {\n if (lhs != null) {\n return lhs;\n } else {\n return rhsFn();\n }\n }\n ",asyncNullishCoalesce:"\n async function asyncNullishCoalesce(lhs, rhsFn) {\n if (lhs != null) {\n return lhs;\n } else {\n return await rhsFn();\n }\n }\n ",optionalChain:"\n function optionalChain(ops) {\n let lastAccessLHS = undefined;\n let value = ops[0];\n let i = 1;\n while (i < ops.length) {\n const op = ops[i];\n const fn = ops[i + 1];\n i += 2;\n if ((op === 'optionalAccess' || op === 'optionalCall') && value == null) {\n return undefined;\n }\n if (op === 'access' || op === 'optionalAccess') {\n lastAccessLHS = value;\n value = fn(value);\n } else if (op === 'call' || op === 'optionalCall') {\n value = fn((...args) => value.call(lastAccessLHS, ...args));\n lastAccessLHS = undefined;\n }\n }\n return value;\n }\n ",asyncOptionalChain:"\n async function asyncOptionalChain(ops) {\n let lastAccessLHS = undefined;\n let value = ops[0];\n let i = 1;\n while (i < ops.length) {\n const op = ops[i];\n const fn = ops[i + 1];\n i += 2;\n if ((op === 'optionalAccess' || op === 'optionalCall') && value == null) {\n return undefined;\n }\n if (op === 'access' || op === 'optionalAccess') {\n lastAccessLHS = value;\n value = await fn(value);\n } else if (op === 'call' || op === 'optionalCall') {\n value = await fn((...args) => value.call(lastAccessLHS, ...args));\n lastAccessLHS = undefined;\n }\n }\n return value;\n }\n ",optionalChainDelete:"\n function optionalChainDelete(ops) {\n const result = OPTIONAL_CHAIN_NAME(ops);\n return result == null ? true : result;\n }\n ",asyncOptionalChainDelete:"\n async function asyncOptionalChainDelete(ops) {\n const result = await ASYNC_OPTIONAL_CHAIN_NAME(ops);\n return result == null ? true : result;\n }\n "};class We{__init(){this.helperNames={}}__init2(){this.createRequireName=null}constructor(e){this.nameManager=e,We.prototype.__init.call(this),We.prototype.__init2.call(this)}getHelperName(e){let t=this.helperNames[e];return t||(t=this.nameManager.claimFreeName(`_${e}`),this.helperNames[e]=t,t)}emitHelpers(){let e="";this.helperNames.optionalChainDelete&&this.getHelperName("optionalChain"),this.helperNames.asyncOptionalChainDelete&&this.getHelperName("asyncOptionalChain");for(const[t,n]of Object.entries(Ve)){const s=this.helperNames[t];let o=n;"optionalChainDelete"===t?o=o.replace("OPTIONAL_CHAIN_NAME",this.helperNames.optionalChain):"asyncOptionalChainDelete"===t?o=o.replace("ASYNC_OPTIONAL_CHAIN_NAME",this.helperNames.asyncOptionalChain):"require"===t&&(null===this.createRequireName&&(this.createRequireName=this.nameManager.claimFreeName("_createRequire")),o=o.replace(/CREATE_REQUIRE_NAME/g,this.createRequireName)),s&&(e+=" ",e+=o.replace(t,s).replace(/\s+/g," ").trim())}return e}}function ze(e,t,n){(function(e,t){for(const n of e.tokens)if(n.type===k.name&&!n.isType&&Z(n)&&t.has(e.identifierNameForToken(n)))return!0;return!1})(e,n)&&function(e,t,n){const s=[];let o=t.length-1;for(let r=e.tokens.length-1;;r--){for(;s.length>0&&s[s.length-1].startTokenIndex===r+1;)s.pop();for(;o>=0&&t[o].endTokenIndex===r+1;)s.push(t[o]),o--;if(r<0)break;const i=e.tokens[r],a=e.identifierNameForToken(i);if(s.length>1&&!i.isType&&i.type===k.name&&n.has(a))if(te(i))Ge(s[s.length-1],e,a);else if(ne(i)){let t=s.length-1;for(;t>0&&!s[t].isFunctionScope;)t--;if(t<0)throw new Error("Did not find parent function scope.");Ge(s[t],e,a)}}if(s.length>0)throw new Error("Expected empty scope stack after processing file.")}(e,t,n)}function Ge(e,t,n){for(let s=e.startTokenIndex;s<e.endTokenIndex;s++){const e=t.tokens[s];e.type!==k.name&&e.type!==k.jsxName||t.identifierNameForToken(e)!==n||(e.shadowsGlobal=!0)}}class Xe{__init(){this.usedNames=new Set}constructor(e,t){Xe.prototype.__init.call(this),this.usedNames=new Set(function(e,t){const n=[];for(const s of t)s.type===k.name&&n.push(e.slice(s.start,s.end));return n}(e,t))}claimFreeName(e){const t=this.findFreeName(e);return this.usedNames.add(t),t}findFreeName(e){if(!this.usedNames.has(e))return e;let t=2;for(;this.usedNames.has(e+String(t));)t++;return e+String(t)}}var Je=n(9361);const Ye={Transform:Je.union(Je.lit("jsx"),Je.lit("typescript"),Je.lit("flow"),Je.lit("imports"),Je.lit("react-hot-loader"),Je.lit("jest")),SourceMapOptions:Je.iface([],{compiledFilename:"string"}),Options:Je.iface([],{transforms:Je.array("Transform"),disableESTransforms:Je.opt("boolean"),jsxRuntime:Je.opt(Je.union(Je.lit("classic"),Je.lit("automatic"),Je.lit("preserve"))),production:Je.opt("boolean"),jsxImportSource:Je.opt("string"),jsxPragma:Je.opt("string"),jsxFragmentPragma:Je.opt("string"),keepUnusedImports:Je.opt("boolean"),preserveDynamicImport:Je.opt("boolean"),injectCreateRequireForImportRequire:Je.opt("boolean"),enableLegacyTypeScriptModuleInterop:Je.opt("boolean"),enableLegacyBabel5ModuleInterop:Je.opt("boolean"),sourceMapOptions:Je.opt("SourceMapOptions"),filePath:Je.opt("string")})},{Options:Qe}=(0,Je.createCheckers)(Ye);function Ze(){re(),fn(!1)}function et(e){re(),ot(e)}function tt(e){Vn(),st(e)}function 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t=e.currentIndex();for(;!e.matches1AtIndex(t,k.braceR);)t++;return e.matchesContextualAtIndex(t+1,m._from)&&e.matches1AtIndex(t+2,k.string)}function mo(e){(e.matches2(k._with,k.braceL)||e.matches2(k.name,k.braceL)&&e.matchesContextual(m._assert))&&(e.removeToken(),e.removeToken(),e.removeBalancedCode(),e.removeToken())}function ko(e,t,n,s){if(!e||t)return!1;const o=n.currentToken();if(null==o.rhsEndIndex)throw new Error("Expected non-null rhsEndIndex on export token.");const r=o.rhsEndIndex-n.currentIndex();if(3!==r&&(4!==r||!n.matches1AtIndex(o.rhsEndIndex-1,k.semi)))return!1;const i=n.tokenAtRelativeIndex(2);if(i.type!==k.name)return!1;const a=n.identifierNameForToken(i);return s.typeDeclarations.has(a)&&!s.valueDeclarations.has(a)}class go extends De{__init(){this.hadExport=!1}__init2(){this.hadNamedExport=!1}__init3(){this.hadDefaultExport=!1}constructor(e,t,n,s,o,r,i,a,c,l,u,h){super(),this.rootTransformer=e,this.tokens=t,this.importProcessor=n,this.nameManager=s,this.helperManager=o,this.reactHotLoaderTransformer=r,this.enableLegacyBabel5ModuleInterop=i,this.enableLegacyTypeScriptModuleInterop=a,this.isTypeScriptTransformEnabled=c,this.isFlowTransformEnabled=l,this.preserveDynamicImport=u,this.keepUnusedImports=h,go.prototype.__init.call(this),go.prototype.__init2.call(this),go.prototype.__init3.call(this),this.declarationInfo=c?po(t):ho}getPrefixCode(){let e="";return this.hadExport&&(e+='Object.defineProperty(exports, "__esModule", {value: true});'),e}getSuffixCode(){return this.enableLegacyBabel5ModuleInterop&&this.hadDefaultExport&&!this.hadNamedExport?"\nmodule.exports = exports.default;\n":""}process(){return this.tokens.matches3(k._import,k.name,k.eq)?this.processImportEquals():this.tokens.matches1(k._import)?(this.processImport(),!0):this.tokens.matches2(k._export,k.eq)?(this.tokens.replaceToken("module.exports"),!0):this.tokens.matches1(k._export)&&!this.tokens.currentToken().isType?(this.hadExport=!0,this.processExport()):!(!this.tokens.matches2(k.name,k.postIncDec)||!this.processPostIncDec())||(this.tokens.matches1(k.name)||this.tokens.matches1(k.jsxName)?this.processIdentifier():this.tokens.matches1(k.eq)?this.processAssignment():this.tokens.matches1(k.assign)?this.processComplexAssignment():!!this.tokens.matches1(k.preIncDec)&&this.processPreIncDec())}processImportEquals(){const e=this.tokens.identifierNameAtIndex(this.tokens.currentIndex()+1);return this.importProcessor.shouldAutomaticallyElideImportedName(e)?uo(this.tokens):this.tokens.replaceToken("const"),!0}processImport(){if(this.tokens.matches2(k._import,k.parenL)){if(this.preserveDynamicImport)return void this.tokens.copyToken();const e=this.enableLegacyTypeScriptModuleInterop?"":`${this.helperManager.getHelperName("interopRequireWildcard")}(`;this.tokens.replaceToken(`Promise.resolve().then(() => ${e}require`);const t=this.tokens.currentToken().contextId;if(null==t)throw new Error("Expected context ID on dynamic import invocation.");for(this.tokens.copyToken();!this.tokens.matchesContextIdAndLabel(k.parenR,t);)this.rootTransformer.processToken();return void this.tokens.replaceToken(e?")))":"))")}if(this.removeImportAndDetectIfShouldElide())this.tokens.removeToken();else{const e=this.tokens.stringValue();this.tokens.replaceTokenTrimmingLeftWhitespace(this.importProcessor.claimImportCode(e)),this.tokens.appendCode(this.importProcessor.claimImportCode(e))}mo(this.tokens),this.tokens.matches1(k.semi)&&this.tokens.removeToken()}removeImportAndDetectIfShouldElide(){if(this.tokens.removeInitialToken(),this.tokens.matchesContextual(m._type)&&!this.tokens.matches1AtIndex(this.tokens.currentIndex()+1,k.comma)&&!this.tokens.matchesContextualAtIndex(this.tokens.currentIndex()+1,m._from))return this.removeRemainingImport(),!0;if(this.tokens.matches1(k.name)||this.tokens.matches1(k.star))return this.removeRemainingImport(),!1;if(this.tokens.matches1(k.string))return!1;let e=!1,t=!1;for(;!this.tokens.matches1(k.string);)(!e&&this.tokens.matches1(k.braceL)||this.tokens.matches1(k.comma))&&(this.tokens.removeToken(),this.tokens.matches1(k.braceR)||(t=!0),(this.tokens.matches2(k.name,k.comma)||this.tokens.matches2(k.name,k.braceR)||this.tokens.matches4(k.name,k.name,k.name,k.comma)||this.tokens.matches4(k.name,k.name,k.name,k.braceR))&&(e=!0)),this.tokens.removeToken();return!this.keepUnusedImports&&(this.isTypeScriptTransformEnabled?!e:!!this.isFlowTransformEnabled&&(t&&!e))}removeRemainingImport(){for(;!this.tokens.matches1(k.string);)this.tokens.removeToken()}processIdentifier(){const e=this.tokens.currentToken();if(e.shadowsGlobal)return!1;if(e.identifierRole===J.ObjectShorthand)return this.processObjectShorthand();if(e.identifierRole!==J.Access)return!1;const t=this.importProcessor.getIdentifierReplacement(this.tokens.identifierNameForToken(e));if(!t)return!1;let n=this.tokens.currentIndex()+1;for(;n<this.tokens.tokens.length&&this.tokens.tokens[n].type===k.parenR;)n++;return this.tokens.tokens[n].type===k.parenL?this.tokens.tokenAtRelativeIndex(1).type===k.parenL&&this.tokens.tokenAtRelativeIndex(-1).type!==k._new?(this.tokens.replaceToken(`${t}.call(void 0, `),this.tokens.removeToken(),this.rootTransformer.processBalancedCode(),this.tokens.copyExpectedToken(k.parenR)):this.tokens.replaceToken(`(0, ${t})`):this.tokens.replaceToken(t),!0}processObjectShorthand(){const e=this.tokens.identifierName(),t=this.importProcessor.getIdentifierReplacement(e);return!!t&&(this.tokens.replaceToken(`${e}: ${t}`),!0)}processExport(){if(this.tokens.matches2(k._export,k._enum)||this.tokens.matches3(k._export,k._const,k._enum))return this.hadNamedExport=!0,!1;if(this.tokens.matches2(k._export,k._default))return this.tokens.matches3(k._export,k._default,k._enum)?(this.hadDefaultExport=!0,!1):(this.processExportDefault(),!0);if(this.tokens.matches2(k._export,k.braceL))return this.processExportBindings(),!0;if(this.tokens.matches2(k._export,k.name)&&this.tokens.matchesContextualAtIndex(this.tokens.currentIndex()+1,m._type)){if(this.tokens.removeInitialToken(),this.tokens.removeToken(),this.tokens.matches1(k.braceL)){for(;!this.tokens.matches1(k.braceR);)this.tokens.removeToken();this.tokens.removeToken()}else this.tokens.removeToken(),this.tokens.matches1(k._as)&&(this.tokens.removeToken(),this.tokens.removeToken());return this.tokens.matchesContextual(m._from)&&this.tokens.matches1AtIndex(this.tokens.currentIndex()+1,k.string)&&(this.tokens.removeToken(),this.tokens.removeToken(),mo(this.tokens)),!0}if(this.hadNamedExport=!0,this.tokens.matches2(k._export,k._var)||this.tokens.matches2(k._export,k._let)||this.tokens.matches2(k._export,k._const))return this.processExportVar(),!0;if(this.tokens.matches2(k._export,k._function)||this.tokens.matches3(k._export,k.name,k._function))return this.processExportFunction(),!0;if(this.tokens.matches2(k._export,k._class)||this.tokens.matches3(k._export,k._abstract,k._class)||this.tokens.matches2(k._export,k.at))return this.processExportClass(),!0;if(this.tokens.matches2(k._export,k.star))return this.processExportStar(),!0;throw new Error("Unrecognized export syntax.")}processAssignment(){const e=this.tokens.currentIndex(),t=this.tokens.tokens[e-1];if(t.isType||t.type!==k.name)return!1;if(t.shadowsGlobal)return!1;if(e>=2&&this.tokens.matches1AtIndex(e-2,k.dot))return!1;if(e>=2&&[k._var,k._let,k._const].includes(this.tokens.tokens[e-2].type))return!1;const n=this.importProcessor.resolveExportBinding(this.tokens.identifierNameForToken(t));return!!n&&(this.tokens.copyToken(),this.tokens.appendCode(` ${n} =`),!0)}processComplexAssignment(){const e=this.tokens.currentIndex(),t=this.tokens.tokens[e-1];if(t.type!==k.name)return!1;if(t.shadowsGlobal)return!1;if(e>=2&&this.tokens.matches1AtIndex(e-2,k.dot))return!1;const n=this.importProcessor.resolveExportBinding(this.tokens.identifierNameForToken(t));return!!n&&(this.tokens.appendCode(` = ${n}`),this.tokens.copyToken(),!0)}processPreIncDec(){const e=this.tokens.currentIndex(),t=this.tokens.tokens[e+1];if(t.type!==k.name)return!1;if(t.shadowsGlobal)return!1;if(e+2<this.tokens.tokens.length&&(this.tokens.matches1AtIndex(e+2,k.dot)||this.tokens.matches1AtIndex(e+2,k.bracketL)||this.tokens.matches1AtIndex(e+2,k.parenL)))return!1;const n=this.tokens.identifierNameForToken(t),s=this.importProcessor.resolveExportBinding(n);return!!s&&(this.tokens.appendCode(`${s} = `),this.tokens.copyToken(),!0)}processPostIncDec(){const e=this.tokens.currentIndex(),t=this.tokens.tokens[e],n=this.tokens.tokens[e+1];if(t.type!==k.name)return!1;if(t.shadowsGlobal)return!1;if(e>=1&&this.tokens.matches1AtIndex(e-1,k.dot))return!1;const s=this.tokens.identifierNameForToken(t),o=this.importProcessor.resolveExportBinding(s);if(!o)return!1;const r=this.tokens.rawCodeForToken(n),i=this.importProcessor.getIdentifierReplacement(s)||s;if("++"===r)this.tokens.replaceToken(`(${i} = ${o} = ${i} + 1, ${i} - 1)`);else{if("--"!==r)throw new Error(`Unexpected operator: ${r}`);this.tokens.replaceToken(`(${i} = ${o} = ${i} - 1, ${i} + 1)`)}return this.tokens.removeToken(),!0}processExportDefault(){let e=!0;if(this.tokens.matches4(k._export,k._default,k._function,k.name)||this.tokens.matches5(k._export,k._default,k.name,k._function,k.name)&&this.tokens.matchesContextualAtIndex(this.tokens.currentIndex()+2,m._async)){this.tokens.removeInitialToken(),this.tokens.removeToken();const e=this.processNamedFunction();this.tokens.appendCode(` exports.default = ${e};`)}else if(this.tokens.matches4(k._export,k._default,k._class,k.name)||this.tokens.matches5(k._export,k._default,k._abstract,k._class,k.name)||this.tokens.matches3(k._export,k._default,k.at)){this.tokens.removeInitialToken(),this.tokens.removeToken(),this.copyDecorators(),this.tokens.matches1(k._abstract)&&this.tokens.removeToken();const e=this.rootTransformer.processNamedClass();this.tokens.appendCode(` exports.default = ${e};`)}else if(ko(this.isTypeScriptTransformEnabled,this.keepUnusedImports,this.tokens,this.declarationInfo))e=!1,this.tokens.removeInitialToken(),this.tokens.removeToken(),this.tokens.removeToken();else if(this.reactHotLoaderTransformer){const e=this.nameManager.claimFreeName("_default");this.tokens.replaceToken(`let ${e}; exports.`),this.tokens.copyToken(),this.tokens.appendCode(` = ${e} =`),this.reactHotLoaderTransformer.setExtractedDefaultExportName(e)}else this.tokens.replaceToken("exports."),this.tokens.copyToken(),this.tokens.appendCode(" =");e&&(this.hadDefaultExport=!0)}copyDecorators(){for(;this.tokens.matches1(k.at);)if(this.tokens.copyToken(),this.tokens.matches1(k.parenL))this.tokens.copyExpectedToken(k.parenL),this.rootTransformer.processBalancedCode(),this.tokens.copyExpectedToken(k.parenR);else{for(this.tokens.copyExpectedToken(k.name);this.tokens.matches1(k.dot);)this.tokens.copyExpectedToken(k.dot),this.tokens.copyExpectedToken(k.name);this.tokens.matches1(k.parenL)&&(this.tokens.copyExpectedToken(k.parenL),this.rootTransformer.processBalancedCode(),this.tokens.copyExpectedToken(k.parenR))}}processExportVar(){this.isSimpleExportVar()?this.processSimpleExportVar():this.processComplexExportVar()}isSimpleExportVar(){let e=this.tokens.currentIndex();if(e++,e++,!this.tokens.matches1AtIndex(e,k.name))return!1;for(e++;e<this.tokens.tokens.length&&this.tokens.tokens[e].isType;)e++;return!!this.tokens.matches1AtIndex(e,k.eq)}processSimpleExportVar(){this.tokens.removeInitialToken(),this.tokens.copyToken();const e=this.tokens.identifierName();for(;!this.tokens.matches1(k.eq);)this.rootTransformer.processToken();const t=this.tokens.currentToken().rhsEndIndex;if(null==t)throw new Error("Expected = token with an end index.");for(;this.tokens.currentIndex()<t;)this.rootTransformer.processToken();this.tokens.appendCode(`; exports.${e} = ${e}`)}processComplexExportVar(){this.tokens.removeInitialToken(),this.tokens.removeToken();const e=this.tokens.matches1(k.braceL);e&&this.tokens.appendCode("(");let t=0;for(;;)if(this.tokens.matches1(k.braceL)||this.tokens.matches1(k.dollarBraceL)||this.tokens.matches1(k.bracketL))t++,this.tokens.copyToken();else if(this.tokens.matches1(k.braceR)||this.tokens.matches1(k.bracketR))t--,this.tokens.copyToken();else{if(0===t&&!this.tokens.matches1(k.name)&&!this.tokens.currentToken().isType)break;if(this.tokens.matches1(k.eq)){const e=this.tokens.currentToken().rhsEndIndex;if(null==e)throw new Error("Expected = token with an end index.");for(;this.tokens.currentIndex()<e;)this.rootTransformer.processToken()}else{const e=this.tokens.currentToken();if(Q(e)){const t=this.tokens.identifierName();let n=this.importProcessor.getIdentifierReplacement(t);if(null===n)throw new Error(`Expected a replacement for ${t} in \`export var\` syntax.`);se(e)&&(n=`${t}: ${n}`),this.tokens.replaceToken(n)}else this.rootTransformer.processToken()}}if(e){const e=this.tokens.currentToken().rhsEndIndex;if(null==e)throw new Error("Expected = token with an end index.");for(;this.tokens.currentIndex()<e;)this.rootTransformer.processToken();this.tokens.appendCode(")")}}processExportFunction(){this.tokens.replaceToken("");const e=this.processNamedFunction();this.tokens.appendCode(` exports.${e} = ${e};`)}processNamedFunction(){if(this.tokens.matches1(k._function))this.tokens.copyToken();else if(this.tokens.matches2(k.name,k._function)){if(!this.tokens.matchesContextual(m._async))throw new Error("Expected async keyword in function export.");this.tokens.copyToken(),this.tokens.copyToken()}if(this.tokens.matches1(k.star)&&this.tokens.copyToken(),!this.tokens.matches1(k.name))throw new Error("Expected identifier for exported function name.");const e=this.tokens.identifierName();if(this.tokens.copyToken(),this.tokens.currentToken().isType)for(this.tokens.removeInitialToken();this.tokens.currentToken().isType;)this.tokens.removeToken();return this.tokens.copyExpectedToken(k.parenL),this.rootTransformer.processBalancedCode(),this.tokens.copyExpectedToken(k.parenR),this.rootTransformer.processPossibleTypeRange(),this.tokens.copyExpectedToken(k.braceL),this.rootTransformer.processBalancedCode(),this.tokens.copyExpectedToken(k.braceR),e}processExportClass(){this.tokens.removeInitialToken(),this.copyDecorators(),this.tokens.matches1(k._abstract)&&this.tokens.removeToken();const e=this.rootTransformer.processNamedClass();this.tokens.appendCode(` exports.${e} = ${e};`)}processExportBindings(){this.tokens.removeInitialToken(),this.tokens.removeToken();const e=fo(this.tokens),t=[];for(;;){if(this.tokens.matches1(k.braceR)){this.tokens.removeToken();break}const n=Ne(this.tokens);for(;this.tokens.currentIndex()<n.endIndex;)this.tokens.removeToken();if(!(n.isType||!e&&this.shouldElideExportedIdentifier(n.leftName))){const e=n.rightName;"default"===e?this.hadDefaultExport=!0:this.hadNamedExport=!0;const s=n.leftName,o=this.importProcessor.getIdentifierReplacement(s);t.push(`exports.${e} = ${o||s};`)}if(this.tokens.matches1(k.braceR)){this.tokens.removeToken();break}if(this.tokens.matches2(k.comma,k.braceR)){this.tokens.removeToken(),this.tokens.removeToken();break}if(!this.tokens.matches1(k.comma))throw new Error(`Unexpected token: ${JSON.stringify(this.tokens.currentToken())}`);this.tokens.removeToken()}if(this.tokens.matchesContextual(m._from)){this.tokens.removeToken();const e=this.tokens.stringValue();this.tokens.replaceTokenTrimmingLeftWhitespace(this.importProcessor.claimImportCode(e)),mo(this.tokens)}else this.tokens.appendCode(t.join(" "));this.tokens.matches1(k.semi)&&this.tokens.removeToken()}processExportStar(){for(this.tokens.removeInitialToken();!this.tokens.matches1(k.string);)this.tokens.removeToken();const e=this.tokens.stringValue();this.tokens.replaceTokenTrimmingLeftWhitespace(this.importProcessor.claimImportCode(e)),mo(this.tokens),this.tokens.matches1(k.semi)&&this.tokens.removeToken()}shouldElideExportedIdentifier(e){return this.isTypeScriptTransformEnabled&&!this.keepUnusedImports&&!this.declarationInfo.valueDeclarations.has(e)}}class xo extends De{constructor(e,t,n,s,o,r,i,a){super(),this.tokens=e,this.nameManager=t,this.helperManager=n,this.reactHotLoaderTransformer=s,this.isTypeScriptTransformEnabled=o,this.isFlowTransformEnabled=r,this.keepUnusedImports=i,this.nonTypeIdentifiers=o&&!i?$e(e,a):new Set,this.declarationInfo=o&&!i?po(e):ho,this.injectCreateRequireForImportRequire=Boolean(a.injectCreateRequireForImportRequire)}process(){if(this.tokens.matches3(k._import,k.name,k.eq))return this.processImportEquals();if(this.tokens.matches4(k._import,k.name,k.name,k.eq)&&this.tokens.matchesContextualAtIndex(this.tokens.currentIndex()+1,m._type)){this.tokens.removeInitialToken();for(let e=0;e<7;e++)this.tokens.removeToken();return!0}if(this.tokens.matches2(k._export,k.eq))return this.tokens.replaceToken("module.exports"),!0;if(this.tokens.matches5(k._export,k._import,k.name,k.name,k.eq)&&this.tokens.matchesContextualAtIndex(this.tokens.currentIndex()+2,m._type)){this.tokens.removeInitialToken();for(let e=0;e<8;e++)this.tokens.removeToken();return!0}if(this.tokens.matches1(k._import))return this.processImport();if(this.tokens.matches2(k._export,k._default))return this.processExportDefault();if(this.tokens.matches2(k._export,k.braceL))return this.processNamedExports();if(this.tokens.matches2(k._export,k.name)&&this.tokens.matchesContextualAtIndex(this.tokens.currentIndex()+1,m._type)){if(this.tokens.removeInitialToken(),this.tokens.removeToken(),this.tokens.matches1(k.braceL)){for(;!this.tokens.matches1(k.braceR);)this.tokens.removeToken();this.tokens.removeToken()}else this.tokens.removeToken(),this.tokens.matches1(k._as)&&(this.tokens.removeToken(),this.tokens.removeToken());return this.tokens.matchesContextual(m._from)&&this.tokens.matches1AtIndex(this.tokens.currentIndex()+1,k.string)&&(this.tokens.removeToken(),this.tokens.removeToken(),mo(this.tokens)),!0}return!1}processImportEquals(){const e=this.tokens.identifierNameAtIndex(this.tokens.currentIndex()+1);return this.shouldAutomaticallyElideImportedName(e)?uo(this.tokens):this.injectCreateRequireForImportRequire?(this.tokens.replaceToken("const"),this.tokens.copyToken(),this.tokens.copyToken(),this.tokens.replaceToken(this.helperManager.getHelperName("require"))):this.tokens.replaceToken("const"),!0}processImport(){if(this.tokens.matches2(k._import,k.parenL))return!1;const e=this.tokens.snapshot();if(this.removeImportTypeBindings()){for(this.tokens.restoreToSnapshot(e);!this.tokens.matches1(k.string);)this.tokens.removeToken();this.tokens.removeToken(),mo(this.tokens),this.tokens.matches1(k.semi)&&this.tokens.removeToken()}return!0}removeImportTypeBindings(){if(this.tokens.copyExpectedToken(k._import),this.tokens.matchesContextual(m._type)&&!this.tokens.matches1AtIndex(this.tokens.currentIndex()+1,k.comma)&&!this.tokens.matchesContextualAtIndex(this.tokens.currentIndex()+1,m._from))return!0;if(this.tokens.matches1(k.string))return this.tokens.copyToken(),!1;this.tokens.matchesContextual(m._module)&&this.tokens.matchesContextualAtIndex(this.tokens.currentIndex()+2,m._from)&&this.tokens.copyToken();let e=!1,t=!1,n=!1;if(this.tokens.matches1(k.name)&&(this.shouldAutomaticallyElideImportedName(this.tokens.identifierName())?(this.tokens.removeToken(),this.tokens.matches1(k.comma)&&this.tokens.removeToken()):(e=!0,this.tokens.copyToken(),this.tokens.matches1(k.comma)&&(n=!0,this.tokens.removeToken()))),this.tokens.matches1(k.star))this.shouldAutomaticallyElideImportedName(this.tokens.identifierNameAtRelativeIndex(2))?(this.tokens.removeToken(),this.tokens.removeToken(),this.tokens.removeToken()):(n&&this.tokens.appendCode(","),e=!0,this.tokens.copyExpectedToken(k.star),this.tokens.copyExpectedToken(k.name),this.tokens.copyExpectedToken(k.name));else if(this.tokens.matches1(k.braceL)){for(n&&this.tokens.appendCode(","),this.tokens.copyToken();!this.tokens.matches1(k.braceR);){t=!0;const n=Ne(this.tokens);if(n.isType||this.shouldAutomaticallyElideImportedName(n.rightName)){for(;this.tokens.currentIndex()<n.endIndex;)this.tokens.removeToken();this.tokens.matches1(k.comma)&&this.tokens.removeToken()}else{for(e=!0;this.tokens.currentIndex()<n.endIndex;)this.tokens.copyToken();this.tokens.matches1(k.comma)&&this.tokens.copyToken()}}this.tokens.copyExpectedToken(k.braceR)}return!this.keepUnusedImports&&(this.isTypeScriptTransformEnabled?!e:!!this.isFlowTransformEnabled&&(t&&!e))}shouldAutomaticallyElideImportedName(e){return this.isTypeScriptTransformEnabled&&!this.keepUnusedImports&&!this.nonTypeIdentifiers.has(e)}processExportDefault(){if(ko(this.isTypeScriptTransformEnabled,this.keepUnusedImports,this.tokens,this.declarationInfo))return this.tokens.removeInitialToken(),this.tokens.removeToken(),this.tokens.removeToken(),!0;if(!(this.tokens.matches4(k._export,k._default,k._function,k.name)||this.tokens.matches5(k._export,k._default,k.name,k._function,k.name)&&this.tokens.matchesContextualAtIndex(this.tokens.currentIndex()+2,m._async)||this.tokens.matches4(k._export,k._default,k._class,k.name)||this.tokens.matches5(k._export,k._default,k._abstract,k._class,k.name))&&this.reactHotLoaderTransformer){const e=this.nameManager.claimFreeName("_default");return this.tokens.replaceToken(`let ${e}; export`),this.tokens.copyToken(),this.tokens.appendCode(` ${e} =`),this.reactHotLoaderTransformer.setExtractedDefaultExportName(e),!0}return!1}processNamedExports(){if(!this.isTypeScriptTransformEnabled)return!1;this.tokens.copyExpectedToken(k._export),this.tokens.copyExpectedToken(k.braceL);const e=fo(this.tokens);let t=!1;for(;!this.tokens.matches1(k.braceR);){const n=Ne(this.tokens);if(n.isType||!e&&this.shouldElideExportedName(n.leftName)){for(;this.tokens.currentIndex()<n.endIndex;)this.tokens.removeToken();this.tokens.matches1(k.comma)&&this.tokens.removeToken()}else{for(t=!0;this.tokens.currentIndex()<n.endIndex;)this.tokens.copyToken();this.tokens.matches1(k.comma)&&this.tokens.copyToken()}}return this.tokens.copyExpectedToken(k.braceR),this.keepUnusedImports||!e||t||(this.tokens.removeToken(),this.tokens.removeToken(),mo(this.tokens)),!0}shouldElideExportedName(e){return this.isTypeScriptTransformEnabled&&!this.keepUnusedImports&&this.declarationInfo.typeDeclarations.has(e)&&!this.declarationInfo.valueDeclarations.has(e)}}class yo extends De{constructor(e,t,n){super(),this.rootTransformer=e,this.tokens=t,this.isImportsTransformEnabled=n}process(){return!!(this.rootTransformer.processPossibleArrowParamEnd()||this.rootTransformer.processPossibleAsyncArrowWithTypeParams()||this.rootTransformer.processPossibleTypeRange())||(this.tokens.matches1(k._enum)?(this.processEnum(),!0):this.tokens.matches2(k._export,k._enum)?(this.processNamedExportEnum(),!0):!!this.tokens.matches3(k._export,k._default,k._enum)&&(this.processDefaultExportEnum(),!0))}processNamedExportEnum(){if(this.isImportsTransformEnabled){this.tokens.removeInitialToken();const e=this.tokens.identifierNameAtRelativeIndex(1);this.processEnum(),this.tokens.appendCode(` exports.${e} = ${e};`)}else this.tokens.copyToken(),this.processEnum()}processDefaultExportEnum(){this.tokens.removeInitialToken(),this.tokens.removeToken();const e=this.tokens.identifierNameAtRelativeIndex(1);this.processEnum(),this.isImportsTransformEnabled?this.tokens.appendCode(` exports.default = ${e};`):this.tokens.appendCode(` export default ${e};`)}processEnum(){this.tokens.replaceToken("const"),this.tokens.copyExpectedToken(k.name);let e=!1;this.tokens.matchesContextual(m._of)&&(this.tokens.removeToken(),e=this.tokens.matchesContextual(m._symbol),this.tokens.removeToken());const t=this.tokens.matches3(k.braceL,k.name,k.eq);this.tokens.appendCode(' = require("flow-enums-runtime")');const n=!e&&!t;for(this.tokens.replaceTokenTrimmingLeftWhitespace(n?".Mirrored([":"({");!this.tokens.matches1(k.braceR);){if(this.tokens.matches1(k.ellipsis)){this.tokens.removeToken();break}this.processEnumElement(e,t),this.tokens.matches1(k.comma)&&this.tokens.copyToken()}this.tokens.replaceToken(n?"]);":"});")}processEnumElement(e,t){if(e){const e=this.tokens.identifierName();this.tokens.copyToken(),this.tokens.appendCode(`: Symbol("${e}")`)}else t?(this.tokens.copyToken(),this.tokens.replaceTokenTrimmingLeftWhitespace(":"),this.tokens.copyToken()):this.tokens.replaceToken(`"${this.tokens.identifierName()}"`)}}const _o="jest",To=["mock","unmock","enableAutomock","disableAutomock"];class bo extends De{__init(){this.hoistedFunctionNames=[]}constructor(e,t,n,s){super(),this.rootTransformer=e,this.tokens=t,this.nameManager=n,this.importProcessor=s,bo.prototype.__init.call(this)}process(){return!(0!==this.tokens.currentToken().scopeDepth||!this.tokens.matches4(k.name,k.dot,k.name,k.parenL)||this.tokens.identifierName()!==_o)&&(!function(e){let t,n=e[0],s=1;for(;s<e.length;){const o=e[s],r=e[s+1];if(s+=2,("optionalAccess"===o||"optionalCall"===o)&&null==n)return;"access"===o||"optionalAccess"===o?(t=n,n=r(n)):"call"!==o&&"optionalCall"!==o||(n=r(((...e)=>n.call(t,...e))),t=void 0)}return n}([this,"access",e=>e.importProcessor,"optionalAccess",e=>e.getGlobalNames,"call",e=>e(),"optionalAccess",e=>e.has,"call",e=>e(_o)])&&this.extractHoistedCalls())}getHoistedCode(){return this.hoistedFunctionNames.length>0?this.hoistedFunctionNames.map((e=>`${e}();`)).join(""):""}extractHoistedCalls(){this.tokens.removeToken();let e=!1;for(;this.tokens.matches3(k.dot,k.name,k.parenL);){const t=this.tokens.identifierNameAtIndex(this.tokens.currentIndex()+1);if(To.includes(t)){const t=this.nameManager.claimFreeName("__jestHoist");this.hoistedFunctionNames.push(t),this.tokens.replaceToken(`function ${t}(){${_o}.`),this.tokens.copyToken(),this.tokens.copyToken(),this.rootTransformer.processBalancedCode(),this.tokens.copyExpectedToken(k.parenR),this.tokens.appendCode(";}"),e=!1}else e?this.tokens.copyToken():this.tokens.replaceToken(`${_o}.`),this.tokens.copyToken(),this.tokens.copyToken(),this.rootTransformer.processBalancedCode(),this.tokens.copyExpectedToken(k.parenR),e=!0}return!0}}class vo extends De{constructor(e){super(),this.tokens=e}process(){if(this.tokens.matches1(k.num)){const e=this.tokens.currentTokenCode();if(e.includes("_"))return this.tokens.replaceToken(e.replace(/_/g,"")),!0}return!1}}class Io extends De{constructor(e,t){super(),this.tokens=e,this.nameManager=t}process(){return!!this.tokens.matches2(k._catch,k.braceL)&&(this.tokens.copyToken(),this.tokens.appendCode(` (${this.nameManager.claimFreeName("e")})`),!0)}}class wo extends De{constructor(e,t){super(),this.tokens=e,this.nameManager=t}process(){if(this.tokens.matches1(k.nullishCoalescing)){const e=this.tokens.currentToken();return this.tokens.tokens[e.nullishStartIndex].isAsyncOperation?this.tokens.replaceTokenTrimmingLeftWhitespace(", async () => ("):this.tokens.replaceTokenTrimmingLeftWhitespace(", () => ("),!0}if(this.tokens.matches1(k._delete)){if(this.tokens.tokenAtRelativeIndex(1).isOptionalChainStart)return this.tokens.removeInitialToken(),!0}const e=this.tokens.currentToken().subscriptStartIndex;if(null!=e&&this.tokens.tokens[e].isOptionalChainStart&&this.tokens.tokenAtRelativeIndex(-1).type!==k._super){const t=this.nameManager.claimFreeName("_");let n;if(n=e>0&&this.tokens.matches1AtIndex(e-1,k._delete)&&this.isLastSubscriptInChain()?`${t} => delete ${t}`:`${t} => ${t}`,this.tokens.tokens[e].isAsyncOperation&&(n=`async ${n}`),this.tokens.matches2(k.questionDot,k.parenL)||this.tokens.matches2(k.questionDot,k.lessThan))this.justSkippedSuper()&&this.tokens.appendCode(".bind(this)"),this.tokens.replaceTokenTrimmingLeftWhitespace(`, 'optionalCall', ${n}`);else if(this.tokens.matches2(k.questionDot,k.bracketL))this.tokens.replaceTokenTrimmingLeftWhitespace(`, 'optionalAccess', ${n}`);else if(this.tokens.matches1(k.questionDot))this.tokens.replaceTokenTrimmingLeftWhitespace(`, 'optionalAccess', ${n}.`);else if(this.tokens.matches1(k.dot))this.tokens.replaceTokenTrimmingLeftWhitespace(`, 'access', ${n}.`);else if(this.tokens.matches1(k.bracketL))this.tokens.replaceTokenTrimmingLeftWhitespace(`, 'access', ${n}[`);else{if(!this.tokens.matches1(k.parenL))throw new Error("Unexpected subscript operator in optional chain.");this.justSkippedSuper()&&this.tokens.appendCode(".bind(this)"),this.tokens.replaceTokenTrimmingLeftWhitespace(`, 'call', ${n}(`)}return!0}return!1}isLastSubscriptInChain(){let e=0;for(let t=this.tokens.currentIndex()+1;;t++){if(t>=this.tokens.tokens.length)throw new Error("Reached the end of the code while finding the end of the access chain.");if(this.tokens.tokens[t].isOptionalChainStart?e++:this.tokens.tokens[t].isOptionalChainEnd&&e--,e<0)return!0;if(0===e&&null!=this.tokens.tokens[t].subscriptStartIndex)return!1}}justSkippedSuper(){let e=0,t=this.tokens.currentIndex()-1;for(;;){if(t<0)throw new Error("Reached the start of the code while finding the start of the access chain.");if(this.tokens.tokens[t].isOptionalChainStart?e--:this.tokens.tokens[t].isOptionalChainEnd&&e++,e<0)return!1;if(0===e&&null!=this.tokens.tokens[t].subscriptStartIndex)return this.tokens.tokens[t-1].type===k._super;t--}}}class Co extends De{constructor(e,t,n,s){super(),this.rootTransformer=e,this.tokens=t,this.importProcessor=n,this.options=s}process(){const e=this.tokens.currentIndex();if("createReactClass"===this.tokens.identifierName()){const t=this.importProcessor&&this.importProcessor.getIdentifierReplacement("createReactClass");return t?this.tokens.replaceToken(`(0, ${t})`):this.tokens.copyToken(),this.tryProcessCreateClassCall(e),!0}if(this.tokens.matches3(k.name,k.dot,k.name)&&"React"===this.tokens.identifierName()&&"createClass"===this.tokens.identifierNameAtIndex(this.tokens.currentIndex()+2)){const t=this.importProcessor&&this.importProcessor.getIdentifierReplacement("React")||"React";return t?(this.tokens.replaceToken(t),this.tokens.copyToken(),this.tokens.copyToken()):(this.tokens.copyToken(),this.tokens.copyToken(),this.tokens.copyToken()),this.tryProcessCreateClassCall(e),!0}return!1}tryProcessCreateClassCall(e){const t=this.findDisplayName(e);t&&this.classNeedsDisplayName()&&(this.tokens.copyExpectedToken(k.parenL),this.tokens.copyExpectedToken(k.braceL),this.tokens.appendCode(`displayName: '${t}',`),this.rootTransformer.processBalancedCode(),this.tokens.copyExpectedToken(k.braceR),this.tokens.copyExpectedToken(k.parenR))}findDisplayName(e){return e<2?null:this.tokens.matches2AtIndex(e-2,k.name,k.eq)||e>=2&&this.tokens.tokens[e-2].identifierRole===J.ObjectKey?this.tokens.identifierNameAtIndex(e-2):this.tokens.matches2AtIndex(e-2,k._export,k._default)?this.getDisplayNameFromFilename():null}getDisplayNameFromFilename(){const e=(this.options.filePath||"unknown").split("/"),t=e[e.length-1],n=t.lastIndexOf("."),s=-1===n?t:t.slice(0,n);return"index"===s&&e[e.length-2]?e[e.length-2]:s}classNeedsDisplayName(){let e=this.tokens.currentIndex();if(!this.tokens.matches2(k.parenL,k.braceL))return!1;const t=e+1,n=this.tokens.tokens[t].contextId;if(null==n)throw new Error("Expected non-null context ID on object open-brace.");for(;e<this.tokens.tokens.length;e++){const t=this.tokens.tokens[e];if(t.type===k.braceR&&t.contextId===n){e++;break}if("displayName"===this.tokens.identifierNameAtIndex(e)&&this.tokens.tokens[e].identifierRole===J.ObjectKey&&t.contextId===n)return!1}if(e===this.tokens.tokens.length)throw new Error("Unexpected end of input when processing React class.");return this.tokens.matches1AtIndex(e,k.parenR)||this.tokens.matches2AtIndex(e,k.comma,k.parenR)}}class Ao extends De{__init(){this.extractedDefaultExportName=null}constructor(e,t){super(),this.tokens=e,this.filePath=t,Ao.prototype.__init.call(this)}setExtractedDefaultExportName(e){this.extractedDefaultExportName=e}getPrefixCode(){return"\n (function () {\n var enterModule = require('react-hot-loader').enterModule;\n enterModule && enterModule(module);\n })();".replace(/\s+/g," ").trim()}getSuffixCode(){const e=new Set;for(const n of this.tokens.tokens)!n.isType&&ee(n)&&n.identifierRole!==J.ImportDeclaration&&e.add(this.tokens.identifierNameForToken(n));const t=Array.from(e).map((e=>({variableName:e,uniqueLocalName:e})));return this.extractedDefaultExportName&&t.push({variableName:this.extractedDefaultExportName,uniqueLocalName:"default"}),`\n;(function () {\n var reactHotLoader = require('react-hot-loader').default;\n var leaveModule = require('react-hot-loader').leaveModule;\n if (!reactHotLoader) {\n return;\n }\n${t.map((({variableName:e,uniqueLocalName:t})=>` reactHotLoader.register(${e}, "${t}", ${JSON.stringify(this.filePath||"")});`)).join("\n")}\n leaveModule(module);\n})();`}process(){return!1}}const Eo=new Set(["break","case","catch","class","const","continue","debugger","default","delete","do","else","export","extends","finally","for","function","if","import","in","instanceof","new","return","super","switch","this","throw","try","typeof","var","void","while","with","yield","enum","implements","interface","let","package","private","protected","public","static","await","false","null","true"]);function So(e){if(0===e.length)return!1;if(!G[e.charCodeAt(0)])return!1;for(let t=1;t<e.length;t++)if(!z[e.charCodeAt(t)])return!1;return!Eo.has(e)}class No extends De{constructor(e,t,n){super(),this.rootTransformer=e,this.tokens=t,this.isImportsTransformEnabled=n}process(){return!!(this.rootTransformer.processPossibleArrowParamEnd()||this.rootTransformer.processPossibleAsyncArrowWithTypeParams()||this.rootTransformer.processPossibleTypeRange())||(this.tokens.matches1(k._public)||this.tokens.matches1(k._protected)||this.tokens.matches1(k._private)||this.tokens.matches1(k._abstract)||this.tokens.matches1(k._readonly)||this.tokens.matches1(k._override)||this.tokens.matches1(k.nonNullAssertion)?(this.tokens.removeInitialToken(),!0):this.tokens.matches1(k._enum)||this.tokens.matches2(k._const,k._enum)?(this.processEnum(),!0):!(!this.tokens.matches2(k._export,k._enum)&&!this.tokens.matches3(k._export,k._const,k._enum))&&(this.processEnum(!0),!0))}processEnum(e=!1){for(this.tokens.removeInitialToken();this.tokens.matches1(k._const)||this.tokens.matches1(k._enum);)this.tokens.removeToken();const t=this.tokens.identifierName();this.tokens.removeToken(),e&&!this.isImportsTransformEnabled&&this.tokens.appendCode("export "),this.tokens.appendCode(`var ${t}; (function (${t})`),this.tokens.copyExpectedToken(k.braceL),this.processEnumBody(t),this.tokens.copyExpectedToken(k.braceR),e&&this.isImportsTransformEnabled?this.tokens.appendCode(`)(${t} || (exports.${t} = ${t} = {}));`):this.tokens.appendCode(`)(${t} || (${t} = {}));`)}processEnumBody(e){let t=null;for(;!this.tokens.matches1(k.braceR);){const{nameStringCode:n,variableName:s}=this.extractEnumKeyInfo(this.tokens.currentToken());this.tokens.removeInitialToken(),this.tokens.matches3(k.eq,k.string,k.comma)||this.tokens.matches3(k.eq,k.string,k.braceR)?this.processStringLiteralEnumMember(e,n,s):this.tokens.matches1(k.eq)?this.processExplicitValueEnumMember(e,n,s):this.processImplicitValueEnumMember(e,n,s,t),this.tokens.matches1(k.comma)&&this.tokens.removeToken(),t=null!=s?s:`${e}[${n}]`}}extractEnumKeyInfo(e){if(e.type===k.name){const t=this.tokens.identifierNameForToken(e);return{nameStringCode:`"${t}"`,variableName:So(t)?t:null}}if(e.type===k.string){const t=this.tokens.stringValueForToken(e);return{nameStringCode:this.tokens.code.slice(e.start,e.end),variableName:So(t)?t:null}}throw new Error("Expected name or string at beginning of enum element.")}processStringLiteralEnumMember(e,t,n){null!=n?(this.tokens.appendCode(`const ${n}`),this.tokens.copyToken(),this.tokens.copyToken(),this.tokens.appendCode(`; ${e}[${t}] = ${n};`)):(this.tokens.appendCode(`${e}[${t}]`),this.tokens.copyToken(),this.tokens.copyToken(),this.tokens.appendCode(";"))}processExplicitValueEnumMember(e,t,n){const s=this.tokens.currentToken().rhsEndIndex;if(null==s)throw new Error("Expected rhsEndIndex on enum assign.");if(null!=n){for(this.tokens.appendCode(`const ${n}`),this.tokens.copyToken();this.tokens.currentIndex()<s;)this.rootTransformer.processToken();this.tokens.appendCode(`; ${e}[${e}[${t}] = ${n}] = ${t};`)}else{for(this.tokens.appendCode(`${e}[${e}[${t}]`),this.tokens.copyToken();this.tokens.currentIndex()<s;)this.rootTransformer.processToken();this.tokens.appendCode(`] = ${t};`)}}processImplicitValueEnumMember(e,t,n,s){let o=null!=s?`${s} + 1`:"0";null!=n&&(this.tokens.appendCode(`const ${n} = ${o}; `),o=n),this.tokens.appendCode(`${e}[${e}[${t}] = ${o}] = ${t};`)}}class jo{__init(){this.transformers=[]}__init2(){this.generatedVariables=[]}constructor(e,t,n,s){jo.prototype.__init.call(this),jo.prototype.__init2.call(this),this.nameManager=e.nameManager,this.helperManager=e.helperManager;const{tokenProcessor:o,importProcessor:r}=e;this.tokens=o,this.isImportsTransformEnabled=t.includes("imports"),this.isReactHotLoaderTransformEnabled=t.includes("react-hot-loader"),this.disableESTransforms=Boolean(s.disableESTransforms),s.disableESTransforms||(this.transformers.push(new wo(o,this.nameManager)),this.transformers.push(new vo(o)),this.transformers.push(new Io(o,this.nameManager))),t.includes("jsx")&&("preserve"!==s.jsxRuntime&&this.transformers.push(new Pe(this,o,r,this.nameManager,s)),this.transformers.push(new Co(this,o,r,s)));let i=null;if(t.includes("react-hot-loader")){if(!s.filePath)throw new Error("filePath is required when using the react-hot-loader transform.");i=new Ao(o,s.filePath),this.transformers.push(i)}if(t.includes("imports")){if(null===r)throw new Error("Expected non-null importProcessor with imports transform enabled.");this.transformers.push(new go(this,o,r,this.nameManager,this.helperManager,i,n,Boolean(s.enableLegacyTypeScriptModuleInterop),t.includes("typescript"),t.includes("flow"),Boolean(s.preserveDynamicImport),Boolean(s.keepUnusedImports)))}else this.transformers.push(new xo(o,this.nameManager,this.helperManager,i,t.includes("typescript"),t.includes("flow"),Boolean(s.keepUnusedImports),s));t.includes("flow")&&this.transformers.push(new yo(this,o,t.includes("imports"))),t.includes("typescript")&&this.transformers.push(new No(this,o,t.includes("imports"))),t.includes("jest")&&this.transformers.push(new bo(this,o,this.nameManager,r))}transform(){this.tokens.reset(),this.processBalancedCode();let e=this.isImportsTransformEnabled?'"use strict";':"";for(const o of this.transformers)e+=o.getPrefixCode();e+=this.helperManager.emitHelpers(),e+=this.generatedVariables.map((e=>` var ${e};`)).join("");for(const o of this.transformers)e+=o.getHoistedCode();let t="";for(const o of this.transformers)t+=o.getSuffixCode();const n=this.tokens.finish();let{code:s}=n;if(s.startsWith("#!")){let o=s.indexOf("\n");return-1===o&&(o=s.length,s+="\n"),{code:s.slice(0,o+1)+e+s.slice(o+1)+t,mappings:this.shiftMappings(n.mappings,e.length)}}return{code:e+s+t,mappings:this.shiftMappings(n.mappings,e.length)}}processBalancedCode(){let e=0,t=0;for(;!this.tokens.isAtEnd();){if(this.tokens.matches1(k.braceL)||this.tokens.matches1(k.dollarBraceL))e++;else if(this.tokens.matches1(k.braceR)){if(0===e)return;e--}if(this.tokens.matches1(k.parenL))t++;else if(this.tokens.matches1(k.parenR)){if(0===t)return;t--}this.processToken()}}processToken(){if(this.tokens.matches1(k._class))this.processClass();else{for(const e of this.transformers){if(e.process())return}this.tokens.copyToken()}}processNamedClass(){if(!this.tokens.matches2(k._class,k.name))throw new Error("Expected identifier for exported class name.");const e=this.tokens.identifierNameAtIndex(this.tokens.currentIndex()+1);return this.processClass(),e}processClass(){const e=ro(this,this.tokens,this.nameManager,this.disableESTransforms),t=(e.headerInfo.isExpression||!e.headerInfo.className)&&e.staticInitializerNames.length+e.instanceInitializerNames.length>0;let n=e.headerInfo.className;t&&(n=this.nameManager.claimFreeName("_class"),this.generatedVariables.push(n),this.tokens.appendCode(` (${n} =`));const s=this.tokens.currentToken().contextId;if(null==s)throw new Error("Expected class to have a context ID.");for(this.tokens.copyExpectedToken(k._class);!this.tokens.matchesContextIdAndLabel(k.braceL,s);)this.processToken();this.processClassBody(e,n);const o=e.staticInitializerNames.map((e=>`${n}.${e}()`));t?this.tokens.appendCode(`, ${o.map((e=>`${e}, `)).join("")}${n})`):e.staticInitializerNames.length>0&&this.tokens.appendCode(` ${o.map((e=>`${e};`)).join(" ")}`)}processClassBody(e,t){const{headerInfo:n,constructorInsertPos:s,constructorInitializerStatements:o,fields:r,instanceInitializerNames:i,rangesToRemove:a}=e;let c=0,l=0;const u=this.tokens.currentToken().contextId;if(null==u)throw new Error("Expected non-null context ID on class.");this.tokens.copyExpectedToken(k.braceL),this.isReactHotLoaderTransformEnabled&&this.tokens.appendCode("__reactstandin__regenerateByEval(key, code) {this[key] = eval(code);}");const h=o.length+i.length>0;if(null===s&&h){const e=this.makeConstructorInitCode(o,i,t);if(n.hasSuperclass){const t=this.nameManager.claimFreeName("args");this.tokens.appendCode(`constructor(...${t}) { super(...${t}); ${e}; }`)}else this.tokens.appendCode(`constructor() { ${e}; }`)}for(;!this.tokens.matchesContextIdAndLabel(k.braceR,u);)if(c<r.length&&this.tokens.currentIndex()===r[c].start){let e=!1;for(this.tokens.matches1(k.bracketL)?this.tokens.copyTokenWithPrefix(`${r[c].initializerName}() {this`):this.tokens.matches1(k.string)||this.tokens.matches1(k.num)?(this.tokens.copyTokenWithPrefix(`${r[c].initializerName}() {this[`),e=!0):this.tokens.copyTokenWithPrefix(`${r[c].initializerName}() {this.`);this.tokens.currentIndex()<r[c].end;)e&&this.tokens.currentIndex()===r[c].equalsIndex&&this.tokens.appendCode("]"),this.processToken();this.tokens.appendCode("}"),c++}else if(l<a.length&&this.tokens.currentIndex()>=a[l].start){for(this.tokens.currentIndex()<a[l].end&&this.tokens.removeInitialToken();this.tokens.currentIndex()<a[l].end;)this.tokens.removeToken();l++}else this.tokens.currentIndex()===s?(this.tokens.copyToken(),h&&this.tokens.appendCode(`;${this.makeConstructorInitCode(o,i,t)};`),this.processToken()):this.processToken();this.tokens.copyExpectedToken(k.braceR)}makeConstructorInitCode(e,t,n){return[...e,...t.map((e=>`${n}.prototype.${e}.call(this)`))].join(";")}processPossibleArrowParamEnd(){if(this.tokens.matches2(k.parenR,k.colon)&&this.tokens.tokenAtRelativeIndex(1).isType){let e=this.tokens.currentIndex()+1;for(;this.tokens.tokens[e].isType;)e++;if(this.tokens.matches1AtIndex(e,k.arrow)){for(this.tokens.removeInitialToken();this.tokens.currentIndex()<e;)this.tokens.removeToken();return this.tokens.replaceTokenTrimmingLeftWhitespace(") =>"),!0}}return!1}processPossibleAsyncArrowWithTypeParams(){if(!this.tokens.matchesContextual(m._async)&&!this.tokens.matches1(k._async))return!1;const e=this.tokens.tokenAtRelativeIndex(1);if(e.type!==k.lessThan||!e.isType)return!1;let 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It tests whether two samples come from the same population distribution. To conduct a permutation test:"]}),(0,s.jsxs)(t.ol,{children:["\n",(0,s.jsx)(t.li,{children:"Shuffle the group labels (i.e. the Trues and Falses) to generate two new samples under the null."}),"\n",(0,s.jsx)(t.li,{children:"Compute the test statistic (i.e. the difference in group means)."}),"\n",(0,s.jsx)(t.li,{children:"Repeat steps 1 and 2 to generate an empirical distribution of the test statistics (i.e. the difference in group means)."}),"\n",(0,s.jsx)(t.li,{children:"See where the observed statistic lies in the empirical distribution. If, in our simulations, we rarely saw a difference in group means as extreme as the observed difference in group means, we have evidence to reject the null."}),"\n"]})]}),"\n",(0,s.jsx)(t.admonition,{type:"note",children:(0,s.jsx)(t.p,{children:"While shuffling, the size of the two new samples should be the same as the observed samples."})}),"\n",(0,s.jsxs)(t.p,{children:["The diagram below provides an overview of conducting a permutation test, although it references a different dataset. ",(0,s.jsx)(t.a,{href:"https://www.jwilber.me/permutationtest/",children:"Here"})," is another useful visualization. For additional helpful visual guides, please visit the ",(0,s.jsx)(t.a,{href:"https://dsc10.com/diagrams/",children:"Diagrams"})," site."]}),"\n",(0,s.jsx)(r.A,{src:"https://docs.google.com/presentation/d/e/2PACX-1vSovXDonR6EmjrT45h4pY1mwmcKFMWVSdgpbKHC5HNTm9sbG7dojvvCDEQCjuk2dk1oA4gmwMogr8ZL/embed?start=true&loop=false&delayms=3000&rm=minimal",sourceLink:"https://docs.google.com/presentation/d/1TTWoQ7FU4tzBGc7EskF6WYccIn1BWQbTSizAiFc2p2o/edit?usp=sharing"}),"\n",(0,s.jsx)(t.hr,{}),"\n",(0,s.jsx)(t.h2,{id:"code-example-absolute-difference",children:"Code Example (Absolute Difference)"}),"\n",(0,s.jsx)(t.h3,{id:"1-state-the-questionhypothesis",children:"1. State the question/hypothesis"}),"\n",(0,s.jsxs)(t.admonition,{title:"Hypotheses",type:"info",children:[(0,s.jsx)(t.p,{children:"We will test the following pair of hypotheses at the standard p = 0.05 significance level:"}),(0,s.jsxs)(t.ul,{children:["\n",(0,s.jsxs)(t.li,{children:[(0,s.jsx)(t.strong,{children:"Null Hypothesis:"})," In the population, weights of dogs and cats have the ",(0,s.jsx)(t.strong,{children:"same"})," distribution, and the observed differences in our samples are due to random chance."]}),"\n",(0,s.jsxs)(t.li,{children:[(0,s.jsx)(t.strong,{children:"Alternative Hypothesis:"})," In the population, dogs and cats have ",(0,s.jsx)(t.strong,{children:"different"})," weights, on average. The observed differences in our samples cannot be explained by random chance alone."]}),"\n"]})]}),"\n",(0,s.jsxs)(t.p,{children:['Since the alternative hypothesis is of the form "A and B are different," the ',(0,s.jsx)(t.strong,{children:"test statistic"})," should measure distance and use an absolute value."]}),"\n",(0,s.jsxs)(t.p,{children:[(0,s.jsxs)(t.span,{className:"katex",children:[(0,s.jsx)(t.span,{className:"katex-mathml",children:(0,s.jsx)(t.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,s.jsxs)(t.semantics,{children:[(0,s.jsx)(t.mrow,{children:(0,s.jsx)(t.mo,{children:"\u2234"})}),(0,s.jsx)(t.annotation,{encoding:"application/x-tex",children:"\\therefore"})]})})}),(0,s.jsx)(t.span,{className:"katex-html","aria-hidden":"true",children:(0,s.jsxs)(t.span,{className:"base",children:[(0,s.jsx)(t.span,{className:"strut",style:{height:"0.6922em"}}),(0,s.jsx)(t.span,{className:"mrel amsrm",children:"\u2234"})]})})]})," We use ",(0,s.jsx)(t.strong,{children:"absolute difference in group means"})," as the test statistic."]}),"\n",(0,s.jsx)(t.hr,{}),"\n",(0,s.jsx)(t.h3,{id:"2-query-the-dataframe",children:"2. Query the DataFrame"}),"\n",(0,s.jsx)(t.p,{children:"Since we want to compare the distributions of only cats and dogs, we need to make sure to only include the relevant pieces of data (e.g., cats and dogs weights)."}),"\n",(0,s.jsx)(t.pre,{children:(0,s.jsx)(t.code,{className:"language-python",children:"# Create a boolean Series that references which rows fulfill either condition.\nquerying_condition = (full_pets.get('Species') == 'dog') | (full_pets.get('Species') == 'cat')\n# Query.\ncats_dogs = full_pets[querying_condition]\n# Display the first 5 rows only.\ncats_dogs.take(np.arange(5)) \n"})}),"\n",(0,s.jsx)(a.A,{data:'{"columns":["ID","Species","Color","Weight","Age","Is_Cat","Owner_Comment"],"index":[0,1,2,3,4],"data":[["dog_001","dog","black",40.0,5.0,false," There are no bad dogs, only bad owners."],["cat_001","cat","golden",1.5,0.2,true,"My best birthday present ever!!!"],["cat_002","cat","black",15.0,9.0,true,"****All you need is love and a cat.****"],["dog_002","dog","white",80.0,2.0,false,"Love is a wet nose and a wagging tail."],["dog_003","dog","black",25.0,0.5,false,"Be the person your dog thinks you are."]]}'}),"\n",(0,s.jsx)(t.hr,{}),"\n",(0,s.jsx)(t.h3,{id:"3-create-a-function-to-calculate-test-statistic",children:"3. Create a function to calculate test statistic"}),"\n",(0,s.jsx)(t.p,{children:"Since our hypotheses depend on the test statistic, create a function to be able to calculate it during every trial of our permutation test."}),"\n",(0,s.jsx)(t.pre,{children:(0,s.jsx)(t.code,{className:"language-python",children:"def difference_in_means(cats_dogs):\n \"\"\"\n Calculate the absolute difference in the mean weight of dogs and cats.\n ---\n Input:\n cats_dogs: a DataFrame containing the columns 'Species' and 'Weight'.\n ---\n Output:\n The absolute difference in the mean weight of dogs and cats.\n \"\"\"\n means = cats_dogs.groupby('Species').mean()\n return np.abs((means.get('Weight').loc['dog'] - means.get('Weight').loc['cat']))\n"})}),"\n",(0,s.jsx)(t.p,{children:(0,s.jsx)(t.em,{children:"Note: Although we can simply do this in the for-loop shown in the next step, we can practice good coding habits by separating our code into readable bits!"})}),"\n",(0,s.jsx)(t.hr,{}),"\n",(0,s.jsx)(t.h3,{id:"4-simulate-the-permutation-test",children:"4. Simulate the permutation test"}),"\n",(0,s.jsx)(t.pre,{children:(0,s.jsx)(t.code,{className:"language-python",children:"n = 500 # Number of simulations.\nstatistics = np.array([]) # Array to keep track of the difference in means for each iteration.\nfor i in np.arange(n): # Run the simulation `n` number of times\n # 1. Shuffle the species.\n shuffled = cats_dogs.assign(Species=np.random.permutation(cats_dogs.get('Species')))\n\n # 2. Compute the test statistic.\n statistic = difference_in_means(shuffled)\n\n # 3. Save the result.\n statistics = np.append(statistics, statistic)\n"})}),"\n",(0,s.jsxs)(t.p,{children:["This code will run the permutation test 500 times, but a different reasonable number can be used instead. It is ",(0,s.jsx)(t.strong,{children:"crucial"})," to keep track of the difference in means each time our for-loop runs so that the number of simulated values can be displayed."]}),"\n",(0,s.jsx)(t.hr,{}),"\n",(0,s.jsx)(t.h3,{id:"5-conclusion",children:"5. Conclusion"}),"\n",(0,s.jsx)(t.pre,{children:(0,s.jsx)(t.code,{className:"language-python",children:'observed = difference_in_means(cats_dogs)\np_value = np.count_nonzero(statistics >= observed) / n\n\nprint("The observed value of the test statistic is:", observed)\nprint("The p-value is:", p_value)\n'})}),"\n",(0,s.jsxs)(t.p,{children:[(0,s.jsx)(t.strong,{children:"The observed value of the test statistic is: 30.361111111111107"})," ",(0,s.jsx)("br",{}),"\n",(0,s.jsx)(t.strong,{children:"The p-value is: 0.004"})]}),"\n",(0,s.jsx)(t.p,{children:"Using a significance level of 0.05:"}),"\n",(0,s.jsx)(t.admonition,{title:"Conclusion",type:"info",children:(0,s.jsxs)(t.ul,{children:["\n",(0,s.jsx)(t.li,{children:"Under the null hypothesis, we rarely see a difference greater than the observed value."}),"\n",(0,s.jsxs)(t.li,{children:["Therefore, we ",(0,s.jsx)(t.strong,{children:"reject"})," the null hypothesis: the evidence implies that the two groups do not come from the same distribution."]}),"\n",(0,s.jsx)(t.li,{children:"Still, we cannot conclude that species causes a different weight because there may be other confounding variables."}),"\n"]})}),"\n",(0,s.jsx)(t.hr,{}),"\n",(0,s.jsx)(t.h3,{id:"6-extra",children:"6. Extra"}),"\n",(0,s.jsx)(t.p,{children:"Let's see how our observed statistic compares to the overall simulated values!"}),"\n",(0,s.jsx)(t.pre,{children:(0,s.jsx)(t.code,{className:"language-python",children:"# Create the histogram.\nbpd.DataFrame().assign(statistics=statistics).plot(kind='hist', bins=20, density=True, ec='w')\n# Don't worry about this line - you won't need to know it for this course!\nplt.axvline(x=observed, c='black', linewidth=4, label='population difference in means')\n"})}),"\n",(0,s.jsx)(t.p,{children:(0,s.jsx)(t.img,{alt:"Distribution",src:n(5771).A+"",width:"576",height:"413"})}),"\n",(0,s.jsxs)(t.p,{children:["From this graph, we can tell that there is barely any data to the ",(0,s.jsx)(t.strong,{children:"right"})," of the black vertical line (our observed statistic), meaning we have a very low p-value!"]})]})}function p(e={}){const{wrapper:t}={...(0,i.R)(),...e.components};return t?(0,s.jsx)(t,{...e,children:(0,s.jsx)(u,{...e})}):u(e)}},8597:(e,t,n)=>{n.d(t,{A:()=>i});n(6540);var s=n(4848);const i=e=>{let{data:t}=e,n=[],i=[],a="",r=[];if(t){const e=JSON.parse(t);n=e.columns||[],i=e.data||[],a=e.indexName||"Index",r=e.index||[]}return(0,s.jsx)("div",{className:"dataframe-container",children:(0,s.jsxs)("table",{className:"dataframe-table",children:[(0,s.jsx)("thead",{children:(0,s.jsxs)("tr",{children:[(0,s.jsx)("th",{children:a}),n.map(((e,t)=>(0,s.jsx)("th",{children:e},t)))]})}),(0,s.jsx)("tbody",{children:i.map(((e,t)=>(0,s.jsxs)("tr",{children:[(0,s.jsx)("td",{className:"index-value",children:r[t]}),e.map(((e,t)=>{return(0,s.jsx)("td",{children:(n=e,"boolean"==typeof n?n.toString().charAt(0).toUpperCase()+n.toString().slice(1):n)},t);var n}))]},t)))})]})})}},5158:(e,t,n)=>{n.d(t,{A:()=>a});var s=n(6540),i=n(4848);const a=function(e){let{src:t,sourceLink:n,aspectRatio:a=16/9}=e;const[r,o]=(0,s.useState)(0),[l,c]=(0,s.useState)(0),d=(0,s.useRef)(null);return(0,s.useEffect)((()=>{const e=()=>{if(d.current){const e=d.current.offsetWidth;c(e/a)}};return e(),window.addEventListener("resize",e),()=>window.removeEventListener("resize",e)}),[a]),(0,i.jsxs)(i.Fragment,{children:[(0,i.jsx)("div",{ref:d,style:{width:"100%",position:"relative",maxWidth:"100%",backgroundColor:"white"},children:(0,i.jsx)("iframe",{src:t,style:{width:"100%",height:`${l}px`,border:"0",allowFullScreen:!0}},r)}),(0,i.jsx)("div",{style:{display:"flex",justifyContent:"center",margin:"20px 0"},children:(0,i.jsx)("a",{href:n,target:"_blank",rel:"noopener noreferrer",children:"(Source)"})}),(0,i.jsx)("div",{style:{display:"flex",justifyContent:"center",margin:"10px 0"},children:(0,i.jsx)("button",{onClick:()=>{o((e=>e+1))},style:{backgroundColor:"#4CAF50",color:"white",padding:"10px 20px",border:"none",borderRadius:"5px",cursor:"pointer",outline:"none",fontSize:"16px",fontWeight:"bold",boxShadow:"0 4px 8px rgba(0,0,0,0.1)",transition:"background-color 0.3s"},onMouseOver:e=>e.currentTarget.style.backgroundColor="#45a049",onMouseOut:e=>e.currentTarget.style.backgroundColor="#4CAF50",children:"Restart Diagram"})})]})}},5771:(e,t,n)=>{n.d(t,{A:()=>s});const s=n.p+"assets/images/permutation-test-fae4df12733e667b05989b96bf08d9a9.png"},8453:(e,t,n)=>{n.d(t,{R:()=>r,x:()=>o});var s=n(6540);const i={},a=s.createContext(i);function r(e){const t=s.useContext(a);return s.useMemo((function(){return"function"==typeof e?e(t):{...t,...e}}),[t,e])}function o(e){let t;return t=e.disableParentContext?"function"==typeof e.components?e.components(i):e.components||i:r(e.components),s.createElement(a.Provider,{value:t},e.children)}}}]); 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If, in our simulations, we rarely saw a difference in group means as extreme as the observed difference in group means, we have evidence to reject the null."}),"\n"]})]}),"\n",(0,s.jsx)(t.admonition,{type:"note",children:(0,s.jsx)(t.p,{children:"While shuffling, the size of the two new samples should be the same as the observed samples."})}),"\n",(0,s.jsxs)(t.p,{children:["The diagram below provides an overview of conducting a permutation test, although it references a different dataset. ",(0,s.jsx)(t.a,{href:"https://www.jwilber.me/permutationtest/",children:"Here"})," is another useful visualization. For additional helpful visual guides, please visit the ",(0,s.jsx)(t.a,{href:"https://dsc10.com/diagrams/",children:"Diagrams"})," site."]}),"\n",(0,s.jsx)(r.A,{src:"https://docs.google.com/presentation/d/e/2PACX-1vSovXDonR6EmjrT45h4pY1mwmcKFMWVSdgpbKHC5HNTm9sbG7dojvvCDEQCjuk2dk1oA4gmwMogr8ZL/embed?start=true&loop=false&delayms=3000&rm=minimal",sourceLink:"https://docs.google.com/presentation/d/1TTWoQ7FU4tzBGc7EskF6WYccIn1BWQbTSizAiFc2p2o/edit?usp=sharing"}),"\n",(0,s.jsx)(t.hr,{}),"\n",(0,s.jsx)(t.h2,{id:"code-example-absolute-difference",children:"Code Example (Absolute Difference)"}),"\n",(0,s.jsx)(t.h3,{id:"1-state-the-questionhypothesis",children:"1. 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The observed differences in our samples cannot be explained by random chance alone."]}),"\n"]})]}),"\n",(0,s.jsxs)(t.p,{children:['Since the alternative hypothesis is of the form "A and B are different," the ',(0,s.jsx)(t.strong,{children:"test statistic"})," should measure distance and use an absolute value."]}),"\n",(0,s.jsxs)(t.p,{children:[(0,s.jsxs)(t.span,{className:"katex",children:[(0,s.jsx)(t.span,{className:"katex-mathml",children:(0,s.jsx)(t.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,s.jsxs)(t.semantics,{children:[(0,s.jsx)(t.mrow,{children:(0,s.jsx)(t.mo,{children:"\u2234"})}),(0,s.jsx)(t.annotation,{encoding:"application/x-tex",children:"\\therefore"})]})})}),(0,s.jsx)(t.span,{className:"katex-html","aria-hidden":"true",children:(0,s.jsxs)(t.span,{className:"base",children:[(0,s.jsx)(t.span,{className:"strut",style:{height:"0.6922em"}}),(0,s.jsx)(t.span,{className:"mrel amsrm",children:"\u2234"})]})})]})," We use ",(0,s.jsx)(t.strong,{children:"absolute difference in group means"})," as the test statistic."]}),"\n",(0,s.jsx)(t.hr,{}),"\n",(0,s.jsx)(t.h3,{id:"2-query-the-dataframe",children:"2. 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Extra",id:"6-extra",level:3}];function d(e){const t={admonition:"admonition",annotation:"annotation",code:"code",em:"em",h2:"h2",h3:"h3",hr:"hr",img:"img",li:"li",math:"math",mo:"mo",mrow:"mrow",ol:"ol",p:"p",pre:"pre",semantics:"semantics",span:"span",strong:"strong",ul:"ul",...(0,i.R)(),...e.components};return(0,n.jsxs)(n.Fragment,{children:[(0,n.jsx)(t.h2,{id:"concept",children:"Concept"}),"\n",(0,n.jsx)(t.admonition,{title:"Note \ud83c\udf1f",type:"note",children:(0,n.jsxs)(t.p,{children:["This page refers to the ",(0,n.jsx)(t.strong,{children:"standard"})," hypothesis test."]})}),"\n",(0,n.jsx)(t.admonition,{title:"Key Idea",type:"tip",children:(0,n.jsx)(t.p,{children:"We use a hypothesis test to test whether a sample was drawn from a population."})}),"\n",(0,n.jsxs)(t.admonition,{title:"Terminology",type:"info",children:[(0,n.jsxs)(t.p,{children:[(0,n.jsx)(t.strong,{children:"Hypothesis Test"}),": A process that test whether a sample was drawn from a population, given a population distribution and a sample."]}),(0,n.jsx)(t.p,{children:"To conduct a hypothesis test:"}),(0,n.jsxs)(t.ol,{children:["\n",(0,n.jsx)(t.li,{children:"Simulate the experiment many times under the assumption that the null hypothesis is true."}),"\n",(0,n.jsx)(t.li,{children:"Compute a test statistic on each of the simulated samples, as well as on the observed sample."}),"\n",(0,n.jsx)(t.li,{children:"Look at the resulting empirical distribution of test statistics and see where the observed test statistic falls. If it seems like an atypical value (too large or too small), we reject the null hypothesis; otherwise, we fail to reject the null."}),"\n"]})]}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h2,{id:"code-example-1-difference",children:"Code Example 1 (Difference)"}),"\n",(0,n.jsx)(t.h3,{id:"1-state-the-questionhypothesis",children:"1. State the question/hypothesis"}),"\n",(0,n.jsxs)(t.admonition,{title:"Hypotheses",type:"info",children:[(0,n.jsx)(t.p,{children:"We will test the following pair of hypotheses at the standard p = 0.05 significance level."}),(0,n.jsxs)(t.ul,{children:["\n",(0,n.jsxs)(t.li,{children:[(0,n.jsx)(t.strong,{children:"Null Hypothesis:"}),' The proportion of "white" dogs among dogs is ',(0,n.jsx)(t.strong,{children:"equal"}),' to the proportion of "white" pets in the overall population.']}),"\n",(0,n.jsxs)(t.li,{children:[(0,n.jsx)(t.strong,{children:"Alternative Hypothesis:"}),' The distribution of "white" dogs among dogs is ',(0,n.jsx)(t.strong,{children:"greater than"}),' the proportion of "white" pets in the overall population.']}),"\n"]})]}),"\n",(0,n.jsxs)(t.p,{children:['Since the alternative hypothesis is of the form "A is ',(0,n.jsx)(t.strong,{children:(0,n.jsx)(t.em,{children:"greater than"})}),' B," the ',(0,n.jsx)(t.strong,{children:"test statistic"})," should measure ",(0,n.jsx)(t.strong,{children:"signed difference"})," rather than absolute difference."]}),"\n",(0,n.jsxs)(t.p,{children:[(0,n.jsxs)(t.span,{className:"katex",children:[(0,n.jsx)(t.span,{className:"katex-mathml",children:(0,n.jsx)(t.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(t.semantics,{children:[(0,n.jsx)(t.mrow,{children:(0,n.jsx)(t.mo,{children:"\u2234"})}),(0,n.jsx)(t.annotation,{encoding:"application/x-tex",children:"\\therefore"})]})})}),(0,n.jsx)(t.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(t.span,{className:"base",children:[(0,n.jsx)(t.span,{className:"strut",style:{height:"0.6922em"}}),(0,n.jsx)(t.span,{className:"mrel amsrm",children:"\u2234"})]})})]})," We use ",(0,n.jsx)(t.strong,{children:"the difference in proportions"})," of white dogs among dogs and white pets in the overall poplulation as the test statistic."]}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"2-calculate-the-overall-proportion",children:"2. Calculate the overall proportion"}),"\n",(0,n.jsx)(t.p,{children:"We first compute the proportion of white pets in the overall population, which will be used for calculating the test statistic."}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:"#Method 1: Obtain a series of boolean values (1s and 0s), and calculate the mean\r\noverall_prop = (full_pets.get('Color')=='white').mean()\r\n\r\n#Method 2: Query the DataFrame and obtain the proportion by using .shape[0]\r\n#overall_prop = full_pets[full_pets.get('Color')=='white'].shape[0]/full_pets.shape[0]\r\n\r\noverall_prop\n"})}),"\n",(0,n.jsx)(t.p,{children:"0.2631578947368421"}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"3-create-a-function-to-calculate-test-statistic",children:"3. Create a function to calculate test statistic"}),"\n",(0,n.jsx)(t.p,{children:"Create a function to calculate the test statistic during every trial of our hypothesis test."}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:'def difference_in_proportions(dogs_prop, overall_prop):\r\n """\r\n Calculate the difference in proportions of white dogs among dogs and white pets in the overall population.\r\n ---\r\n Input:\r\n dogs_prop: the proportion of white dogs among all dogs.\r\n overall_prop: the proportion of white pets in the overall population.\r\n ---\r\n Output:\r\n The difference in proportions of white dogs among dogs and white pets in the overall population.\r\n """\r\n return dogs_prop - overall_prop\n'})}),"\n",(0,n.jsx)(t.p,{children:(0,n.jsx)(t.em,{children:"Note: Although we can simply do this in the for-loop shown in the next step, we can practice good coding habits by separating our code into readable bits!"})}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"4-compute-the-observed-statistic",children:"4. Compute the observed statistic"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:"# Query the DataFrame to only include dogs\r\ndogs_df = full_pets[full_pets.get('Species') == 'dog']\r\n# Compute the observed proportion of white dogs among all dogs\r\nobs_dogs_prop = (dogs_df.get('Color') == 'white').mean()\r\n# Calculate the observed statistic\r\nobserved_stat = difference_in_proportions(obs_dogs_prop, overall_prop)\r\nobserved_stat\n"})}),"\n",(0,n.jsx)(t.p,{children:"0.18128654970760233"}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"5-simulate-the-hypothesis-test-under-the-null-hypothesis",children:"5. Simulate the hypothesis test under the null hypothesis"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:'n = 500 # Number of simulations.\r\ntest_statistics = np.array([]) # Array to keep track of the test statistic for each iteration.\r\n\r\n# Calculte the smaple size (number of dogs)\r\nsample_size = dogs_df.shape[0]\r\n\r\n# Under the null hypothesis, proportion of "white" dogs among dogs is equal to the proportion of white pets among the overall population\r\nmodel_proportions = np.array([obs_dogs_prop, 1-obs_dogs_prop]) \r\n\r\nfor i in np.arange(n): # Run the simulation `n` number of times\r\n \r\n # 1. Simulate the dogs distribution\r\n # Calculate the the proportion of white dogs among all dogs.\r\n simulation_proportion = np.random.multinomial(sample_size, model_proportions)[0] / sample_size\r\n \r\n # 2. Compute the test statistic\r\n test_stat = difference_in_proportions(simulation_proportion, overall_prop)\r\n\r\n # 3. Save the result\r\n test_statistics = np.append(test_statistics, test_stat)\n'})}),"\n",(0,n.jsxs)(t.p,{children:["This code will run the hypothesis test 500 times, but a different reasonable number can be used instead. It is ",(0,n.jsx)(t.strong,{children:"crucial"})," to keep track of the test statistic each time our for-loop runs so that the number of simulated values can be stored."]}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"6-conclusion",children:"6. Conclusion"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:'p_value = np.count_nonzero(test_statistics >= observed_stat) / n\r\n\r\nprint("The observed value of the test statistic is:", observed_stat)\r\nprint("The p-value is:", p_value)\n'})}),"\n",(0,n.jsxs)(t.p,{children:[(0,n.jsx)(t.strong,{children:"The observed value of the test statistic is:"})," 0.18128654970760233 ",(0,n.jsx)("br",{}),"\r\n",(0,n.jsx)(t.strong,{children:"The p-value is:"})," 0.616"]}),"\n",(0,n.jsx)(t.p,{children:"Using a significance level of 0.05:"}),"\n",(0,n.jsx)(t.admonition,{title:"Conclusion",type:"info",children:(0,n.jsxs)(t.ul,{children:["\n",(0,n.jsx)(t.li,{children:"Under the null hypothesis, there is a sufficiently large probability of seeing a difference greater than the observed value. The data are consistent with the null hypothesis."}),"\n",(0,n.jsxs)(t.li,{children:["Since our p-value is greater than 0.05, we ",(0,n.jsx)(t.strong,{children:"fail to reject"})," the null hypothesis."]}),"\n"]})}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"7-extra",children:"7. Extra"}),"\n",(0,n.jsx)(t.p,{children:"Let's see how our observed statistic compares to the overall simulated values!"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:"# Create the histogram.\r\nbpd.DataFrame().assign(test_statistics=test_statistics).plot(kind='hist', bins= 10, density=True, ec='w')\r\n# Don't worry about these lines - you won't need to know it for this course!\r\nplt.axvline(x=observed_stat, c='black', linewidth=4);\r\nyticks = plt.gca().get_yticks()\r\nplt.yticks(yticks, np.round(yticks * 0.1, 2))\r\nplt.show()\n"})}),"\n",(0,n.jsx)(t.p,{children:(0,n.jsx)(t.img,{alt:"Distribution",src:s(1647).A+"",width:"640",height:"480"})}),"\n",(0,n.jsxs)(t.p,{children:["From this graph, we can see that more than half of the data are to the ",(0,n.jsx)(t.strong,{children:"right"})," of the black vertical line (our observed statistic), meaning we have a relatively high p-value!"]}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h2,{id:"code-example-2-tvd",children:"Code Example 2 (TVD)"}),"\n",(0,n.jsx)(t.h3,{id:"1-state-the-questionhypothesis-1",children:"1. State the question/hypothesis"}),"\n",(0,n.jsx)(t.p,{children:"We found that the color distribution of dogs seems different from that of all pets."}),"\n",(0,n.jsx)(o.A,{data:'{"columns":["Pets_Dist","Dogs_Dist"],"index":["black","golden","white"],"data":[[0.53,0.44],[0.21,0.12],[0.26,0.44]]}'}),"\n",(0,n.jsx)(t.p,{children:"To see whether this difference is due to random chance, we will test the following pair of hypotheses at the standard p = 0.05 significance level."}),"\n",(0,n.jsx)(t.admonition,{title:"Hypotheses",type:"info",children:(0,n.jsxs)(t.ul,{children:["\n",(0,n.jsxs)(t.li,{children:[(0,n.jsx)(t.strong,{children:"Null Hypothesis:"})," The color distribution of dogs is the ",(0,n.jsx)(t.strong,{children:"same as"})," the color distribution of pets."]}),"\n",(0,n.jsxs)(t.li,{children:[(0,n.jsx)(t.strong,{children:"Alternative Hypothesis:"})," The color distribution of dogs is ",(0,n.jsx)(t.strong,{children:"different from"})," the color distribution of pets."]}),"\n"]})}),"\n",(0,n.jsxs)(t.p,{children:["Since we are comparing two ",(0,n.jsx)(t.strong,{children:"categorical"})," distributions, we use Total Variation Distance (TVD) between the two distributions as our ",(0,n.jsx)(t.strong,{children:"test statistic"}),"."]}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"2-create-a-function-to-calculate-test-statistic-tvd",children:"2. Create a function to calculate test statistic (TVD)"}),"\n",(0,n.jsx)(t.p,{children:"Create a function to calculate the test statistic during every trial of our hypothesis test."}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:"def total_variation_distance(dist1, dist2):\r\n '''Computes the TVD between two categorical distributions, \r\n assuming the categories appear in the same order.'''\r\n return np.abs((dist1 - dist2)).sum() / 2\n"})}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"3-compute-the-observed-statistic",children:"3. Compute the observed statistic"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:"pets_color_dist = np.array([0.53, 0.21, 0.26])\r\ndogs_color_dist = np.array([0.44, 0.12, 0.44])\r\nobserved_tvd = total_variation_distance(dogs_color_dist, pets_color_dist)\r\nobserved_tvd\n"})}),"\n",(0,n.jsx)(t.p,{children:"0.18"}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"4-simulate-the-hypothesis-test-under-the-null-hypothesis",children:"4. Simulate the hypothesis test under the null hypothesis"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:"n = 5000 # Number of simulations.\r\ntvds = np.array([]) # Array to keep track of the test statistic for each iteration.\r\n\r\n# Get sample df (dogs df)\r\ndog_df = full_pets[full_pets.get('Species') == 'dog'] \r\n\r\n# Calculte the smaple size (number of dogs)\r\nsample_size = dog_df.shape[0]\r\n\r\nfor i in np.arange(n): # Run the simulation `n` number of times\r\n \r\n # 1. Simulate the color distribution of dogs.\r\n # Under the null hypothesis, color distribution of dogs should be equal to the color distribution of pets among the overall population\r\n sample_distribution = np.random.multinomial(sample_size, pets_color_dist) / sample_size\r\n\r\n # 2. Compute the test statistic (TVD)\r\n new_tvd = total_variation_distance(sample_distribution, pets_color_dist)\r\n\r\n # 3. Save the result\r\n tvds = np.append(tvds, new_tvd)\n"})}),"\n",(0,n.jsxs)(t.p,{children:["This code will run the hypothesis test 5000 times, but a different reasonable number can be used instead. It is ",(0,n.jsx)(t.strong,{children:"crucial"})," to keep track of the test statistic each time our for-loop runs so that the number of simulated values can be stored."]}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"5-conclusion",children:"5. Conclusion"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:'p_value = np.count_nonzero(tvds >= observed_tvd) / n\r\n\r\nprint("The observed value of the test statistic is:", observed_tvd)\r\nprint("The p-value is:", p_value)\n'})}),"\n",(0,n.jsxs)(t.p,{children:[(0,n.jsx)(t.strong,{children:"The observed value of the test statistic is:"})," 0.18",(0,n.jsx)("br",{}),"\r\n",(0,n.jsx)(t.strong,{children:"The p-value is:"})," 0.4972"]}),"\n",(0,n.jsx)(t.p,{children:"Using a significance level of 0.05:"}),"\n",(0,n.jsx)(t.admonition,{title:"Conclusion",type:"info",children:(0,n.jsxs)(t.ul,{children:["\n",(0,n.jsx)(t.li,{children:"Under the null hypothesis, there is a sufficiently large probability of seeing a difference greater than the observed value. The data are consistent with the null hypothesis."}),"\n",(0,n.jsxs)(t.li,{children:["Since our p-value is greater than 0.05, we ",(0,n.jsx)(t.strong,{children:"fail to reject"})," the null hypothesis."]}),"\n"]})}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"6-extra",children:"6. Extra"}),"\n",(0,n.jsx)(t.p,{children:"Let's see how our observed statistic compares to the overall simulated values!"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:"# Create the histogram.\r\nbpd.DataFrame().assign(tvds=tvds).plot(kind='hist', density=True, bins=20, ec='w', figsize=(10, 5), title='Empirical Distribution of TVD Between Pets Colors and Dogs Colors')\r\n# Don't worry about these lines - you won't need to know it for this course!\r\nplt.axvline(observed_tvd, color='black', linewidth=4, label='Observed Statistic')\r\nplt.legend();\n"})}),"\n",(0,n.jsx)(t.p,{children:(0,n.jsx)(t.img,{alt:"Distribution",src:s(2477).A+"",width:"1000",height:"500"})}),"\n",(0,n.jsxs)(t.p,{children:["From this graph, we can see that almost half of the data are to the ",(0,n.jsx)(t.strong,{children:"right"})," of the black vertical line (our observed statistic), meaning we have a relatively high p-value!"]})]})}function p(e={}){const{wrapper:t}={...(0,i.R)(),...e.components};return t?(0,n.jsx)(t,{...e,children:(0,n.jsx)(d,{...e})}):d(e)}},8597:(e,t,s)=>{s.d(t,{A:()=>i});s(6540);var n=s(4848);const i=e=>{let{data:t}=e,s=[],i=[],o="",r=[];if(t){const e=JSON.parse(t);s=e.columns||[],i=e.data||[],o=e.indexName||"Index",r=e.index||[]}return(0,n.jsx)("div",{className:"dataframe-container",children:(0,n.jsxs)("table",{className:"dataframe-table",children:[(0,n.jsx)("thead",{children:(0,n.jsxs)("tr",{children:[(0,n.jsx)("th",{children:o}),s.map(((e,t)=>(0,n.jsx)("th",{children:e},t)))]})}),(0,n.jsx)("tbody",{children:i.map(((e,t)=>(0,n.jsxs)("tr",{children:[(0,n.jsx)("td",{className:"index-value",children:r[t]}),e.map(((e,t)=>{return(0,n.jsx)("td",{children:(s=e,"boolean"==typeof s?s.toString().charAt(0).toUpperCase()+s.toString().slice(1):s)},t);var s}))]},t)))})]})})}},5158:(e,t,s)=>{s.d(t,{A:()=>o});var n=s(6540),i=s(4848);const o=function(e){let{src:t,sourceLink:s,aspectRatio:o=16/9}=e;const[r,a]=(0,n.useState)(0),[l,h]=(0,n.useState)(0),c=(0,n.useRef)(null);return(0,n.useEffect)((()=>{const e=()=>{if(c.current){const e=c.current.offsetWidth;h(e/o)}};return e(),window.addEventListener("resize",e),()=>window.removeEventListener("resize",e)}),[o]),(0,i.jsxs)(i.Fragment,{children:[(0,i.jsx)("div",{ref:c,style:{width:"100%",position:"relative",maxWidth:"100%",backgroundColor:"white"},children:(0,i.jsx)("iframe",{src:t,style:{width:"100%",height:`${l}px`,border:"0",allowFullScreen:!0}},r)}),(0,i.jsx)("div",{style:{display:"flex",justifyContent:"center",margin:"20px 0"},children:(0,i.jsx)("a",{href:s,target:"_blank",rel:"noopener noreferrer",children:"(Source)"})}),(0,i.jsx)("div",{style:{display:"flex",justifyContent:"center",margin:"10px 0"},children:(0,i.jsx)("button",{onClick:()=>{a((e=>e+1))},style:{backgroundColor:"#4CAF50",color:"white",padding:"10px 20px",border:"none",borderRadius:"5px",cursor:"pointer",outline:"none",fontSize:"16px",fontWeight:"bold",boxShadow:"0 4px 8px rgba(0,0,0,0.1)",transition:"background-color 0.3s"},onMouseOver:e=>e.currentTarget.style.backgroundColor="#45a049",onMouseOut:e=>e.currentTarget.style.backgroundColor="#4CAF50",children:"Restart Diagram"})})]})}},1647:(e,t,s)=>{s.d(t,{A:()=>n});const n=s.p+"assets/images/hypothesis-test-200177f66e9f7f0e360b809bc6c6f3c8.png"},2477:(e,t,s)=>{s.d(t,{A:()=>n});const n=s.p+"assets/images/hypothesis-test2-7615aa5325b73c6c19541b78e2619a30.png"},8453:(e,t,s)=>{s.d(t,{R:()=>r,x:()=>a});var n=s(6540);const i={},o=n.createContext(i);function r(e){const t=n.useContext(o);return n.useMemo((function(){return"function"==typeof e?e(t):{...t,...e}}),[t,e])}function a(e){let t;return t=e.disableParentContext?"function"==typeof e.components?e.components(i):e.components||i:r(e.components),n.createElement(o.Provider,{value:t},e.children)}}}]); 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Extra",id:"6-extra",level:3}];function d(e){const t={admonition:"admonition",annotation:"annotation",code:"code",em:"em",h2:"h2",h3:"h3",hr:"hr",img:"img",li:"li",math:"math",mo:"mo",mrow:"mrow",ol:"ol",p:"p",pre:"pre",semantics:"semantics",span:"span",strong:"strong",ul:"ul",...(0,i.R)(),...e.components};return(0,n.jsxs)(n.Fragment,{children:[(0,n.jsx)(t.h2,{id:"concept",children:"Concept"}),"\n",(0,n.jsx)(t.admonition,{title:"Note \ud83c\udf1f",type:"note",children:(0,n.jsxs)(t.p,{children:["This page refers to the ",(0,n.jsx)(t.strong,{children:"standard"})," hypothesis test."]})}),"\n",(0,n.jsx)(t.admonition,{title:"Key Idea",type:"tip",children:(0,n.jsx)(t.p,{children:"We use a hypothesis test to test whether a sample was drawn from a population."})}),"\n",(0,n.jsxs)(t.admonition,{title:"Terminology",type:"info",children:[(0,n.jsxs)(t.p,{children:[(0,n.jsx)(t.strong,{children:"Hypothesis Test"}),": A process that test whether a sample was drawn from a population, given a population distribution and a sample."]}),(0,n.jsx)(t.p,{children:"To conduct a hypothesis test:"}),(0,n.jsxs)(t.ol,{children:["\n",(0,n.jsx)(t.li,{children:"Simulate the experiment many times under the assumption that the null hypothesis is true."}),"\n",(0,n.jsx)(t.li,{children:"Compute a test statistic on each of the simulated samples, as well as on the observed sample."}),"\n",(0,n.jsx)(t.li,{children:"Look at the resulting empirical distribution of test statistics and see where the observed test statistic falls. If it seems like an atypical value (too large or too small), we reject the null hypothesis; otherwise, we fail to reject the null."}),"\n"]})]}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h2,{id:"code-example-1-difference",children:"Code Example 1 (Difference)"}),"\n",(0,n.jsx)(t.h3,{id:"1-state-the-questionhypothesis",children:"1. State the question/hypothesis"}),"\n",(0,n.jsxs)(t.admonition,{title:"Hypotheses",type:"info",children:[(0,n.jsx)(t.p,{children:"We will test the following pair of hypotheses at the standard p = 0.05 significance level."}),(0,n.jsxs)(t.ul,{children:["\n",(0,n.jsxs)(t.li,{children:[(0,n.jsx)(t.strong,{children:"Null Hypothesis:"}),' The proportion of "white" dogs among dogs is ',(0,n.jsx)(t.strong,{children:"equal"}),' to the proportion of "white" pets in the overall population.']}),"\n",(0,n.jsxs)(t.li,{children:[(0,n.jsx)(t.strong,{children:"Alternative Hypothesis:"}),' The distribution of "white" dogs among dogs is ',(0,n.jsx)(t.strong,{children:"greater than"}),' the proportion of "white" pets in the overall population.']}),"\n"]})]}),"\n",(0,n.jsxs)(t.p,{children:['Since the alternative hypothesis is of the form "A is ',(0,n.jsx)(t.strong,{children:(0,n.jsx)(t.em,{children:"greater than"})}),' B," the ',(0,n.jsx)(t.strong,{children:"test statistic"})," should measure ",(0,n.jsx)(t.strong,{children:"signed difference"})," rather than absolute difference."]}),"\n",(0,n.jsxs)(t.p,{children:[(0,n.jsxs)(t.span,{className:"katex",children:[(0,n.jsx)(t.span,{className:"katex-mathml",children:(0,n.jsx)(t.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,n.jsxs)(t.semantics,{children:[(0,n.jsx)(t.mrow,{children:(0,n.jsx)(t.mo,{children:"\u2234"})}),(0,n.jsx)(t.annotation,{encoding:"application/x-tex",children:"\\therefore"})]})})}),(0,n.jsx)(t.span,{className:"katex-html","aria-hidden":"true",children:(0,n.jsxs)(t.span,{className:"base",children:[(0,n.jsx)(t.span,{className:"strut",style:{height:"0.6922em"}}),(0,n.jsx)(t.span,{className:"mrel amsrm",children:"\u2234"})]})})]})," We use ",(0,n.jsx)(t.strong,{children:"the difference in proportions"})," of white dogs among dogs and white pets in the overall poplulation as the test statistic."]}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"2-calculate-the-overall-proportion",children:"2. Calculate the overall proportion"}),"\n",(0,n.jsx)(t.p,{children:"We first compute the proportion of white pets in the overall population, which will be used for calculating the test statistic."}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:"#Method 1: Obtain a series of boolean values (1s and 0s), and calculate the mean\noverall_prop = (full_pets.get('Color')=='white').mean()\n\n#Method 2: Query the DataFrame and obtain the proportion by using .shape[0]\n#overall_prop = full_pets[full_pets.get('Color')=='white'].shape[0]/full_pets.shape[0]\n\noverall_prop\n"})}),"\n",(0,n.jsx)(t.p,{children:"0.2631578947368421"}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"3-create-a-function-to-calculate-test-statistic",children:"3. Create a function to calculate test statistic"}),"\n",(0,n.jsx)(t.p,{children:"Create a function to calculate the test statistic during every trial of our hypothesis test."}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:'def difference_in_proportions(dogs_prop, overall_prop):\n """\n Calculate the difference in proportions of white dogs among dogs and white pets in the overall population.\n ---\n Input:\n dogs_prop: the proportion of white dogs among all dogs.\n overall_prop: the proportion of white pets in the overall population.\n ---\n Output:\n The difference in proportions of white dogs among dogs and white pets in the overall population.\n """\n return dogs_prop - overall_prop\n'})}),"\n",(0,n.jsx)(t.p,{children:(0,n.jsx)(t.em,{children:"Note: Although we can simply do this in the for-loop shown in the next step, we can practice good coding habits by separating our code into readable bits!"})}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"4-compute-the-observed-statistic",children:"4. Compute the observed statistic"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:"# Query the DataFrame to only include dogs\ndogs_df = full_pets[full_pets.get('Species') == 'dog']\n# Compute the observed proportion of white dogs among all dogs\nobs_dogs_prop = (dogs_df.get('Color') == 'white').mean()\n# Calculate the observed statistic\nobserved_stat = difference_in_proportions(obs_dogs_prop, overall_prop)\nobserved_stat\n"})}),"\n",(0,n.jsx)(t.p,{children:"0.18128654970760233"}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"5-simulate-the-hypothesis-test-under-the-null-hypothesis",children:"5. Simulate the hypothesis test under the null hypothesis"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:'n = 500 # Number of simulations.\ntest_statistics = np.array([]) # Array to keep track of the test statistic for each iteration.\n\n# Calculte the smaple size (number of dogs)\nsample_size = dogs_df.shape[0]\n\n# Under the null hypothesis, proportion of "white" dogs among dogs is equal to the proportion of white pets among the overall population\nmodel_proportions = np.array([obs_dogs_prop, 1-obs_dogs_prop]) \n\nfor i in np.arange(n): # Run the simulation `n` number of times\n \n # 1. Simulate the dogs distribution\n # Calculate the the proportion of white dogs among all dogs.\n simulation_proportion = np.random.multinomial(sample_size, model_proportions)[0] / sample_size\n \n # 2. Compute the test statistic\n test_stat = difference_in_proportions(simulation_proportion, overall_prop)\n\n # 3. Save the result\n test_statistics = np.append(test_statistics, test_stat)\n'})}),"\n",(0,n.jsxs)(t.p,{children:["This code will run the hypothesis test 500 times, but a different reasonable number can be used instead. It is ",(0,n.jsx)(t.strong,{children:"crucial"})," to keep track of the test statistic each time our for-loop runs so that the number of simulated values can be stored."]}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"6-conclusion",children:"6. Conclusion"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:'p_value = np.count_nonzero(test_statistics >= observed_stat) / n\n\nprint("The observed value of the test statistic is:", observed_stat)\nprint("The p-value is:", p_value)\n'})}),"\n",(0,n.jsxs)(t.p,{children:[(0,n.jsx)(t.strong,{children:"The observed value of the test statistic is:"})," 0.18128654970760233 ",(0,n.jsx)("br",{}),"\n",(0,n.jsx)(t.strong,{children:"The p-value is:"})," 0.616"]}),"\n",(0,n.jsx)(t.p,{children:"Using a significance level of 0.05:"}),"\n",(0,n.jsx)(t.admonition,{title:"Conclusion",type:"info",children:(0,n.jsxs)(t.ul,{children:["\n",(0,n.jsx)(t.li,{children:"Under the null hypothesis, there is a sufficiently large probability of seeing a difference greater than the observed value. The data are consistent with the null hypothesis."}),"\n",(0,n.jsxs)(t.li,{children:["Since our p-value is greater than 0.05, we ",(0,n.jsx)(t.strong,{children:"fail to reject"})," the null hypothesis."]}),"\n"]})}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"7-extra",children:"7. Extra"}),"\n",(0,n.jsx)(t.p,{children:"Let's see how our observed statistic compares to the overall simulated values!"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:"# Create the histogram.\nbpd.DataFrame().assign(test_statistics=test_statistics).plot(kind='hist', bins= 10, density=True, ec='w')\n# Don't worry about these lines - you won't need to know it for this course!\nplt.axvline(x=observed_stat, c='black', linewidth=4);\nyticks = plt.gca().get_yticks()\nplt.yticks(yticks, np.round(yticks * 0.1, 2))\nplt.show()\n"})}),"\n",(0,n.jsx)(t.p,{children:(0,n.jsx)(t.img,{alt:"Distribution",src:s(4183).A+"",width:"640",height:"480"})}),"\n",(0,n.jsxs)(t.p,{children:["From this graph, we can see that more than half of the data are to the ",(0,n.jsx)(t.strong,{children:"right"})," of the black vertical line (our observed statistic), meaning we have a relatively high p-value!"]}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h2,{id:"code-example-2-tvd",children:"Code Example 2 (TVD)"}),"\n",(0,n.jsx)(t.h3,{id:"1-state-the-questionhypothesis-1",children:"1. State the question/hypothesis"}),"\n",(0,n.jsx)(t.p,{children:"We found that the color distribution of dogs seems different from that of all pets."}),"\n",(0,n.jsx)(o.A,{data:'{"columns":["Pets_Dist","Dogs_Dist"],"index":["black","golden","white"],"data":[[0.53,0.44],[0.21,0.12],[0.26,0.44]]}'}),"\n",(0,n.jsx)(t.p,{children:"To see whether this difference is due to random chance, we will test the following pair of hypotheses at the standard p = 0.05 significance level."}),"\n",(0,n.jsx)(t.admonition,{title:"Hypotheses",type:"info",children:(0,n.jsxs)(t.ul,{children:["\n",(0,n.jsxs)(t.li,{children:[(0,n.jsx)(t.strong,{children:"Null Hypothesis:"})," The color distribution of dogs is the ",(0,n.jsx)(t.strong,{children:"same as"})," the color distribution of pets."]}),"\n",(0,n.jsxs)(t.li,{children:[(0,n.jsx)(t.strong,{children:"Alternative Hypothesis:"})," The color distribution of dogs is ",(0,n.jsx)(t.strong,{children:"different from"})," the color distribution of pets."]}),"\n"]})}),"\n",(0,n.jsxs)(t.p,{children:["Since we are comparing two ",(0,n.jsx)(t.strong,{children:"categorical"})," distributions, we use Total Variation Distance (TVD) between the two distributions as our ",(0,n.jsx)(t.strong,{children:"test statistic"}),"."]}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"2-create-a-function-to-calculate-test-statistic-tvd",children:"2. Create a function to calculate test statistic (TVD)"}),"\n",(0,n.jsx)(t.p,{children:"Create a function to calculate the test statistic during every trial of our hypothesis test."}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:"def total_variation_distance(dist1, dist2):\n '''Computes the TVD between two categorical distributions, \n assuming the categories appear in the same order.'''\n return np.abs((dist1 - dist2)).sum() / 2\n"})}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"3-compute-the-observed-statistic",children:"3. Compute the observed statistic"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:"pets_color_dist = np.array([0.53, 0.21, 0.26])\ndogs_color_dist = np.array([0.44, 0.12, 0.44])\nobserved_tvd = total_variation_distance(dogs_color_dist, pets_color_dist)\nobserved_tvd\n"})}),"\n",(0,n.jsx)(t.p,{children:"0.18"}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"4-simulate-the-hypothesis-test-under-the-null-hypothesis",children:"4. Simulate the hypothesis test under the null hypothesis"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:"n = 5000 # Number of simulations.\ntvds = np.array([]) # Array to keep track of the test statistic for each iteration.\n\n# Get sample df (dogs df)\ndog_df = full_pets[full_pets.get('Species') == 'dog'] \n\n# Calculte the smaple size (number of dogs)\nsample_size = dog_df.shape[0]\n\nfor i in np.arange(n): # Run the simulation `n` number of times\n \n # 1. Simulate the color distribution of dogs.\n # Under the null hypothesis, color distribution of dogs should be equal to the color distribution of pets among the overall population\n sample_distribution = np.random.multinomial(sample_size, pets_color_dist) / sample_size\n\n # 2. Compute the test statistic (TVD)\n new_tvd = total_variation_distance(sample_distribution, pets_color_dist)\n\n # 3. Save the result\n tvds = np.append(tvds, new_tvd)\n"})}),"\n",(0,n.jsxs)(t.p,{children:["This code will run the hypothesis test 5000 times, but a different reasonable number can be used instead. It is ",(0,n.jsx)(t.strong,{children:"crucial"})," to keep track of the test statistic each time our for-loop runs so that the number of simulated values can be stored."]}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"5-conclusion",children:"5. Conclusion"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:'p_value = np.count_nonzero(tvds >= observed_tvd) / n\n\nprint("The observed value of the test statistic is:", observed_tvd)\nprint("The p-value is:", p_value)\n'})}),"\n",(0,n.jsxs)(t.p,{children:[(0,n.jsx)(t.strong,{children:"The observed value of the test statistic is:"})," 0.18",(0,n.jsx)("br",{}),"\n",(0,n.jsx)(t.strong,{children:"The p-value is:"})," 0.4972"]}),"\n",(0,n.jsx)(t.p,{children:"Using a significance level of 0.05:"}),"\n",(0,n.jsx)(t.admonition,{title:"Conclusion",type:"info",children:(0,n.jsxs)(t.ul,{children:["\n",(0,n.jsx)(t.li,{children:"Under the null hypothesis, there is a sufficiently large probability of seeing a difference greater than the observed value. The data are consistent with the null hypothesis."}),"\n",(0,n.jsxs)(t.li,{children:["Since our p-value is greater than 0.05, we ",(0,n.jsx)(t.strong,{children:"fail to reject"})," the null hypothesis."]}),"\n"]})}),"\n",(0,n.jsx)(t.hr,{}),"\n",(0,n.jsx)(t.h3,{id:"6-extra",children:"6. Extra"}),"\n",(0,n.jsx)(t.p,{children:"Let's see how our observed statistic compares to the overall simulated values!"}),"\n",(0,n.jsx)(t.pre,{children:(0,n.jsx)(t.code,{className:"language-python",children:"# Create the histogram.\nbpd.DataFrame().assign(tvds=tvds).plot(kind='hist', density=True, bins=20, ec='w', figsize=(10, 5), title='Empirical Distribution of TVD Between Pets Colors and Dogs Colors')\n# Don't worry about these lines - you won't need to know it for this course!\nplt.axvline(observed_tvd, color='black', linewidth=4, label='Observed Statistic')\nplt.legend();\n"})}),"\n",(0,n.jsx)(t.p,{children:(0,n.jsx)(t.img,{alt:"Distribution",src:s(789).A+"",width:"1000",height:"500"})}),"\n",(0,n.jsxs)(t.p,{children:["From this graph, we can see that almost half of the data are to the ",(0,n.jsx)(t.strong,{children:"right"})," of the black vertical line (our observed statistic), meaning we have a relatively high p-value!"]})]})}function p(e={}){const{wrapper:t}={...(0,i.R)(),...e.components};return t?(0,n.jsx)(t,{...e,children:(0,n.jsx)(d,{...e})}):d(e)}},8597:(e,t,s)=>{s.d(t,{A:()=>i});s(6540);var n=s(4848);const i=e=>{let{data:t}=e,s=[],i=[],o="",r=[];if(t){const e=JSON.parse(t);s=e.columns||[],i=e.data||[],o=e.indexName||"Index",r=e.index||[]}return(0,n.jsx)("div",{className:"dataframe-container",children:(0,n.jsxs)("table",{className:"dataframe-table",children:[(0,n.jsx)("thead",{children:(0,n.jsxs)("tr",{children:[(0,n.jsx)("th",{children:o}),s.map(((e,t)=>(0,n.jsx)("th",{children:e},t)))]})}),(0,n.jsx)("tbody",{children:i.map(((e,t)=>(0,n.jsxs)("tr",{children:[(0,n.jsx)("td",{className:"index-value",children:r[t]}),e.map(((e,t)=>{return(0,n.jsx)("td",{children:(s=e,"boolean"==typeof s?s.toString().charAt(0).toUpperCase()+s.toString().slice(1):s)},t);var s}))]},t)))})]})})}},5158:(e,t,s)=>{s.d(t,{A:()=>o});var n=s(6540),i=s(4848);const o=function(e){let{src:t,sourceLink:s,aspectRatio:o=16/9}=e;const[r,a]=(0,n.useState)(0),[l,h]=(0,n.useState)(0),c=(0,n.useRef)(null);return(0,n.useEffect)((()=>{const e=()=>{if(c.current){const e=c.current.offsetWidth;h(e/o)}};return e(),window.addEventListener("resize",e),()=>window.removeEventListener("resize",e)}),[o]),(0,i.jsxs)(i.Fragment,{children:[(0,i.jsx)("div",{ref:c,style:{width:"100%",position:"relative",maxWidth:"100%",backgroundColor:"white"},children:(0,i.jsx)("iframe",{src:t,style:{width:"100%",height:`${l}px`,border:"0",allowFullScreen:!0}},r)}),(0,i.jsx)("div",{style:{display:"flex",justifyContent:"center",margin:"20px 0"},children:(0,i.jsx)("a",{href:s,target:"_blank",rel:"noopener noreferrer",children:"(Source)"})}),(0,i.jsx)("div",{style:{display:"flex",justifyContent:"center",margin:"10px 0"},children:(0,i.jsx)("button",{onClick:()=>{a((e=>e+1))},style:{backgroundColor:"#4CAF50",color:"white",padding:"10px 20px",border:"none",borderRadius:"5px",cursor:"pointer",outline:"none",fontSize:"16px",fontWeight:"bold",boxShadow:"0 4px 8px rgba(0,0,0,0.1)",transition:"background-color 0.3s"},onMouseOver:e=>e.currentTarget.style.backgroundColor="#45a049",onMouseOut:e=>e.currentTarget.style.backgroundColor="#4CAF50",children:"Restart Diagram"})})]})}},4183:(e,t,s)=>{s.d(t,{A:()=>n});const n=s.p+"assets/images/hypothesis-test-200177f66e9f7f0e360b809bc6c6f3c8.png"},789:(e,t,s)=>{s.d(t,{A:()=>n});const n=s.p+"assets/images/hypothesis-test2-7615aa5325b73c6c19541b78e2619a30.png"},8453:(e,t,s)=>{s.d(t,{R:()=>r,x:()=>a});var n=s(6540);const i={},o=n.createContext(i);function r(e){const t=n.useContext(o);return n.useMemo((function(){return"function"==typeof e?e(t):{...t,...e}}),[t,e])}function a(e){let t;return t=e.disableParentContext?"function"==typeof e.components?e.components(i):e.components||i:r(e.components),n.createElement(o.Provider,{value:t},e.children)}}}]); \ No newline at end of file diff --git a/assets/js/f095f4cd.32321c37.js b/assets/js/f095f4cd.32321c37.js deleted file mode 100644 index 3c7b8afc..00000000 --- a/assets/js/f095f4cd.32321c37.js +++ /dev/null @@ -1 +0,0 @@ -"use strict";(self.webpackChunkbpd_reference=self.webpackChunkbpd_reference||[]).push([[28],{8406:(e,A,t)=>{t.r(A),t.d(A,{assets:()=>d,contentTitle:()=>o,default:()=>h,frontMatter:()=>i,metadata:()=>l,toc:()=>c});var n=t(4848),a=t(8453),r=t(8597),s=t(5158);const i={sidebar_position:8,sidebar_label:"Boostrapping and Confidence Intervals",title:"Bootstrapping and Confidence Intervals",tags:["for-loop","histogram"]},o=void 0,l={id:"statistical-inference/bootstrapping",title:"Bootstrapping and Confidence Intervals",description:"Concept",source:"@site/docs/statistical-inference/bootstrapping.md",sourceDirName:"statistical-inference",slug:"/statistical-inference/bootstrapping",permalink:"/bpd-reference/docs/statistical-inference/bootstrapping",draft:!1,unlisted:!1,editUrl:"https://github.com/dsc-courses/bpd-reference/tree/main/docs/statistical-inference/bootstrapping.md",tags:[{label:"for-loop",permalink:"/bpd-reference/docs/tags/for-loop"},{label:"histogram",permalink:"/bpd-reference/docs/tags/histogram"}],version:"current",sidebarPosition:8,frontMatter:{sidebar_position:8,sidebar_label:"Boostrapping and Confidence Intervals",title:"Bootstrapping and Confidence Intervals",tags:["for-loop","histogram"]},sidebar:"statsSidebar",previous:{title:"Spread of a Distribution",permalink:"/bpd-reference/docs/statistical-inference/spread_of_a_distribution"},next:{title:"Permutation Test",permalink:"/bpd-reference/docs/statistical-inference/permutation_test"}},d={},c=[{value:"Concept",id:"concept",level:2},{value:"Code Example",id:"code-example",level:2},{value:"1. Take a random sample of size 12 from the <code>full_pets</code> DataFrame.",id:"1-take-a-random-sample-of-size-12-from-the-full_pets-dataframe",level:3},{value:"2. Find the observed parameter",id:"2-find-the-observed-parameter",level:3},{value:"3. Bootstrap the sample 10,000 times with replacement",id:"3-bootstrap-the-sample-10000-times-with-replacement",level:3},{value:"4. Create a 95% confidence interval",id:"4-create-a-95-confidence-interval",level:3},{value:"5. Conclusion",id:"5-conclusion",level:3},{value:"6. Extra",id:"6-extra",level:3}];function p(e){const A={a:"a",admonition:"admonition",code:"code",h2:"h2",h3:"h3",hr:"hr",img:"img",li:"li",ol:"ol",p:"p",pre:"pre",strong:"strong",ul:"ul",...(0,a.R)(),...e.components};return(0,n.jsxs)(n.Fragment,{children:[(0,n.jsx)(A.h2,{id:"concept",children:"Concept"}),"\n",(0,n.jsx)(A.admonition,{title:"Key Idea",type:"tip",children:(0,n.jsx)(A.p,{children:"We use a bootstrapping to estimate the distribution of the sample statistic to see how different our it could have been. We use confidence intervals to define a range that captures most of the bootstrapped distribution of the sample statistic."})}),"\n",(0,n.jsxs)(A.admonition,{title:"Terminology",type:"info",children:[(0,n.jsxs)(A.p,{children:[(0,n.jsx)(A.strong,{children:"Bootstrapping"}),": Bootstrapping is a type of hypothesis test that involves resampling from a single sample to estimate the\r\ndistribution of the sample statistic. It answers the question of how different the sample statistic could have been if given a different sample. To conduct bootstrapping:"]}),(0,n.jsxs)(A.ol,{children:["\n",(0,n.jsx)(A.li,{children:"Resample from the original sample with replacement."}),"\n",(0,n.jsx)(A.li,{children:"Calculate the sample statistic on the bootstrapped resample."}),"\n",(0,n.jsx)(A.li,{children:"Save the results into an array."}),"\n",(0,n.jsx)(A.li,{children:"Repeat steps 1 through 3 to generate an empirical distribution of the test statistic."}),"\n",(0,n.jsx)(A.li,{children:"Calculate the confidence interval and see if the observed statistic lies in it. If the observed statistic is not\r\nin our confidence interval, we have evidence to reject the null."}),"\n"]}),(0,n.jsxs)(A.p,{children:[(0,n.jsx)(A.strong,{children:"Confidence Intervals:"})," A confidence interval is a range that captures most of the distribution of the bootstrapped sample statistic in\r\nthe hopes of also containing the true population parameter within it. If\r\nwe were to construct a 95% confidence interval, we aren't saying that there is a 95% chance that the true population parameter lies in the\r\ninterval as the interval either contains it or it doesn't. Instead, we are saying that approximately 95% of the time, the intervals you\r\ncreate will contain the true population parameter. For example, if we generated 100 confidence intervals, about 95 of them will have the\r\ntrue population parameter."]})]}),"\n",(0,n.jsx)(A.admonition,{type:"note",children:(0,n.jsx)(A.p,{children:"When resampling, the size of the resample should be the same as the original sample with replacement."})}),"\n",(0,n.jsx)(A.p,{children:"The diagram below provides an overview of conducting bootstrapping, although it references a different dataset."}),"\n",(0,n.jsx)(s.A,{src:"https://docs.google.com/presentation/d/e/2PACX-1vS_iYHJYXSVMMZ-YQVFwMEFR6EFN3FDSAvaMyUm-YJfLQgRMTHm3vI-wWJJ5999eFJq70nWp2hyItZg/embed?start=true&loop=false&delayms=3000&rm=minimal",sourceLink:"https://docs.google.com/presentation/d/1oYakqMdI7z61BthvgWUJvbT21bKTXg01KmAibglepBI/edit?usp=sharing"}),"\n",(0,n.jsxs)(A.p,{children:["The diagram below provides an overview of creating confidence intervals, although it references a different situation. For additional helpful visual guides, please visit the ",(0,n.jsx)(A.a,{href:"https://dsc10.com/diagrams/",children:"Diagrams"})," site."]}),"\n",(0,n.jsx)(s.A,{src:"https://docs.google.com/presentation/d/e/2PACX-1vTaPZsueXI6fey_5cj2Y1TevkR1joBvpwaWVsZNvgBlnJSrw1EiBLHJywkFH_QNLU5Tdr6JZgDrhFxG/embed?start=true&loop=false&delayms=3000&rm=minimal",sourceLink:"https://docs.google.com/presentation/d/1l5GVyl60FrornEaZnGL6REV4gjEydRncNVi6k1hHUsA/edit?usp=sharing"}),"\n",(0,n.jsx)(A.hr,{}),"\n",(0,n.jsx)(A.h2,{id:"code-example",children:"Code Example"}),"\n",(0,n.jsxs)(A.h3,{id:"1-take-a-random-sample-of-size-12-from-the-full_pets-dataframe",children:["1. Take a random sample of size 12 from the ",(0,n.jsx)(A.code,{children:"full_pets"})," DataFrame."]}),"\n",(0,n.jsxs)(A.p,{children:["Let's say we didn't have access to all of the information in the ",(0,n.jsx)(A.code,{children:"full_pets"})," DataFrame and were only able to collect a sample of 12 pets."]}),"\n",(0,n.jsx)(A.pre,{children:(0,n.jsx)(A.code,{className:"language-python",children:"# Magic to ensure that we get the same results every time this code is run. \r\nnp.random.seed(42)\r\n\r\n# sample\r\npets_sample = full_pets.sample(12, replace=False)\r\npets_sample\n"})}),"\n",(0,n.jsx)(r.A,{data:'{"columns":["Unnamed: 0","ID","Species","Color","Weight","Age","Is_Cat","Owner_Comment"],"index":[18,14,4,13,10,7,6,3,2,15,17,8],"data":[[18,"cat_006","cat","black",3.0,0.5,true,"No, thank you!"],[14,"dog_007","dog","white",50.0,6.1,false,"No, thank you!"],[4,"dog_003","dog","black",25.0,0.5,false,"Be the person your dog thinks you are."],[13,"ham_003","hamster","black",0.5,0.1,false,"No, thank you!"],[10,"dog_006","dog","golden",35.0,4.0,false,"No, thank you!"],[7,"cat_003","cat","black",10.0,0.0,true,"No, thank you!"],[6,"ham_002","hamster","golden",0.25,0.2,false,"No, thank you!"],[3,"dog_002","dog","white",80.0,2.0,false,"Love is a wet nose and a wagging tail."],[2,"cat_002","cat","black",15.0,9.0,true,"****All you need is love and a cat.****"],[15,"ham_004","hamster","golden",0.25,0.2,false,"No, thank you!"],[17,"dog_009","dog","white",30.0,4.8,false,"No, thank you!"],[8,"dog_004","dog","black",45.0,6.7,false,"No, thank you!"]]}'}),"\n",(0,n.jsx)(A.hr,{}),"\n",(0,n.jsx)(A.h3,{id:"2-find-the-observed-parameter",children:"2. Find the observed parameter"}),"\n",(0,n.jsx)(A.p,{children:"In this case, we are interested in finding the median weight of the entire population."}),"\n",(0,n.jsx)(A.pre,{children:(0,n.jsx)(A.code,{className:"language-python",children:"pets_sample = full_pets.sample(12, replace=False)\r\nprint('Median of pets_sample weight:', pets_sample.get('Weight').median())\n"})}),"\n",(0,n.jsx)(A.p,{children:"Median of pets_sample weight: 20.0"}),"\n",(0,n.jsx)(A.hr,{}),"\n",(0,n.jsx)(A.h3,{id:"3-bootstrap-the-sample-10000-times-with-replacement",children:"3. Bootstrap the sample 10,000 times with replacement"}),"\n",(0,n.jsx)(A.p,{children:"Since we were only able to collect one random sample from the full population, we can't be sure if this singular guess predicts the\r\ntrue population parameter well. We can't go out and collect\r\nanother random sample, so we will resample from the original sample with replacement to simulate what could've been."}),"\n",(0,n.jsx)(A.pre,{children:(0,n.jsx)(A.code,{className:"language-python",children:"boot_medians = np.array([])\r\nfor i in np.arange(10000):\r\n # 1. resample the data\r\n resample = pets_sample.sample(pets_sample.shape[0], replace=True)\r\n\r\n # 2. calculate the median of the resample\r\n boot_median = resample.get('Weight').median()\r\n\r\n # 3. append the median to the array\r\n boot_medians = np.append(boot_medians, boot_median)\n"})}),"\n",(0,n.jsx)(A.p,{children:"This code will create 10,000 bootstrapped samples and calculate the median for each of them, but a different\r\nreasonable number can be used instead. Since these samples are all random, the information in each sample and\r\nmedian will be different from one another."}),"\n",(0,n.jsx)(A.hr,{}),"\n",(0,n.jsx)(A.h3,{id:"4-create-a-95-confidence-interval",children:"4. Create a 95% confidence interval"}),"\n",(0,n.jsx)(A.p,{children:"Instead of using a single number to estimate the true population parameter, we create a range of where we think it is."}),"\n",(0,n.jsx)(A.pre,{children:(0,n.jsx)(A.code,{className:"language-python",children:"# Get the 95% confidence interval\r\nleft = np.percentile(boot_medians, 2.5) # 2.5th percentile\r\nright = np.percentile(boot_medians, 97.5) # 97.5th percentile\n"})}),"\n",(0,n.jsx)(A.p,{children:"Remember that the 95% confidence interval does not mean we have a 95% chance of containing the true population parameter. It means\r\nthat about 95% of all intervals we create will contain the true population parameter."}),"\n",(0,n.jsx)(A.hr,{}),"\n",(0,n.jsx)(A.h3,{id:"5-conclusion",children:"5. Conclusion"}),"\n",(0,n.jsx)(A.pre,{children:(0,n.jsx)(A.code,{className:"language-python",children:"left, right\n"})}),"\n",(0,n.jsx)(A.p,{children:"(1.75, 40.0)"}),"\n",(0,n.jsx)(A.admonition,{title:"Conclusion",type:"info",children:(0,n.jsxs)(A.ul,{children:["\n",(0,n.jsx)(A.li,{children:"From this interval, we are 95% confident that the true population median lies somewhere between 1.75 and 40."}),"\n",(0,n.jsx)(A.li,{children:"We have no way of knowing where exactly in this interval does the true population median falls or even if it is contained at all."}),"\n",(0,n.jsx)(A.li,{children:"What we do know is that if we were to repeat the process and generate multiple confidence intervals, roughly 95% of them will\r\ncontain the true population median."}),"\n"]})}),"\n",(0,n.jsx)(A.hr,{}),"\n",(0,n.jsx)(A.h3,{id:"6-extra",children:"6. Extra"}),"\n",(0,n.jsx)(A.p,{children:"Let's look at the distribution of the bootstrapped medians!"}),"\n",(0,n.jsx)(A.pre,{children:(0,n.jsx)(A.code,{className:"language-python",children:"# Create the histogram.\r\n# Plot the histogram of boot_medians\r\nplt.hist(boot_medians, bins=20, density=True, ec = 'w')\r\n\r\nplt.show()\n"})}),"\n",(0,n.jsx)(A.p,{children:(0,n.jsx)(A.img,{alt:"Distribution",src:t(2922).A+"",width:"556",height:"413"})}),"\n",(0,n.jsxs)(A.p,{children:["A 95% confidence level means that ",(0,n.jsx)(A.strong,{children:"approximately 95% of the time, the intervals you create through this process will contain the true population parameter"}),"."]})]})}function h(e={}){const{wrapper:A}={...(0,a.R)(),...e.components};return A?(0,n.jsx)(A,{...e,children:(0,n.jsx)(p,{...e})}):p(e)}},8597:(e,A,t)=>{t.d(A,{A:()=>a});t(6540);var n=t(4848);const a=e=>{let{data:A}=e,t=[],a=[],r="",s=[];if(A){const 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0,l={id:"statistical-inference/bootstrapping",title:"Bootstrapping and Confidence Intervals",description:"Concept",source:"@site/docs/statistical-inference/bootstrapping.md",sourceDirName:"statistical-inference",slug:"/statistical-inference/bootstrapping",permalink:"/bpd-reference/docs/statistical-inference/bootstrapping",draft:!1,unlisted:!1,editUrl:"https://github.com/dsc-courses/bpd-reference/tree/main/docs/statistical-inference/bootstrapping.md",tags:[{label:"for-loop",permalink:"/bpd-reference/docs/tags/for-loop"},{label:"histogram",permalink:"/bpd-reference/docs/tags/histogram"}],version:"current",sidebarPosition:8,frontMatter:{sidebar_position:8,sidebar_label:"Boostrapping and Confidence Intervals",title:"Bootstrapping and Confidence Intervals",tags:["for-loop","histogram"]},sidebar:"statsSidebar",previous:{title:"Spread of a Distribution",permalink:"/bpd-reference/docs/statistical-inference/spread_of_a_distribution"},next:{title:"Permutation Test",permalink:"/bpd-reference/docs/statistical-inference/permutation_test"}},d={},c=[{value:"Concept",id:"concept",level:2},{value:"Code Example",id:"code-example",level:2},{value:"1. Take a random sample of size 12 from the <code>full_pets</code> DataFrame.",id:"1-take-a-random-sample-of-size-12-from-the-full_pets-dataframe",level:3},{value:"2. Find the observed parameter",id:"2-find-the-observed-parameter",level:3},{value:"3. Bootstrap the sample 10,000 times with replacement",id:"3-bootstrap-the-sample-10000-times-with-replacement",level:3},{value:"4. Create a 95% confidence interval",id:"4-create-a-95-confidence-interval",level:3},{value:"5. Conclusion",id:"5-conclusion",level:3},{value:"6. Extra",id:"6-extra",level:3}];function p(e){const A={a:"a",admonition:"admonition",code:"code",h2:"h2",h3:"h3",hr:"hr",img:"img",li:"li",ol:"ol",p:"p",pre:"pre",strong:"strong",ul:"ul",...(0,a.R)(),...e.components};return(0,n.jsxs)(n.Fragment,{children:[(0,n.jsx)(A.h2,{id:"concept",children:"Concept"}),"\n",(0,n.jsx)(A.admonition,{title:"Key Idea",type:"tip",children:(0,n.jsx)(A.p,{children:"We use a bootstrapping to estimate the distribution of the sample statistic to see how different our it could have been. We use confidence intervals to define a range that captures most of the bootstrapped distribution of the sample statistic."})}),"\n",(0,n.jsxs)(A.admonition,{title:"Terminology",type:"info",children:[(0,n.jsxs)(A.p,{children:[(0,n.jsx)(A.strong,{children:"Bootstrapping"}),": Bootstrapping is a type of hypothesis test that involves resampling from a single sample to estimate the\ndistribution of the sample statistic. It answers the question of how different the sample statistic could have been if given a different sample. To conduct bootstrapping:"]}),(0,n.jsxs)(A.ol,{children:["\n",(0,n.jsx)(A.li,{children:"Resample from the original sample with replacement."}),"\n",(0,n.jsx)(A.li,{children:"Calculate the sample statistic on the bootstrapped resample."}),"\n",(0,n.jsx)(A.li,{children:"Save the results into an array."}),"\n",(0,n.jsx)(A.li,{children:"Repeat steps 1 through 3 to generate an empirical distribution of the test statistic."}),"\n",(0,n.jsx)(A.li,{children:"Calculate the confidence interval and see if the observed statistic lies in it. If the observed statistic is not\nin our confidence interval, we have evidence to reject the null."}),"\n"]}),(0,n.jsxs)(A.p,{children:[(0,n.jsx)(A.strong,{children:"Confidence Intervals:"})," A confidence interval is a range that captures most of the distribution of the bootstrapped sample statistic in\nthe hopes of also containing the true population parameter within it. If\nwe were to construct a 95% confidence interval, we aren't saying that there is a 95% chance that the true population parameter lies in the\ninterval as the interval either contains it or it doesn't. Instead, we are saying that approximately 95% of the time, the intervals you\ncreate will contain the true population parameter. For example, if we generated 100 confidence intervals, about 95 of them will have the\ntrue population parameter."]})]}),"\n",(0,n.jsx)(A.admonition,{type:"note",children:(0,n.jsx)(A.p,{children:"When resampling, the size of the resample should be the same as the original sample with replacement."})}),"\n",(0,n.jsx)(A.p,{children:"The diagram below provides an overview of conducting bootstrapping, although it references a different dataset."}),"\n",(0,n.jsx)(r.A,{src:"https://docs.google.com/presentation/d/e/2PACX-1vS_iYHJYXSVMMZ-YQVFwMEFR6EFN3FDSAvaMyUm-YJfLQgRMTHm3vI-wWJJ5999eFJq70nWp2hyItZg/embed?start=true&loop=false&delayms=3000&rm=minimal",sourceLink:"https://docs.google.com/presentation/d/1oYakqMdI7z61BthvgWUJvbT21bKTXg01KmAibglepBI/edit?usp=sharing"}),"\n",(0,n.jsxs)(A.p,{children:["The diagram below provides an overview of creating confidence intervals, although it references a different situation. For additional helpful visual guides, please visit the ",(0,n.jsx)(A.a,{href:"https://dsc10.com/diagrams/",children:"Diagrams"})," site."]}),"\n",(0,n.jsx)(r.A,{src:"https://docs.google.com/presentation/d/e/2PACX-1vTaPZsueXI6fey_5cj2Y1TevkR1joBvpwaWVsZNvgBlnJSrw1EiBLHJywkFH_QNLU5Tdr6JZgDrhFxG/embed?start=true&loop=false&delayms=3000&rm=minimal",sourceLink:"https://docs.google.com/presentation/d/1l5GVyl60FrornEaZnGL6REV4gjEydRncNVi6k1hHUsA/edit?usp=sharing"}),"\n",(0,n.jsx)(A.hr,{}),"\n",(0,n.jsx)(A.h2,{id:"code-example",children:"Code Example"}),"\n",(0,n.jsxs)(A.h3,{id:"1-take-a-random-sample-of-size-12-from-the-full_pets-dataframe",children:["1. Take a random sample of size 12 from the ",(0,n.jsx)(A.code,{children:"full_pets"})," DataFrame."]}),"\n",(0,n.jsxs)(A.p,{children:["Let's say we didn't have access to all of the information in the ",(0,n.jsx)(A.code,{children:"full_pets"})," DataFrame and were only able to collect a sample of 12 pets."]}),"\n",(0,n.jsx)(A.pre,{children:(0,n.jsx)(A.code,{className:"language-python",children:"# Magic to ensure that we get the same results every time this code is run. \nnp.random.seed(42)\n\n# sample\npets_sample = full_pets.sample(12, replace=False)\npets_sample\n"})}),"\n",(0,n.jsx)(s.A,{data:'{"columns":["Unnamed: 0","ID","Species","Color","Weight","Age","Is_Cat","Owner_Comment"],"index":[18,14,4,13,10,7,6,3,2,15,17,8],"data":[[18,"cat_006","cat","black",3.0,0.5,true,"No, thank you!"],[14,"dog_007","dog","white",50.0,6.1,false,"No, thank you!"],[4,"dog_003","dog","black",25.0,0.5,false,"Be the person your dog thinks you are."],[13,"ham_003","hamster","black",0.5,0.1,false,"No, thank you!"],[10,"dog_006","dog","golden",35.0,4.0,false,"No, thank you!"],[7,"cat_003","cat","black",10.0,0.0,true,"No, thank you!"],[6,"ham_002","hamster","golden",0.25,0.2,false,"No, thank you!"],[3,"dog_002","dog","white",80.0,2.0,false,"Love is a wet nose and a wagging tail."],[2,"cat_002","cat","black",15.0,9.0,true,"****All you need is love and a cat.****"],[15,"ham_004","hamster","golden",0.25,0.2,false,"No, thank you!"],[17,"dog_009","dog","white",30.0,4.8,false,"No, thank you!"],[8,"dog_004","dog","black",45.0,6.7,false,"No, thank you!"]]}'}),"\n",(0,n.jsx)(A.hr,{}),"\n",(0,n.jsx)(A.h3,{id:"2-find-the-observed-parameter",children:"2. Find the observed parameter"}),"\n",(0,n.jsx)(A.p,{children:"In this case, we are interested in finding the median weight of the entire population."}),"\n",(0,n.jsx)(A.pre,{children:(0,n.jsx)(A.code,{className:"language-python",children:"pets_sample = full_pets.sample(12, replace=False)\nprint('Median of pets_sample weight:', pets_sample.get('Weight').median())\n"})}),"\n",(0,n.jsx)(A.p,{children:"Median of pets_sample weight: 20.0"}),"\n",(0,n.jsx)(A.hr,{}),"\n",(0,n.jsx)(A.h3,{id:"3-bootstrap-the-sample-10000-times-with-replacement",children:"3. Bootstrap the sample 10,000 times with replacement"}),"\n",(0,n.jsx)(A.p,{children:"Since we were only able to collect one random sample from the full population, we can't be sure if this singular guess predicts the\ntrue population parameter well. We can't go out and collect\nanother random sample, so we will resample from the original sample with replacement to simulate what could've been."}),"\n",(0,n.jsx)(A.pre,{children:(0,n.jsx)(A.code,{className:"language-python",children:"boot_medians = np.array([])\nfor i in np.arange(10000):\n # 1. resample the data\n resample = pets_sample.sample(pets_sample.shape[0], replace=True)\n\n # 2. calculate the median of the resample\n boot_median = resample.get('Weight').median()\n\n # 3. append the median to the array\n boot_medians = np.append(boot_medians, boot_median)\n"})}),"\n",(0,n.jsx)(A.p,{children:"This code will create 10,000 bootstrapped samples and calculate the median for each of them, but a different\nreasonable number can be used instead. Since these samples are all random, the information in each sample and\nmedian will be different from one another."}),"\n",(0,n.jsx)(A.hr,{}),"\n",(0,n.jsx)(A.h3,{id:"4-create-a-95-confidence-interval",children:"4. Create a 95% confidence interval"}),"\n",(0,n.jsx)(A.p,{children:"Instead of using a single number to estimate the true population parameter, we create a range of where we think it is."}),"\n",(0,n.jsx)(A.pre,{children:(0,n.jsx)(A.code,{className:"language-python",children:"# Get the 95% confidence interval\nleft = np.percentile(boot_medians, 2.5) # 2.5th percentile\nright = np.percentile(boot_medians, 97.5) # 97.5th percentile\n"})}),"\n",(0,n.jsx)(A.p,{children:"Remember that the 95% confidence interval does not mean we have a 95% chance of containing the true population parameter. It means\nthat about 95% of all intervals we create will contain the true population parameter."}),"\n",(0,n.jsx)(A.hr,{}),"\n",(0,n.jsx)(A.h3,{id:"5-conclusion",children:"5. Conclusion"}),"\n",(0,n.jsx)(A.pre,{children:(0,n.jsx)(A.code,{className:"language-python",children:"left, right\n"})}),"\n",(0,n.jsx)(A.p,{children:"(1.75, 40.0)"}),"\n",(0,n.jsx)(A.admonition,{title:"Conclusion",type:"info",children:(0,n.jsxs)(A.ul,{children:["\n",(0,n.jsx)(A.li,{children:"From this interval, we are 95% confident that the true population median lies somewhere between 1.75 and 40."}),"\n",(0,n.jsx)(A.li,{children:"We have no way of knowing where exactly in this interval does the true population median falls or even if it is contained at all."}),"\n",(0,n.jsx)(A.li,{children:"What we do know is that if we were to repeat the process and generate multiple confidence intervals, roughly 95% of them will\ncontain the true population median."}),"\n"]})}),"\n",(0,n.jsx)(A.hr,{}),"\n",(0,n.jsx)(A.h3,{id:"6-extra",children:"6. Extra"}),"\n",(0,n.jsx)(A.p,{children:"Let's look at the distribution of the bootstrapped medians!"}),"\n",(0,n.jsx)(A.pre,{children:(0,n.jsx)(A.code,{className:"language-python",children:"# Create the histogram.\n# Plot the histogram of boot_medians\nplt.hist(boot_medians, bins=20, density=True, ec = 'w')\n\nplt.show()\n"})}),"\n",(0,n.jsx)(A.p,{children:(0,n.jsx)(A.img,{alt:"Distribution",src:t(3698).A+"",width:"556",height:"413"})}),"\n",(0,n.jsxs)(A.p,{children:["A 95% confidence level means that ",(0,n.jsx)(A.strong,{children:"approximately 95% of the time, the intervals you create through this process will contain the true population parameter"}),"."]})]})}function h(e={}){const{wrapper:A}={...(0,a.R)(),...e.components};return A?(0,n.jsx)(A,{...e,children:(0,n.jsx)(p,{...e})}):p(e)}},8597:(e,A,t)=>{t.d(A,{A:()=>a});t(6540);var n=t(4848);const a=e=>{let{data:A}=e,t=[],a=[],s="",r=[];if(A){const 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deviation: \nweights = full_pets.get('Weight')\nstandard_deviation = np.std(weights, ddof=0)\n\n# how to implement the standard deviation formula\nmean = weights.mean()\nnumerator = 0\nfor value in weights.values:\n numerator += (value - mean) ** 2\nvariance = numerator / (full_pets.shape[0])\nstandard_deviation2 = variance ** 0.5 \nstandard_deviation2\n"})}),"\n",(0,n.jsx)(e.h3,{id:"chebyshevs-inequality",children:"Chebyshev\u2019s Inequality"}),"\n",(0,n.jsxs)(e.table,{children:[(0,n.jsx)(e.thead,{children:(0,n.jsxs)(e.tr,{children:[(0,n.jsx)(e.th,{children:"Range"}),(0,n.jsx)(e.th,{children:"All Distributions"}),(0,n.jsx)(e.th,{children:"Normal Distribution"})]})}),(0,n.jsxs)(e.tbody,{children:[(0,n.jsxs)(e.tr,{children:[(0,n.jsx)(e.td,{children:"mean \xb1 1 SD"}),(0,n.jsx)(e.td,{children:"at least 0%"}),(0,n.jsx)(e.td,{children:"about 68%"})]}),(0,n.jsxs)(e.tr,{children:[(0,n.jsx)(e.td,{children:"mean \xb1 2 SD"}),(0,n.jsx)(e.td,{children:"at least 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These estimates are higher than the lower bounds provided by Chebyshev's Inequality because they take advantage of the normal distribution's properties."}),"\n"]})}),"\n",(0,n.jsx)(e.h4,{id:"chebyshevs-inequality-visualized-on-a-normal-distribution",children:"Chebyshev\u2019s Inequality visualized on a normal distribution"}),"\n",(0,n.jsx)(e.p,{children:(0,n.jsx)(e.img,{alt:"Curve",src:a(3537).A+"",width:"618",height:"391"})}),"\n",(0,n.jsxs)(e.admonition,{type:"note",children:[(0,n.jsx)(e.p,{children:"The graph above illustrates the distribution of weights sampled from a normal distribution with a mean of 70 and a standard deviation of 10. 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256&t.flags?(t.flags&=-257,Bs(e,t,s,r=ds(Error(a(422))))):null!==t.memoizedState?(t.child=e.child,t.flags|=128,null):(i=r.fallback,o=t.mode,r=Ic({mode:"visible",children:r.children},o,0,null),(i=Mc(i,o,s,null)).flags|=2,r.return=t,i.return=t,r.sibling=i,t.child=r,1&t.mode&&Za(t,e.child,null,s),t.child.memoizedState=Is(s),t.memoizedState=Ms,i);if(!(1&t.mode))return Bs(e,t,s,null);if("$!"===o.data){if(r=o.nextSibling&&o.nextSibling.dataset)var l=r.dgst;return r=l,Bs(e,t,s,r=ds(i=Error(a(419)),r,void 0))}if(l=!!(s&e.childLanes),ws||l){if(null!==(r=jl)){switch(s&-s){case 4:o=2;break;case 16:o=8;break;case 64:case 128:case 256:case 512:case 1024:case 2048:case 4096:case 8192:case 16384:case 32768:case 65536:case 131072:case 262144:case 524288:case 1048576:case 2097152:case 4194304:case 8388608:case 16777216:case 33554432:case 67108864:o=32;break;case 536870912:o=268435456;break;default:o=0}0!==(o=o&(r.suspendedLanes|s)?0:o)&&o!==i.retryLane&&(i.retryLane=o,ja(e,o),rc(r,e,o,-1))}return 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b/blog/archive/index.html @@ -6,13 +6,17 @@ <title data-rh="true">Archive | bpd + + + + - - + +

Archive

Archive

2021​

2019​

diff --git a/blog/first-blog-post/index.html b/blog/first-blog-post/index.html index 2719d83b..21dfaac4 100644 --- a/blog/first-blog-post/index.html +++ b/blog/first-blog-post/index.html @@ -6,13 +6,17 @@ First Blog Post | bpd + + + + - - + +

First Blog Post

· One min read
Gao Wei
Gao Wei
Docusaurus Core Team

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Pellentesque elementum dignissim ultricies. Fusce rhoncus ipsum tempor eros aliquam consequat. Lorem ipsum dolor sit amet

diff --git a/blog/index.html b/blog/index.html index a61a96f6..95bc6024 100644 --- a/blog/index.html +++ b/blog/index.html @@ -6,13 +6,17 @@ Blog | bpd + + + + - - + +

Welcome

· One min read
Sébastien Lorber
Sébastien Lorber
Docusaurus maintainer
Yangshun Tay
Yangshun Tay
Front End Engineer @ Facebook

Docusaurus blogging features are powered by the blog plugin.

diff --git a/blog/long-blog-post/index.html b/blog/long-blog-post/index.html index 8c6b7dc0..1c639e9b 100644 --- a/blog/long-blog-post/index.html +++ b/blog/long-blog-post/index.html @@ -6,13 +6,17 @@ Long Blog Post | bpd + + + + - - + +

Long Blog Post

· 3 min read
Endilie Yacop Sucipto
Endilie Yacop Sucipto
Maintainer of Docusaurus

This is the summary of a very long blog post,

diff --git a/blog/mdx-blog-post/index.html b/blog/mdx-blog-post/index.html index f7ccac12..099e7d07 100644 --- a/blog/mdx-blog-post/index.html +++ b/blog/mdx-blog-post/index.html @@ -6,13 +6,17 @@ MDX Blog Post | bpd + + + + - - + +

MDX Blog Post

· One min read
Sébastien Lorber
Sébastien Lorber
Docusaurus maintainer

Blog posts support Docusaurus Markdown features, such as MDX.

diff --git a/blog/tags/docusaurus/index.html b/blog/tags/docusaurus/index.html index 95f18fd7..2940cecb 100644 --- a/blog/tags/docusaurus/index.html +++ b/blog/tags/docusaurus/index.html @@ -6,13 +6,17 @@ 4 posts tagged with "docusaurus" | bpd + + + + - - + +

4 posts tagged with "docusaurus"

View All Tags

Welcome

· One min read
Sébastien Lorber
Sébastien Lorber
Docusaurus maintainer
Yangshun Tay
Yangshun Tay
Front End Engineer @ Facebook

Docusaurus blogging features are powered by the blog plugin.

diff --git a/blog/tags/facebook/index.html b/blog/tags/facebook/index.html index 498f37d1..e06ab379 100644 --- a/blog/tags/facebook/index.html +++ b/blog/tags/facebook/index.html @@ -6,13 +6,17 @@ One post tagged with "facebook" | bpd + + + + - - + +

One post tagged with "facebook"

View All Tags

Welcome

· One min read
Sébastien Lorber
Sébastien Lorber
Docusaurus maintainer
Yangshun Tay
Yangshun Tay
Front End Engineer @ Facebook

Docusaurus blogging features are powered by the blog plugin.

diff --git a/blog/tags/hello/index.html b/blog/tags/hello/index.html index d7c00668..b6f434df 100644 --- a/blog/tags/hello/index.html +++ b/blog/tags/hello/index.html @@ -6,13 +6,17 @@ 2 posts tagged with "hello" | bpd + + + + - - + +

2 posts tagged with "hello"

View All Tags

Welcome

· One min read
Sébastien Lorber
Sébastien Lorber
Docusaurus maintainer
Yangshun Tay
Yangshun Tay
Front End Engineer @ Facebook

Docusaurus blogging features are powered by the blog plugin.

diff --git a/blog/tags/hola/index.html b/blog/tags/hola/index.html index cbacd771..bd20a6c1 100644 --- a/blog/tags/hola/index.html +++ b/blog/tags/hola/index.html @@ -6,13 +6,17 @@ One post tagged with "hola" | bpd + + + + - - + +

One post tagged with "hola"

View All Tags

First Blog Post

· One min read
Gao Wei
Gao Wei
Docusaurus Core Team

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Pellentesque elementum dignissim ultricies. Fusce rhoncus ipsum tempor eros aliquam consequat. Lorem ipsum dolor sit amet

diff --git a/blog/tags/index.html b/blog/tags/index.html index 89b5ad99..60e03ad5 100644 --- a/blog/tags/index.html +++ b/blog/tags/index.html @@ -6,13 +6,17 @@ Tags | bpd + + + + - - + +

Tags

diff --git a/blog/welcome/index.html b/blog/welcome/index.html index b40a99e2..7babb37a 100644 --- a/blog/welcome/index.html +++ b/blog/welcome/index.html @@ -6,13 +6,17 @@ Welcome | bpd + + + + - - + +

Welcome

· One min read
Sébastien Lorber
Sébastien Lorber
Docusaurus maintainer
Yangshun Tay
Yangshun Tay
Front End Engineer @ Facebook

Docusaurus blogging features are powered by the blog plugin.

diff --git a/docs/category/if-statements/index.html b/docs/category/if-statements/index.html index e7b79e34..2112f632 100644 --- a/docs/category/if-statements/index.html +++ b/docs/category/if-statements/index.html @@ -6,13 +6,17 @@ if-statements | bpd + + + + - - + +

if-statements

Conditionals

diff --git a/docs/category/querying/index.html b/docs/category/querying/index.html index 4d77aa1a..da28625a 100644 --- a/docs/category/querying/index.html +++ b/docs/category/querying/index.html @@ -6,13 +6,17 @@ Querying | bpd + + + + - - + +

Querying

Create a new dataframe containing only rows satisfying a condition

diff --git a/docs/documentation/Functions/Applying Functions/index.html b/docs/documentation/Functions/Applying Functions/index.html index e7b1f49b..ef79dcc5 100644 --- a/docs/documentation/Functions/Applying Functions/index.html +++ b/docs/documentation/Functions/Applying Functions/index.html @@ -6,13 +6,17 @@ Applying Functions | bpd + + + + - - + +

Applying Functions

df.get(column_name).apply(function_name) diff --git a/docs/documentation/Functions/Writing Functions/index.html b/docs/documentation/Functions/Writing Functions/index.html index 1b0f1fe0..3ef919d8 100644 --- a/docs/documentation/Functions/Writing Functions/index.html +++ b/docs/documentation/Functions/Writing Functions/index.html @@ -6,13 +6,17 @@ Writing Functions | bpd + + + + - - + +

Writing Functions

def function_name(parameters): diff --git a/docs/documentation/Grouping/aggregation/count()/index.html b/docs/documentation/Grouping/aggregation/count()/index.html index ca4129fe..c373a8e1 100644 --- a/docs/documentation/Grouping/aggregation/count()/index.html +++ b/docs/documentation/Grouping/aggregation/count()/index.html @@ -6,13 +6,17 @@ count() | bpd + + + + - - + +

count()

df.groupby(column_name).count() diff --git a/docs/documentation/Grouping/aggregation/max()/index.html b/docs/documentation/Grouping/aggregation/max()/index.html index 1f40adb2..2794d137 100644 --- a/docs/documentation/Grouping/aggregation/max()/index.html +++ b/docs/documentation/Grouping/aggregation/max()/index.html @@ -6,13 +6,17 @@ max() | bpd + + + + - - + +

max()

df.groupby(column_name).max() diff --git a/docs/documentation/Grouping/aggregation/mean()/index.html b/docs/documentation/Grouping/aggregation/mean()/index.html index 7679ce72..9488b0bb 100644 --- a/docs/documentation/Grouping/aggregation/mean()/index.html +++ b/docs/documentation/Grouping/aggregation/mean()/index.html @@ -6,13 +6,17 @@ mean() | bpd + + + + - - + +

mean()

df.groupby(column_name).mean() diff --git a/docs/documentation/Grouping/aggregation/median()/index.html b/docs/documentation/Grouping/aggregation/median()/index.html index d669fed9..724bb807 100644 --- a/docs/documentation/Grouping/aggregation/median()/index.html +++ b/docs/documentation/Grouping/aggregation/median()/index.html @@ -6,13 +6,17 @@ median() | bpd + + + + - - + +

median()

df.groupby(column_name).median() diff --git a/docs/documentation/Grouping/aggregation/min()/index.html b/docs/documentation/Grouping/aggregation/min()/index.html index d783c615..ed981dbe 100644 --- a/docs/documentation/Grouping/aggregation/min()/index.html +++ b/docs/documentation/Grouping/aggregation/min()/index.html @@ -6,13 +6,17 @@ min() | bpd + + + + - - + +

min()

df.groupby(column_name).min() diff --git a/docs/documentation/Grouping/aggregation/sum()/index.html b/docs/documentation/Grouping/aggregation/sum()/index.html index 1563ba2f..af96a9bd 100644 --- a/docs/documentation/Grouping/aggregation/sum()/index.html +++ b/docs/documentation/Grouping/aggregation/sum()/index.html @@ -6,13 +6,17 @@ sum() | bpd + + + + - - + +

sum()

df.groupby(column_name).sum() diff --git a/docs/documentation/Grouping/groupby/index.html b/docs/documentation/Grouping/groupby/index.html index 4ff88e40..ef4aa529 100644 --- a/docs/documentation/Grouping/groupby/index.html +++ b/docs/documentation/Grouping/groupby/index.html @@ -6,13 +6,17 @@ groupby | bpd + + + + - - + +

groupby

df.groupby(column_name) diff --git a/docs/documentation/accessing-data/df.columns/index.html b/docs/documentation/accessing-data/df.columns/index.html index b0cea5ea..d5631625 100644 --- a/docs/documentation/accessing-data/df.columns/index.html +++ b/docs/documentation/accessing-data/df.columns/index.html @@ -6,13 +6,17 @@ df.columns | bpd + + + + - - + +

df.columns

df.columns diff --git a/docs/documentation/accessing-data/df.get()/index.html b/docs/documentation/accessing-data/df.get()/index.html index d2f9e39f..18e610b3 100644 --- a/docs/documentation/accessing-data/df.get()/index.html +++ b/docs/documentation/accessing-data/df.get()/index.html @@ -6,13 +6,17 @@ df.get() | bpd + + + + - - + +

df.get()

df.get(column_name) diff --git a/docs/documentation/accessing-data/df.index/index.html b/docs/documentation/accessing-data/df.index/index.html index 3a4ae766..766a3b1b 100644 --- a/docs/documentation/accessing-data/df.index/index.html +++ b/docs/documentation/accessing-data/df.index/index.html @@ -6,13 +6,17 @@ df.index | bpd + + + + - - + +

df.index

df.index diff --git a/docs/documentation/accessing-data/df.shape/index.html b/docs/documentation/accessing-data/df.shape/index.html index bef99ec4..0e34a5a0 100644 --- a/docs/documentation/accessing-data/df.shape/index.html +++ b/docs/documentation/accessing-data/df.shape/index.html @@ -6,13 +6,17 @@ df.shape | bpd + + + + - - + +

df.shape

df.shape diff --git a/docs/documentation/accessing-data/df.take()/index.html b/docs/documentation/accessing-data/df.take()/index.html index dccd8f83..f9c06b39 100644 --- a/docs/documentation/accessing-data/df.take()/index.html +++ b/docs/documentation/accessing-data/df.take()/index.html @@ -6,13 +6,17 @@ df.take() | bpd + + + + - - + +

df.take()

df.take(indices) diff --git a/docs/documentation/accessing-data/index.html b/docs/documentation/accessing-data/index.html index 55e27cd7..8223d99f 100644 --- a/docs/documentation/accessing-data/index.html +++ b/docs/documentation/accessing-data/index.html @@ -6,13 +6,17 @@ Accessing Data | bpd + + + + - - + +

Accessing Data

diff --git a/docs/documentation/accessing-data/ser.iloc[]/index.html b/docs/documentation/accessing-data/ser.iloc[]/index.html index 312cadba..c2790d6b 100644 --- a/docs/documentation/accessing-data/ser.iloc[]/index.html +++ b/docs/documentation/accessing-data/ser.iloc[]/index.html @@ -6,13 +6,17 @@ ser.iloc[] | bpd + + + + - - + +

ser.iloc[]

ser.iloc[position] diff --git a/docs/documentation/accessing-data/ser.loc[]/index.html b/docs/documentation/accessing-data/ser.loc[]/index.html index b08d9f06..4fcd2b00 100644 --- a/docs/documentation/accessing-data/ser.loc[]/index.html +++ b/docs/documentation/accessing-data/ser.loc[]/index.html @@ -6,13 +6,17 @@ ser.loc[] | bpd + + + + - - + +

ser.loc[]

ser.loc[label] diff --git a/docs/documentation/arrays-and-numpy/arr[]/index.html b/docs/documentation/arrays-and-numpy/arr[]/index.html index f6812914..22a31958 100644 --- a/docs/documentation/arrays-and-numpy/arr[]/index.html +++ b/docs/documentation/arrays-and-numpy/arr[]/index.html @@ -6,13 +6,17 @@ arr[] | bpd + + + + - - + +

arr[]

arr[index] diff --git a/docs/documentation/arrays-and-numpy/index.html b/docs/documentation/arrays-and-numpy/index.html index 88dd8e05..9f8fe16d 100644 --- a/docs/documentation/arrays-and-numpy/index.html +++ b/docs/documentation/arrays-and-numpy/index.html @@ -6,13 +6,17 @@ Arrays and NumPy | bpd + + + + - - + +

Arrays and NumPy

Functions/methods for working with Arrays and NumPy.

diff --git a/docs/documentation/arrays-and-numpy/np.append()/index.html b/docs/documentation/arrays-and-numpy/np.append()/index.html index e6f1e19c..90668fe5 100644 --- a/docs/documentation/arrays-and-numpy/np.append()/index.html +++ b/docs/documentation/arrays-and-numpy/np.append()/index.html @@ -6,13 +6,17 @@ np.append() | bpd + + + + - - + +

np.append()

np.append(arr, value) diff --git a/docs/documentation/arrays-and-numpy/np.arange()/index.html b/docs/documentation/arrays-and-numpy/np.arange()/index.html index 2c1e0003..bcd8d0be 100644 --- a/docs/documentation/arrays-and-numpy/np.arange()/index.html +++ b/docs/documentation/arrays-and-numpy/np.arange()/index.html @@ -6,13 +6,17 @@ np.arange() | bpd + + + + - - + +

np.arange()

np.arange(start, stop, step) diff --git a/docs/documentation/arrays-and-numpy/np.count_nonzero()/index.html b/docs/documentation/arrays-and-numpy/np.count_nonzero()/index.html index 45ab9743..c8fe6251 100644 --- a/docs/documentation/arrays-and-numpy/np.count_nonzero()/index.html +++ b/docs/documentation/arrays-and-numpy/np.count_nonzero()/index.html @@ -6,13 +6,17 @@ np.count_nonzero() | bpd + + + + - - + +

np.count_nonzero()

np.count_nonzero(arr) diff --git a/docs/documentation/arrays-and-numpy/np.percentile()/index.html b/docs/documentation/arrays-and-numpy/np.percentile()/index.html index eeec59d5..2b20ff64 100644 --- a/docs/documentation/arrays-and-numpy/np.percentile()/index.html +++ b/docs/documentation/arrays-and-numpy/np.percentile()/index.html @@ -6,13 +6,17 @@ np.percentile() | bpd + + + + - - + +

np.percentile()

np.percentile(arr, p) diff --git a/docs/documentation/arrays-and-numpy/np.round()/index.html b/docs/documentation/arrays-and-numpy/np.round()/index.html index 3a232303..4624dd56 100644 --- a/docs/documentation/arrays-and-numpy/np.round()/index.html +++ b/docs/documentation/arrays-and-numpy/np.round()/index.html @@ -6,13 +6,17 @@ np.round() | bpd + + + + - - + +

np.round()

np.round(arr, decimals) diff --git a/docs/documentation/building-organizing/bpd.DataFrame()/index.html b/docs/documentation/building-organizing/bpd.DataFrame()/index.html index 8fe713d3..df0c20ac 100644 --- a/docs/documentation/building-organizing/bpd.DataFrame()/index.html +++ b/docs/documentation/building-organizing/bpd.DataFrame()/index.html @@ -6,13 +6,17 @@ bpd.DataFrame() | bpd + + + + - - + +

bpd.DataFrame()

bpd.DataFrame() diff --git a/docs/documentation/building-organizing/bpd.read_csv()/index.html b/docs/documentation/building-organizing/bpd.read_csv()/index.html index 3817a8d2..aa2ca86a 100644 --- a/docs/documentation/building-organizing/bpd.read_csv()/index.html +++ b/docs/documentation/building-organizing/bpd.read_csv()/index.html @@ -6,13 +6,17 @@ bpd.read_csv() | bpd + + + + - - + +

bpd.read_csv()

bpd.read_csv(filepath) diff --git a/docs/documentation/building-organizing/df.assign()/index.html b/docs/documentation/building-organizing/df.assign()/index.html index 65022b4e..49307e24 100644 --- a/docs/documentation/building-organizing/df.assign()/index.html +++ b/docs/documentation/building-organizing/df.assign()/index.html @@ -6,13 +6,17 @@ df.assign() | bpd + + + + - - + +

df.assign()

df.assign(name_of_column=column_data) diff --git a/docs/documentation/building-organizing/df.drop()/index.html b/docs/documentation/building-organizing/df.drop()/index.html index 18eea659..befbb7c5 100644 --- a/docs/documentation/building-organizing/df.drop()/index.html +++ b/docs/documentation/building-organizing/df.drop()/index.html @@ -6,13 +6,17 @@ df.drop() | bpd + + + + - - + +

df.drop()

df.drop(columns=column_name or [col_1_name, ..., col_k_name]) diff --git a/docs/documentation/building-organizing/df.merge()/index.html b/docs/documentation/building-organizing/df.merge()/index.html index 7d12e2ec..acfe1b08 100644 --- a/docs/documentation/building-organizing/df.merge()/index.html +++ b/docs/documentation/building-organizing/df.merge()/index.html @@ -6,13 +6,17 @@ df.merge() | bpd + + + + - - + +

df.merge()

df.merge(right, on=column, left_on=left_column, right_on=right_column, left_index=False, right_index=False) diff --git a/docs/documentation/building-organizing/df.reset_index()/index.html b/docs/documentation/building-organizing/df.reset_index()/index.html index 30e6a7fc..5344cae4 100644 --- a/docs/documentation/building-organizing/df.reset_index()/index.html +++ b/docs/documentation/building-organizing/df.reset_index()/index.html @@ -6,13 +6,17 @@ df.reset_index() | bpd + + + + - - + +

df.reset_index()

df.reset_index(drop=False) diff --git a/docs/documentation/building-organizing/df.set_index()/index.html b/docs/documentation/building-organizing/df.set_index()/index.html index 818013ca..b53b97ef 100644 --- a/docs/documentation/building-organizing/df.set_index()/index.html +++ b/docs/documentation/building-organizing/df.set_index()/index.html @@ -6,13 +6,17 @@ df.set_index() | bpd + + + + - - + +

df.set_index()

df.set_index(column_name) diff --git a/docs/documentation/building-organizing/df.sort_values()/index.html b/docs/documentation/building-organizing/df.sort_values()/index.html index 1c328670..d4d9ca5b 100644 --- a/docs/documentation/building-organizing/df.sort_values()/index.html +++ b/docs/documentation/building-organizing/df.sort_values()/index.html @@ -6,13 +6,17 @@ df.sort_values() | bpd + + + + - - + +

df.sort_values()

df.sort_values(by=column_name, ascending=True) diff --git a/docs/documentation/building-organizing/index.html b/docs/documentation/building-organizing/index.html index 80b185bb..e4422dfd 100644 --- a/docs/documentation/building-organizing/index.html +++ b/docs/documentation/building-organizing/index.html @@ -6,28 +6,32 @@ Building and Organizing DataFrames | bpd + + + + - - + +

Building and Organizing DataFrames

Each function/method creates a new DataFrame. Remember to save it!

Manipulating​


bpd.DataFrame()

Creates an empty DataFrame.

-

bpd.read_csv(filepath)

Read a comma-separated values (csv) file into DataFrame.

+

bpd.read_csv(filepath)

Reads a CSV (comma-separated values) file into a DataFrame.

df.assign(name_of_column=column_data)

Adds a new column to the DataFrame.

-

df.drop(columns=column_name or [col_1_name, ..., col_k_name])

Drops a single column, or every column in a list of column names.

+

df.drop(columns=column_name or [col_1_name, ..., col_k_name])

Drops a single column, or every column in a list of column names, from the DataFrame.

Indexing​


-

df.set_index(column_name)

Moves a column to the index.

+

df.set_index(column_name)

Moves a column to the DataFrame's index.

Organizing​


-

df.reset_index(drop=False)

Moves a column to the index.

+

df.reset_index(drop=False)

Moves the index to a new column and uses the default index instead.

df.sort_values(by=column_name, ascending=True)

Sorts the entire DataFrame in ascending order by the values in the column.

Merging​


diff --git a/docs/documentation/data format conversion/index.html b/docs/documentation/data format conversion/index.html index 986ed163..63bb63d6 100644 --- a/docs/documentation/data format conversion/index.html +++ b/docs/documentation/data format conversion/index.html @@ -6,13 +6,17 @@ Data Format Conversion | bpd + + + + - - + +

Data Format Conversion

Converting things to arrays!

diff --git a/docs/documentation/data format conversion/list()/index.html b/docs/documentation/data format conversion/list()/index.html index 1f5ce9f8..0f8bcd18 100644 --- a/docs/documentation/data format conversion/list()/index.html +++ b/docs/documentation/data format conversion/list()/index.html @@ -6,13 +6,17 @@ list() | bpd + + + + - - + +

list()

list(arr) diff --git a/docs/documentation/data format conversion/np.array()/index.html b/docs/documentation/data format conversion/np.array()/index.html index 963ca906..af6dae92 100644 --- a/docs/documentation/data format conversion/np.array()/index.html +++ b/docs/documentation/data format conversion/np.array()/index.html @@ -6,13 +6,17 @@ np.array() | bpd + + + + - - + +

np.array()

np.array(input) diff --git a/docs/documentation/for-loops/index.html b/docs/documentation/for-loops/index.html index 9529baf8..fc786062 100644 --- a/docs/documentation/for-loops/index.html +++ b/docs/documentation/for-loops/index.html @@ -6,13 +6,17 @@ for-loops | bpd + + + + - - + +

for-loops

for <loop variable> in <sequence>:
diff --git a/docs/documentation/if-statements/Logical Operators/index.html b/docs/documentation/if-statements/Logical Operators/index.html index b2b09ee8..3b7b9664 100644 --- a/docs/documentation/if-statements/Logical Operators/index.html +++ b/docs/documentation/if-statements/Logical Operators/index.html @@ -6,13 +6,17 @@ Logical Operators | bpd + + + + - - + +

Logical Operators

if <condition> and <condition>:
diff --git a/docs/documentation/if-statements/if-elif-else/index.html b/docs/documentation/if-statements/if-elif-else/index.html index 03b34038..89deb83e 100644 --- a/docs/documentation/if-statements/if-elif-else/index.html +++ b/docs/documentation/if-statements/if-elif-else/index.html @@ -6,13 +6,17 @@ if-elif-else | bpd + + + + - - + +

if-elif-else

if <condition>:
diff --git "a/docs/documentation/if-statements/in \342\201\204 not in/index.html" "b/docs/documentation/if-statements/in \342\201\204 not in/index.html" index 71a57513..821a6731 100644 --- "a/docs/documentation/if-statements/in \342\201\204 not in/index.html" +++ "b/docs/documentation/if-statements/in \342\201\204 not in/index.html" @@ -6,13 +6,17 @@ in ⁄ not in | bpd + + + + - - + +

in ⁄ not in

if <object> in <sequence>:
diff --git a/docs/documentation/intro/index.html b/docs/documentation/intro/index.html index 516f0e47..6e1ca734 100644 --- a/docs/documentation/intro/index.html +++ b/docs/documentation/intro/index.html @@ -3,24 +3,28 @@ -intro | bpd +intro | bpd + + + + - - + +

BabyPandas Documentation

-

Assumption: Assume that df is a DataFrame, ser is a Series, arr is an array, and we have already run import babypandas as bpd and import numpy as np.

+

Assumption: Assume that df is a DataFrame, ser is a Series, arr is an array, and we already ran import babypandas as bpd and import numpy as np.

This section contains common and useful methods in the BabyPandas package. For this section, pets refers to the DataFrame below.

pets
IndexIDSpeciesColorWeightAgeIs_CatOwner_Comment
0dog_001dogblack405False There are no bad dogs, only bad owners.
1cat_001catgolden1.50.2TrueMy best birthday present ever!!!
2cat_002catblack159True****All you need is love and a cat.****
3dog_002dogwhite802FalseLove is a wet nose and a wagging tail.
4dog_003dogblack250.5FalseBe the person your dog thinks you are.
5ham_001hamsterblack13FalseNo, thank you!
6ham_002hamstergolden0.250.2FalseNo, thank you!
7cat_003catblack100TrueNo, thank you!
-

Download this data

+

Download this data

\ No newline at end of file diff --git a/docs/documentation/plotting/Bar Plot/index.html b/docs/documentation/plotting/Bar Plot/index.html index 83350c97..cfb8e6ec 100644 --- a/docs/documentation/plotting/Bar Plot/index.html +++ b/docs/documentation/plotting/Bar Plot/index.html @@ -6,13 +6,17 @@ Bar Plot | bpd + + + + - - + +

Bar Plot

df.plot(kind='bar', x=data_col, y=data_col) diff --git a/docs/documentation/plotting/Histogram/index.html b/docs/documentation/plotting/Histogram/index.html index 5534bbbc..619cf811 100644 --- a/docs/documentation/plotting/Histogram/index.html +++ b/docs/documentation/plotting/Histogram/index.html @@ -6,13 +6,17 @@ Histogram | bpd + + + + - - + +

Histogram

df.plot(kind='hist', y=data_col, bins=the_bins, density=True, ec='w') diff --git a/docs/documentation/plotting/Line Plot/index.html b/docs/documentation/plotting/Line Plot/index.html index 5e1eab34..c03b9442 100644 --- a/docs/documentation/plotting/Line Plot/index.html +++ b/docs/documentation/plotting/Line Plot/index.html @@ -6,13 +6,17 @@ Line Plot | bpd + + + + - - + +

Line Plot

df.plot(kind='line', x = data_col, y=data_col) diff --git a/docs/documentation/plotting/Scatter Plot/index.html b/docs/documentation/plotting/Scatter Plot/index.html index 651f7fca..e6b84ec6 100644 --- a/docs/documentation/plotting/Scatter Plot/index.html +++ b/docs/documentation/plotting/Scatter Plot/index.html @@ -6,13 +6,17 @@ Scatter Plot | bpd + + + + - - + +

Scatter Plot

df.plot(kind='scatter', x=data_col, y=data_col) diff --git a/docs/documentation/plotting/index.html b/docs/documentation/plotting/index.html index 40083aaf..14cd91a4 100644 --- a/docs/documentation/plotting/index.html +++ b/docs/documentation/plotting/index.html @@ -6,13 +6,17 @@ Plotting | bpd + + + + - - + +

Plotting

Plotting and visualization of DataFrames.

diff --git a/docs/documentation/querying/df[]/index.html b/docs/documentation/querying/df[]/index.html index bf3bb7c1..0d3cc47e 100644 --- a/docs/documentation/querying/df[]/index.html +++ b/docs/documentation/querying/df[]/index.html @@ -6,13 +6,17 @@ df[] | bpd + + + + - - + +

df[]

df[condition] diff --git a/docs/documentation/series-methods/index.html b/docs/documentation/series-methods/index.html index 5a91fd7a..7d03ae8b 100644 --- a/docs/documentation/series-methods/index.html +++ b/docs/documentation/series-methods/index.html @@ -6,13 +6,17 @@ Series Methods | bpd + + + + - - + +

Series Methods

Methods that can be performed on a Series.

diff --git a/docs/documentation/series-methods/ser.count()/index.html b/docs/documentation/series-methods/ser.count()/index.html index 8fb98e45..3875a790 100644 --- a/docs/documentation/series-methods/ser.count()/index.html +++ b/docs/documentation/series-methods/ser.count()/index.html @@ -6,13 +6,17 @@ ser.count() | bpd + + + + - - + +

ser.count()

ser.count() diff --git a/docs/documentation/series-methods/ser.max()/index.html b/docs/documentation/series-methods/ser.max()/index.html index d176d8b7..e0a403ea 100644 --- a/docs/documentation/series-methods/ser.max()/index.html +++ b/docs/documentation/series-methods/ser.max()/index.html @@ -6,13 +6,17 @@ ser.max() | bpd + + + + - - + +

ser.max()

ser.max() diff --git a/docs/documentation/series-methods/ser.mean()/index.html b/docs/documentation/series-methods/ser.mean()/index.html index 7383ecb9..a01525e0 100644 --- a/docs/documentation/series-methods/ser.mean()/index.html +++ b/docs/documentation/series-methods/ser.mean()/index.html @@ -6,13 +6,17 @@ ser.mean() | bpd + + + + - - + +

ser.mean()

ser.mean() diff --git a/docs/documentation/series-methods/ser.median()/index.html b/docs/documentation/series-methods/ser.median()/index.html index 2642ad4c..3ee7127c 100644 --- a/docs/documentation/series-methods/ser.median()/index.html +++ b/docs/documentation/series-methods/ser.median()/index.html @@ -6,13 +6,17 @@ ser.median() | bpd + + + + - - + +

ser.median()

ser.median() diff --git a/docs/documentation/series-methods/ser.min()/index.html b/docs/documentation/series-methods/ser.min()/index.html index 38058944..026226c6 100644 --- a/docs/documentation/series-methods/ser.min()/index.html +++ b/docs/documentation/series-methods/ser.min()/index.html @@ -6,13 +6,17 @@ ser.min() | bpd + + + + - - + +

ser.min()

ser.min() diff --git a/docs/documentation/series-methods/ser.str.capitalize()/index.html b/docs/documentation/series-methods/ser.str.capitalize()/index.html index b367d8cf..45a02d5b 100644 --- a/docs/documentation/series-methods/ser.str.capitalize()/index.html +++ b/docs/documentation/series-methods/ser.str.capitalize()/index.html @@ -6,13 +6,17 @@ ser.str.capitalize() | bpd + + + + - - + +

ser.str.capitalize()

ser.str.capitalize() diff --git a/docs/documentation/series-methods/ser.str.contains()/index.html b/docs/documentation/series-methods/ser.str.contains()/index.html index dbfedc72..ce6c4cd8 100644 --- a/docs/documentation/series-methods/ser.str.contains()/index.html +++ b/docs/documentation/series-methods/ser.str.contains()/index.html @@ -6,13 +6,17 @@ ser.str.contains() | bpd + + + + - - + +

ser.str.contains()

ser.str.contains(substring) diff --git a/docs/documentation/series-methods/ser.str.len()/index.html b/docs/documentation/series-methods/ser.str.len()/index.html index 5ceeba22..3411ac12 100644 --- a/docs/documentation/series-methods/ser.str.len()/index.html +++ b/docs/documentation/series-methods/ser.str.len()/index.html @@ -6,13 +6,17 @@ ser.str.len() | bpd + + + + - - + +

ser.str.len()

ser.str.len() diff --git a/docs/documentation/series-methods/ser.str.lower()/index.html b/docs/documentation/series-methods/ser.str.lower()/index.html index 1f071808..909f296b 100644 --- a/docs/documentation/series-methods/ser.str.lower()/index.html +++ b/docs/documentation/series-methods/ser.str.lower()/index.html @@ -6,13 +6,17 @@ ser.str.lower() | bpd + + + + - - + +

ser.str.lower()

ser.str.lower() diff --git a/docs/documentation/series-methods/ser.str.replace()/index.html b/docs/documentation/series-methods/ser.str.replace()/index.html index eae156c2..bc7c74d9 100644 --- a/docs/documentation/series-methods/ser.str.replace()/index.html +++ b/docs/documentation/series-methods/ser.str.replace()/index.html @@ -6,13 +6,17 @@ ser.str.replace() | bpd + + + + - - + +

ser.str.replace()

ser.str.replace(old, new) diff --git a/docs/documentation/series-methods/ser.str.split()/index.html b/docs/documentation/series-methods/ser.str.split()/index.html index 2e29e5e0..47f71023 100644 --- a/docs/documentation/series-methods/ser.str.split()/index.html +++ b/docs/documentation/series-methods/ser.str.split()/index.html @@ -6,13 +6,17 @@ ser.str.split() | bpd + + + + - - + +

ser.str.split()

ser.str.split(pat = None) diff --git a/docs/documentation/series-methods/ser.str.strip()/index.html b/docs/documentation/series-methods/ser.str.strip()/index.html index be148056..ffcd5796 100644 --- a/docs/documentation/series-methods/ser.str.strip()/index.html +++ b/docs/documentation/series-methods/ser.str.strip()/index.html @@ -6,13 +6,17 @@ ser.str.strip() | bpd + + + + - - + +

ser.str.strip()

ser.str.strip(to_strip = None) diff --git a/docs/documentation/series-methods/ser.str.title()/index.html b/docs/documentation/series-methods/ser.str.title()/index.html index 0c070c25..dabc40bb 100644 --- a/docs/documentation/series-methods/ser.str.title()/index.html +++ b/docs/documentation/series-methods/ser.str.title()/index.html @@ -6,13 +6,17 @@ ser.str.title() | bpd + + + + - - + +

ser.str.title()

ser.str.title() diff --git a/docs/documentation/series-methods/ser.str.upper()/index.html b/docs/documentation/series-methods/ser.str.upper()/index.html index 86ac73a1..03d95f5c 100644 --- a/docs/documentation/series-methods/ser.str.upper()/index.html +++ b/docs/documentation/series-methods/ser.str.upper()/index.html @@ -6,13 +6,17 @@ ser.str.upper() | bpd + + + + - - + +

ser.str.upper()

ser.str.upper() diff --git a/docs/documentation/series-methods/ser.sum()/index.html b/docs/documentation/series-methods/ser.sum()/index.html index 20f60fa9..40f511ba 100644 --- a/docs/documentation/series-methods/ser.sum()/index.html +++ b/docs/documentation/series-methods/ser.sum()/index.html @@ -6,13 +6,17 @@ ser.sum() | bpd + + + + - - + +

ser.sum()

ser.sum() diff --git a/docs/documentation/series-methods/ser.unique()/index.html b/docs/documentation/series-methods/ser.unique()/index.html index 8177b9cc..4c5438d7 100644 --- a/docs/documentation/series-methods/ser.unique()/index.html +++ b/docs/documentation/series-methods/ser.unique()/index.html @@ -6,13 +6,17 @@ ser.unique() | bpd + + + + - - + +

ser.unique()

ser.unique() diff --git a/docs/statistical-inference/bootstrapping/index.html b/docs/statistical-inference/bootstrapping/index.html index 522f40c5..582e754c 100644 --- a/docs/statistical-inference/bootstrapping/index.html +++ b/docs/statistical-inference/bootstrapping/index.html @@ -6,13 +6,17 @@ Bootstrapping and Confidence Intervals | bpd + + + + - - + +

Bootstrapping and Confidence Intervals

Concept​

diff --git a/docs/statistical-inference/central_limit_theorem/index.html b/docs/statistical-inference/central_limit_theorem/index.html index c5560e6c..bd9733c4 100644 --- a/docs/statistical-inference/central_limit_theorem/index.html +++ b/docs/statistical-inference/central_limit_theorem/index.html @@ -6,13 +6,17 @@ The Central Limit Theorem | bpd + + + + - - + +

The Central Limit Theorem

Concept​

diff --git a/docs/statistical-inference/concept check/bootstrapping_vs_the_CLT/index.html b/docs/statistical-inference/concept check/bootstrapping_vs_the_CLT/index.html index 895c2903..f65aec68 100644 --- a/docs/statistical-inference/concept check/bootstrapping_vs_the_CLT/index.html +++ b/docs/statistical-inference/concept check/bootstrapping_vs_the_CLT/index.html @@ -6,13 +6,17 @@ Bootstrapping vs. the CLT | bpd + + + + - - + +

Bootstrapping vs. the CLT

Difference​

diff --git a/docs/statistical-inference/concept check/hypothesis_vs_permutation/index.html b/docs/statistical-inference/concept check/hypothesis_vs_permutation/index.html index fafafe89..cceca08e 100644 --- a/docs/statistical-inference/concept check/hypothesis_vs_permutation/index.html +++ b/docs/statistical-inference/concept check/hypothesis_vs_permutation/index.html @@ -6,13 +6,17 @@ Hypothesis Test vs. Permutation Test | bpd + + + + - - + +

Hypothesis Test vs. Permutation Test

Difference​

diff --git a/docs/statistical-inference/hypothesis_test/index.html b/docs/statistical-inference/hypothesis_test/index.html index ed7e0c0f..79b7ce30 100644 --- a/docs/statistical-inference/hypothesis_test/index.html +++ b/docs/statistical-inference/hypothesis_test/index.html @@ -6,13 +6,17 @@ Hypothesis Test | bpd + + + + - - + +

Hypothesis Test

Concept​

diff --git a/docs/statistical-inference/intro/index.html b/docs/statistical-inference/intro/index.html index 5425c007..476e346a 100644 --- a/docs/statistical-inference/intro/index.html +++ b/docs/statistical-inference/intro/index.html @@ -6,13 +6,17 @@ intro | bpd + + + + - - + +

Statistical Inference

@@ -21,6 +25,6 @@

This section provides explanations and code implementations of theories covered in DSC 10. For examples in this section, refer to the full_pets DataFrame, which has more data than pets DataFrame (which is used in the Documentation section).

full_pets
IndexIDSpeciesColorWeightAgeIs_CatOwner_Comment
0dog_001dogblack405False There are no bad dogs, only bad owners.
1cat_001catgolden1.50.2TrueMy best birthday present ever!!!
2cat_002catblack159True****All you need is love and a cat.****
3dog_002dogwhite802FalseLove is a wet nose and a wagging tail.
4dog_003dogblack250.5FalseBe the person your dog thinks you are.
5ham_001hamsterblack13FalseNo, thank you!
6ham_002hamstergolden0.250.2FalseNo, thank you!
7cat_003catblack100TrueNo, thank you!
8dog_004dogblack456.7FalseNo, thank you!
9dog_005dogwhite107FalseNo, thank you!
10dog_006doggolden354FalseNo, thank you!
11cat_004catblack101.2TrueNo, thank you!
12cat_005catwhite152.5TrueNo, thank you!
13ham_003hamsterblack0.50.1FalseNo, thank you!
14dog_007dogwhite506.1FalseNo, thank you!
15ham_004hamstergolden0.250.2FalseNo, thank you!
16dog_008dogblack405FalseNo, thank you!
17dog_009dogwhite304.8FalseNo, thank you!
18cat_006catblack30.5TrueNo, thank you!
-

Download this data

+

Download this data

\ No newline at end of file diff --git a/docs/statistical-inference/null_and_alt/index.html b/docs/statistical-inference/null_and_alt/index.html index 86a97d9d..5e57f6c4 100644 --- a/docs/statistical-inference/null_and_alt/index.html +++ b/docs/statistical-inference/null_and_alt/index.html @@ -6,13 +6,17 @@ Null & Alternative Hypothesis | bpd + + + + - - + +

Null & Alternative Hypothesis

Concept​

diff --git a/docs/statistical-inference/obs_and_test_stats/index.html b/docs/statistical-inference/obs_and_test_stats/index.html index 288e4e66..1e2103b5 100644 --- a/docs/statistical-inference/obs_and_test_stats/index.html +++ b/docs/statistical-inference/obs_and_test_stats/index.html @@ -6,13 +6,17 @@ Observed & Test Statistic | bpd + + + + - - + +

Observed & Test Statistic

Concept​

diff --git a/docs/statistical-inference/p_value/index.html b/docs/statistical-inference/p_value/index.html index 3d7f4c7a..88ba1509 100644 --- a/docs/statistical-inference/p_value/index.html +++ b/docs/statistical-inference/p_value/index.html @@ -6,13 +6,17 @@ P-value | bpd + + + + - - + +

P-value

Concept​

diff --git a/docs/statistical-inference/parameters-and-statistics/index.html b/docs/statistical-inference/parameters-and-statistics/index.html index 32f04a7d..20030fd7 100644 --- a/docs/statistical-inference/parameters-and-statistics/index.html +++ b/docs/statistical-inference/parameters-and-statistics/index.html @@ -6,13 +6,17 @@ Parameters and Statistics | bpd + + + + - - + +

Parameters and Statistics

Concept​

diff --git a/docs/statistical-inference/permutation_test/index.html b/docs/statistical-inference/permutation_test/index.html index 6f7c8572..22d59121 100644 --- a/docs/statistical-inference/permutation_test/index.html +++ b/docs/statistical-inference/permutation_test/index.html @@ -6,13 +6,17 @@ Permutation Test | bpd + + + + - - + +

Permutation Test

Concept​

diff --git a/docs/statistical-inference/random sampling/df.sample()/index.html b/docs/statistical-inference/random sampling/df.sample()/index.html index 534967e0..ffa11733 100644 --- a/docs/statistical-inference/random sampling/df.sample()/index.html +++ b/docs/statistical-inference/random sampling/df.sample()/index.html @@ -6,13 +6,17 @@ Sample | bpd + + + + - - + +

Sample

df.sample(n, replace=False) diff --git a/docs/statistical-inference/random sampling/np.random.choice()/index.html b/docs/statistical-inference/random sampling/np.random.choice()/index.html index 04ded339..c5b0bd92 100644 --- a/docs/statistical-inference/random sampling/np.random.choice()/index.html +++ b/docs/statistical-inference/random sampling/np.random.choice()/index.html @@ -6,13 +6,17 @@ Random Choice | bpd + + + + - - + +

Random Choice

np.random.choice(arr, size, replace=True, p=[p_0, p_1, ...]) diff --git a/docs/statistical-inference/random sampling/np.random.multinomial()/index.html b/docs/statistical-inference/random sampling/np.random.multinomial()/index.html index 95e5a592..6c009269 100644 --- a/docs/statistical-inference/random sampling/np.random.multinomial()/index.html +++ b/docs/statistical-inference/random sampling/np.random.multinomial()/index.html @@ -6,13 +6,17 @@ Random Multinomial | bpd + + + + - - + +

Random Multinomial

np.random.multinomial(n, [p_0, p_1, p_2, ...]) diff --git a/docs/statistical-inference/random sampling/np.random.permutation()/index.html b/docs/statistical-inference/random sampling/np.random.permutation()/index.html index cbf9aef4..b707ab97 100644 --- a/docs/statistical-inference/random sampling/np.random.permutation()/index.html +++ b/docs/statistical-inference/random sampling/np.random.permutation()/index.html @@ -6,13 +6,17 @@ Random Permutation | bpd + + + + - - + +

Random Permutation

np.random.permutation(arr) diff --git a/docs/statistical-inference/random sampling/sampling/index.html b/docs/statistical-inference/random sampling/sampling/index.html index ceb210f0..096d2911 100644 --- a/docs/statistical-inference/random sampling/sampling/index.html +++ b/docs/statistical-inference/random sampling/sampling/index.html @@ -6,13 +6,17 @@ Sampling | bpd + + + + - - + +

Sampling

Concept​

diff --git a/docs/statistical-inference/spread_of_a_distribution/index.html b/docs/statistical-inference/spread_of_a_distribution/index.html index 8e0aab50..62419ce4 100644 --- a/docs/statistical-inference/spread_of_a_distribution/index.html +++ b/docs/statistical-inference/spread_of_a_distribution/index.html @@ -6,13 +6,17 @@ Spread of a Distribution | bpd + + + + - - + +

Spread of a Distribution

Concept​

diff --git a/docs/statistical-inference/standard_normal_distribution/index.html b/docs/statistical-inference/standard_normal_distribution/index.html index 29d08005..54374cb1 100644 --- a/docs/statistical-inference/standard_normal_distribution/index.html +++ b/docs/statistical-inference/standard_normal_distribution/index.html @@ -6,13 +6,17 @@ The Standard Normal Distribution | bpd + + + + - - + +

The Standard Normal Distribution

Concept​

diff --git a/docs/statistical-inference/standard_units/index.html b/docs/statistical-inference/standard_units/index.html index 91b6bb87..93326642 100644 --- a/docs/statistical-inference/standard_units/index.html +++ b/docs/statistical-inference/standard_units/index.html @@ -6,13 +6,17 @@ Standard Units, Correlation, Regression | bpd + + + + - - + +

Standard Units, Correlation, Regression

Concept​

diff --git a/docs/tags/bootstrapping/index.html b/docs/tags/bootstrapping/index.html index d6cddd41..9618c775 100644 --- a/docs/tags/bootstrapping/index.html +++ b/docs/tags/bootstrapping/index.html @@ -6,13 +6,17 @@ One doc tagged with "bootstrapping" | bpd + + + + - - + +

One doc tagged with "bootstrapping"

View All Tags
diff --git a/docs/tags/chebyshevs-inequality/index.html b/docs/tags/chebyshevs-inequality/index.html index 1632678a..97603d18 100644 --- a/docs/tags/chebyshevs-inequality/index.html +++ b/docs/tags/chebyshevs-inequality/index.html @@ -6,13 +6,17 @@ One doc tagged with "chebyshev’s inequality" | bpd + + + + - - + +

One doc tagged with "chebyshev’s inequality"

View All Tags
diff --git a/docs/tags/confidence-intervals/index.html b/docs/tags/confidence-intervals/index.html index c7722794..4f9e2819 100644 --- a/docs/tags/confidence-intervals/index.html +++ b/docs/tags/confidence-intervals/index.html @@ -6,13 +6,17 @@ One doc tagged with "confidence intervals" | bpd + + + + - - + +

One doc tagged with "confidence intervals"

View All Tags
diff --git a/docs/tags/correlation/index.html b/docs/tags/correlation/index.html index baf3a6f0..9edf4b6e 100644 --- a/docs/tags/correlation/index.html +++ b/docs/tags/correlation/index.html @@ -6,13 +6,17 @@ One doc tagged with "correlation" | bpd + + + + - - + +

One doc tagged with "correlation"

View All Tags
diff --git a/docs/tags/for-loop/index.html b/docs/tags/for-loop/index.html index 8204835a..185d12df 100644 --- a/docs/tags/for-loop/index.html +++ b/docs/tags/for-loop/index.html @@ -6,13 +6,17 @@ 3 docs tagged with "for-loop" | bpd + + + + - - + +

3 docs tagged with "for-loop"

View All Tags
diff --git a/docs/tags/functions/index.html b/docs/tags/functions/index.html index 63ab34c0..421c43d1 100644 --- a/docs/tags/functions/index.html +++ b/docs/tags/functions/index.html @@ -6,13 +6,17 @@ 2 docs tagged with "functions" | bpd + + + + - - + +

2 docs tagged with "functions"

View All Tags
diff --git a/docs/tags/histogram/index.html b/docs/tags/histogram/index.html index 36080396..c53fb135 100644 --- a/docs/tags/histogram/index.html +++ b/docs/tags/histogram/index.html @@ -6,13 +6,17 @@ 3 docs tagged with "histogram" | bpd + + + + - - + +

3 docs tagged with "histogram"

View All Tags
diff --git a/docs/tags/hypothesis-test/index.html b/docs/tags/hypothesis-test/index.html index 61eb50f2..f8c303e7 100644 --- a/docs/tags/hypothesis-test/index.html +++ b/docs/tags/hypothesis-test/index.html @@ -6,13 +6,17 @@ One doc tagged with "hypothesis test" | bpd + + + + - - + +

One doc tagged with "hypothesis test"

View All Tags
diff --git a/docs/tags/index.html b/docs/tags/index.html index 539205ca..0762924d 100644 --- a/docs/tags/index.html +++ b/docs/tags/index.html @@ -6,13 +6,17 @@ Tags | bpd + + + + - - + +

Tags

diff --git a/docs/tags/normal-distributions/index.html b/docs/tags/normal-distributions/index.html index c4eef251..691aab5a 100644 --- a/docs/tags/normal-distributions/index.html +++ b/docs/tags/normal-distributions/index.html @@ -6,13 +6,17 @@ One doc tagged with "normal distributions" | bpd + + + + - - + +

One doc tagged with "normal distributions"

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diff --git a/docs/tags/permutation-test/index.html b/docs/tags/permutation-test/index.html index 859988ea..12cc1c50 100644 --- a/docs/tags/permutation-test/index.html +++ b/docs/tags/permutation-test/index.html @@ -6,13 +6,17 @@ One doc tagged with "permutation test" | bpd + + + + - - + +

One doc tagged with "permutation test"

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diff --git a/docs/tags/querying/index.html b/docs/tags/querying/index.html index 520c168e..d8206d7e 100644 --- a/docs/tags/querying/index.html +++ b/docs/tags/querying/index.html @@ -6,13 +6,17 @@ 2 docs tagged with "querying" | bpd + + + + - - + +

2 docs tagged with "querying"

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diff --git a/docs/tags/regression/index.html b/docs/tags/regression/index.html index fe9db5ba..5c13738a 100644 --- a/docs/tags/regression/index.html +++ b/docs/tags/regression/index.html @@ -6,13 +6,17 @@ One doc tagged with "regression" | bpd + + + + - - + +

One doc tagged with "regression"

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diff --git a/docs/tags/standard-deviation/index.html b/docs/tags/standard-deviation/index.html index d38a2bfd..4ab88ffd 100644 --- a/docs/tags/standard-deviation/index.html +++ b/docs/tags/standard-deviation/index.html @@ -6,13 +6,17 @@ One doc tagged with "standard deviation" | bpd + + + + - - + +

One doc tagged with "standard deviation"

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diff --git a/docs/tags/standard-units/index.html b/docs/tags/standard-units/index.html index 07761c23..dbdcfde1 100644 --- a/docs/tags/standard-units/index.html +++ b/docs/tags/standard-units/index.html @@ -6,13 +6,17 @@ 2 docs tagged with "standard units" | bpd + + + + - - + +

2 docs tagged with "standard units"

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diff --git a/docs/tags/the-central-limit-theorem/index.html b/docs/tags/the-central-limit-theorem/index.html index af023f64..0e149fad 100644 --- a/docs/tags/the-central-limit-theorem/index.html +++ b/docs/tags/the-central-limit-theorem/index.html @@ -6,13 +6,17 @@ One doc tagged with "the central limit theorem" | bpd + + + + - - + +

One doc tagged with "the central limit theorem"

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diff --git a/docs/tags/the-standard-normal-distribution/index.html b/docs/tags/the-standard-normal-distribution/index.html index 45448a60..25aba23e 100644 --- a/docs/tags/the-standard-normal-distribution/index.html +++ b/docs/tags/the-standard-normal-distribution/index.html @@ -6,13 +6,17 @@ One doc tagged with "the standard normal distribution" | bpd + + + + - - + +

One doc tagged with "the standard normal distribution"

View All Tags
diff --git a/img/.DS_Store b/img/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..9180f405ce6f50341eb79a2905ff65b96eccf911 GIT binary patch literal 8196 zcmeHM!EVz)5S?ucbyO%70#UUBS>oE3MzjbC4k45SSAyUGDA=)^x^=u!>@QV|^7f9}{qw;8ku^8VP%4R?tv=6&Yekbt9COsLkxmaj(1IT0yds2W+ z;jc`a)I>BMPB~fxlry3`9cVU)Ly)aMYWaCOj0zBz}ynO zllQ_*b6T9=OWS6>zxwSsO0&()?_y?l?$YIXXWm(G-qrSGuaCEfG7x|^7eI<1hQ9^-6TjAwx%yQC8tzhx^;B4U0!p`D=h=(l7U$r^)l!G&nCbBKbLc}L0bka1Jf}e=5}g3Rp<_W35~)y z*LG3gqjF)rzLpAtMy2DBDjkPB{lgG_7pjb@7}?hnBPjp=MZn}=EcW@Ymc%v}fPvp9 CL2mp2 literal 0 HcmV?d00001 diff --git a/index.html b/index.html index 2a06daa8..57e0ab7e 100644 --- a/index.html +++ b/index.html @@ -6,13 +6,17 @@ bpd reference sheet | bpd + + + + - - + +

bpd

DSC 10 ❤️ bpd

DSC 10: Principles of Data Science

(4)

This first course in data science introduces students to data exploration, statistical inference, and prediction. It introduces Python programming language as a tool for tabular data manipulation, visualization, and simulation. Through homework assignments and projects, students are given an opportunity to develop their analytical skills while working with real-world datasets from a variety of domains.

DSC 10 ChartGrAPE
diff --git a/search/index.html b/search/index.html index 09dc97b7..0db3381d 100644 --- a/search/index.html +++ b/search/index.html @@ -6,13 +6,17 @@ Search the documentation | bpd + + + + - - + +

Search the documentation