notebooks/statistical-heaping.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Some evidence of statistical heaping in the review scores.\n",
    "\n",
    "\n",
    "Awhile back I read a [really cool blog post](https://gutterstats.wordpress.com/2015/11/03/are-nfl-officials-biased-with-their-ball-placement/) about bias in decisions about the line of scrimmage in American Football. The post reported that NFL officials tend to place the line of scrimmage at tidy yard numbers (i.e., 10s and 5s) more often than at less-tidy numbers (e.g., 4s and 6s). The technical term for this is [statistical heaping](http://ww2.amstat.org/sections/SRMS/Proceedings/y1958/Patterns%20Of%20Heaping%20In%20The%20Reporting%20Of%20Numerical%20Data.pdf), and its observed commonly in survey data.\n",
    "\n",
    "\n",
    "Recently, I have been thinking about whether a similar principle is at work when reviewers assign a score to an album. My guess is that authors usually have  a _general_ sense of the album's score, but they need to pick a _specific_ value (Is this a 7.8? 7.9? 7.7?). In this notebook, I'll just quickly establish the presence of statistical heaping in the review data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading libraries and data..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "TRUE"
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      "text/latex": [
       "TRUE"
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      "text/markdown": [
       "TRUE"
      ],
      "text/plain": [
       "[1] TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"SCORES SUMMARY\"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "     score       \n",
       " Min.   : 0.000  \n",
       " 1st Qu.: 6.400  \n",
       " Median : 7.200  \n",
       " Mean   : 7.006  \n",
       " 3rd Qu.: 7.800  \n",
       " Max.   :10.000  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"SCORES STANDARD DEV\"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "1.29367450215408"
      ],
      "text/latex": [
       "1.29367450215408"
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      "text/markdown": [
       "1.29367450215408"
      ],
      "text/plain": [
       "[1] 1.293675"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rm(list=ls())\n",
    "\n",
    "library(sqldf)\n",
    "library(ggplot2)\n",
    "\n",
    "con = dbConnect(SQLite(), dbname=\"../pitchfork.db\")\n",
    "scores = dbGetQuery( con, 'SELECT score FROM reviews')\n",
    "dbDisconnect(con)\n",
    "\n",
    "print('SCORES SUMMARY')\n",
    "summary(scores)\n",
    "\n",
    "print('SCORES STANDARD DEV')\n",
    "sd(scores$score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Models\n",
    "\n",
    "If there is _no_ statistical heaping in the data, then \"round\" scores, such as 7.0 and 8.0, should not be more frequently chosen than alternatives (such as 7.1 or 7.9). I'll define two models which characterize what ought to happen, assuming no bias: a _Uniform_ model and a _Normal_ model.\n",
    "\n",
    "### Uniform Model\n",
    "\n",
    "This model proposes that reviewers draw each score at random, uniformly between 0.0 and 10.0:\n",
    "\n",
    "$$\n",
    "score = uniform(0.0, 10.0)\n",
    "$$\n",
    "\n",
    "This is not a very plausible model because we _know_ scores are not uniformly distributed. But it's still worth considering for this issue (I think). Under this model, each score is equally probable, and so each decimal place ( \\*.0, \\*.1) is also equally likely. The only kink is that \\*.0 is a little more probable because 10.0 is a possibility but 10.1-10.9 are not.\n",
    "\n",
    "### Normal Model\n",
    "\n",
    "This model is based on the observation that scores are (roughly) normally distributed, with $\\mu=7.006$ and $\\sigma=1.294$:\n",
    "\n",
    "$$\n",
    "score = normal(\\mu=7.006, \\sigma=1.294)\n",
    "$$\n",
    "\n",
    "Obviously, under this model, scores around 7.0 are the most probable.\n",
    "\n",
    "## Analysis\n",
    "\n",
    "I'm basically going to count the number of reviews with scores ending at each decimal place, and compare that to what we'd expect under both models. Simple? Let's go!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>decimal</th><th scope=col>count</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0   </td><td>2776</td></tr>\n",
       "\t<tr><td>0.1 </td><td>1392</td></tr>\n",
       "\t<tr><td>0.2 </td><td>1749</td></tr>\n",
       "\t<tr><td>0.3 </td><td>1602</td></tr>\n",
       "\t<tr><td>0.4 </td><td>1723</td></tr>\n",
       "\t<tr><td>0.5 </td><td>2049</td></tr>\n",
       "\t<tr><td>0.6 </td><td>1571</td></tr>\n",
       "\t<tr><td>0.7 </td><td>1662</td></tr>\n",
       "\t<tr><td>0.8 </td><td>2151</td></tr>\n",
       "\t<tr><td>0.9 </td><td>1718</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " decimal & count\\\\\n",
       "\\hline\n",
       "\t 0    & 2776\\\\\n",
       "\t 0.1  & 1392\\\\\n",
       "\t 0.2  & 1749\\\\\n",
       "\t 0.3  & 1602\\\\\n",
       "\t 0.4  & 1723\\\\\n",
       "\t 0.5  & 2049\\\\\n",
       "\t 0.6  & 1571\\\\\n",
       "\t 0.7  & 1662\\\\\n",
       "\t 0.8  & 2151\\\\\n",
       "\t 0.9  & 1718\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "decimal | count | \n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 0    | 2776 | \n",
       "| 0.1  | 1392 | \n",
       "| 0.2  | 1749 | \n",
       "| 0.3  | 1602 | \n",
       "| 0.4  | 1723 | \n",
       "| 0.5  | 2049 | \n",
       "| 0.6  | 1571 | \n",
       "| 0.7  | 1662 | \n",
       "| 0.8  | 2151 | \n",
       "| 0.9  | 1718 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   decimal count\n",
       "1  0       2776 \n",
       "2  0.1     1392 \n",
       "3  0.2     1749 \n",
       "4  0.3     1602 \n",
       "5  0.4     1723 \n",
       "6  0.5     2049 \n",
       "7  0.6     1571 \n",
       "8  0.7     1662 \n",
       "9  0.8     2151 \n",
       "10 0.9     1718 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ----- Get observed counts\n",
    "# the rounding is due to a weird issue with the mod operator,\n",
    "# some scores have a mod of like 0.00000002003 or something nutty.\n",
    "value = round(as.vector(scores$score) %% 1.0, 1) \n",
    "observed = as.data.frame(table(value))\n",
    "colnames(observed) <- c('decimal','count')\n",
    "observed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>decimal</th><th scope=col>count</th><th scope=col>proportion</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0        </td><td>2003.198 </td><td>0.1089109</td></tr>\n",
       "\t<tr><td>0.1      </td><td>1821.089 </td><td>0.0990099</td></tr>\n",
       "\t<tr><td>0.2      </td><td>1821.089 </td><td>0.0990099</td></tr>\n",
       "\t<tr><td>0.3      </td><td>1821.089 </td><td>0.0990099</td></tr>\n",
       "\t<tr><td>0.4      </td><td>1821.089 </td><td>0.0990099</td></tr>\n",
       "\t<tr><td>0.5      </td><td>1821.089 </td><td>0.0990099</td></tr>\n",
       "\t<tr><td>0.6      </td><td>1821.089 </td><td>0.0990099</td></tr>\n",
       "\t<tr><td>0.7      </td><td>1821.089 </td><td>0.0990099</td></tr>\n",
       "\t<tr><td>0.8      </td><td>1821.089 </td><td>0.0990099</td></tr>\n",
       "\t<tr><td>0.9      </td><td>1821.089 </td><td>0.0990099</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " decimal & count & proportion\\\\\n",
       "\\hline\n",
       "\t 0         & 2003.198  & 0.1089109\\\\\n",
       "\t 0.1       & 1821.089  & 0.0990099\\\\\n",
       "\t 0.2       & 1821.089  & 0.0990099\\\\\n",
       "\t 0.3       & 1821.089  & 0.0990099\\\\\n",
       "\t 0.4       & 1821.089  & 0.0990099\\\\\n",
       "\t 0.5       & 1821.089  & 0.0990099\\\\\n",
       "\t 0.6       & 1821.089  & 0.0990099\\\\\n",
       "\t 0.7       & 1821.089  & 0.0990099\\\\\n",
       "\t 0.8       & 1821.089  & 0.0990099\\\\\n",
       "\t 0.9       & 1821.089  & 0.0990099\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "decimal | count | proportion | \n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 0         | 2003.198  | 0.1089109 | \n",
       "| 0.1       | 1821.089  | 0.0990099 | \n",
       "| 0.2       | 1821.089  | 0.0990099 | \n",
       "| 0.3       | 1821.089  | 0.0990099 | \n",
       "| 0.4       | 1821.089  | 0.0990099 | \n",
       "| 0.5       | 1821.089  | 0.0990099 | \n",
       "| 0.6       | 1821.089  | 0.0990099 | \n",
       "| 0.7       | 1821.089  | 0.0990099 | \n",
       "| 0.8       | 1821.089  | 0.0990099 | \n",
       "| 0.9       | 1821.089  | 0.0990099 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   decimal count    proportion\n",
       "1  0       2003.198 0.1089109 \n",
       "2  0.1     1821.089 0.0990099 \n",
       "3  0.2     1821.089 0.0990099 \n",
       "4  0.3     1821.089 0.0990099 \n",
       "5  0.4     1821.089 0.0990099 \n",
       "6  0.5     1821.089 0.0990099 \n",
       "7  0.6     1821.089 0.0990099 \n",
       "8  0.7     1821.089 0.0990099 \n",
       "9  0.8     1821.089 0.0990099 \n",
       "10 0.9     1821.089 0.0990099 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ----- Compute expected values assuming uniform choices\n",
    "uniform = as.data.frame(table(round(seq(0,10,0.1) %% 1.0,1)))\n",
    "colnames(uniform) = c('decimal','count')\n",
    "uniform$proportion = uniform$count / sum(uniform$count)\n",
    "uniform$count = uniform$proportion * sum(observed$count)\n",
    "uniform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>decimal</th><th scope=col>proportion</th><th scope=col>count</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.0       </td><td>0.10065429</td><td>1851.334  </td></tr>\n",
       "\t<tr><td>0.1       </td><td>0.09893412</td><td>1819.695  </td></tr>\n",
       "\t<tr><td>0.2       </td><td>0.09928866</td><td>1826.216  </td></tr>\n",
       "\t<tr><td>0.3       </td><td>0.09958802</td><td>1831.722  </td></tr>\n",
       "\t<tr><td>0.4       </td><td>0.09983921</td><td>1836.343  </td></tr>\n",
       "\t<tr><td>0.5       </td><td>0.10004867</td><td>1840.195  </td></tr>\n",
       "\t<tr><td>0.6       </td><td>0.10022226</td><td>1843.388  </td></tr>\n",
       "\t<tr><td>0.7       </td><td>0.10036521</td><td>1846.017  </td></tr>\n",
       "\t<tr><td>0.8       </td><td>0.10048221</td><td>1848.169  </td></tr>\n",
       "\t<tr><td>0.9       </td><td>0.10057736</td><td>1849.919  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " decimal & proportion & count\\\\\n",
       "\\hline\n",
       "\t 0.0        & 0.10065429 & 1851.334  \\\\\n",
       "\t 0.1        & 0.09893412 & 1819.695  \\\\\n",
       "\t 0.2        & 0.09928866 & 1826.216  \\\\\n",
       "\t 0.3        & 0.09958802 & 1831.722  \\\\\n",
       "\t 0.4        & 0.09983921 & 1836.343  \\\\\n",
       "\t 0.5        & 0.10004867 & 1840.195  \\\\\n",
       "\t 0.6        & 0.10022226 & 1843.388  \\\\\n",
       "\t 0.7        & 0.10036521 & 1846.017  \\\\\n",
       "\t 0.8        & 0.10048221 & 1848.169  \\\\\n",
       "\t 0.9        & 0.10057736 & 1849.919  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "decimal | proportion | count | \n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 0.0        | 0.10065429 | 1851.334   | \n",
       "| 0.1        | 0.09893412 | 1819.695   | \n",
       "| 0.2        | 0.09928866 | 1826.216   | \n",
       "| 0.3        | 0.09958802 | 1831.722   | \n",
       "| 0.4        | 0.09983921 | 1836.343   | \n",
       "| 0.5        | 0.10004867 | 1840.195   | \n",
       "| 0.6        | 0.10022226 | 1843.388   | \n",
       "| 0.7        | 0.10036521 | 1846.017   | \n",
       "| 0.8        | 0.10048221 | 1848.169   | \n",
       "| 0.9        | 0.10057736 | 1849.919   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   decimal proportion count   \n",
       "1  0.0     0.10065429 1851.334\n",
       "2  0.1     0.09893412 1819.695\n",
       "3  0.2     0.09928866 1826.216\n",
       "4  0.3     0.09958802 1831.722\n",
       "5  0.4     0.09983921 1836.343\n",
       "6  0.5     0.10004867 1840.195\n",
       "7  0.6     0.10022226 1843.388\n",
       "8  0.7     0.10036521 1846.017\n",
       "9  0.8     0.10048221 1848.169\n",
       "10 0.9     0.10057736 1849.919"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ----- compute expected values assuming normal choices\n",
    "x = seq(0,10,0.1)\n",
    "m = mean(scores$score)\n",
    "s = sd(scores$score)\n",
    "density = dnorm(x, mean = m, sd = s)\n",
    "p = density / sum(density)\n",
    "idx = round(x %% 1.0,1)\n",
    "normal = data.frame(list(score = x, decimal = idx, prob = p))\n",
    "normal = aggregate(normal$prob, by=list(normal$decimal), FUN=sum)\n",
    "colnames(normal) = c('decimal','proportion')\n",
    "normal$count = normal$proportion * sum(observed$count)\n",
    "normal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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q2sL6QKdk8VJIIiCZVnXxbaxwlDdrtuRbP4QkFzccRfO0gH5ivXDj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IECBAgEApBZrqg3ThhRemSy+9NJ177rnZ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\ngAABAgTaRuD/BylbPX4QgqDMAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# get x ticks !\n",
    "xticklabs = character()\n",
    "for (i in 0:9) {\n",
    "\txticklabs = c(xticklabs, paste0('*.',toString(i)))\n",
    "}\n",
    "\n",
    "plot = ggplot(NULL, aes(x = decimal, y = count)) + \n",
    "\tgeom_bar(data = observed, stat = 'identity', colour = '#004D40' , fill = '#004D40') + \n",
    "\tgeom_point(data = uniform, aes(colour = 'Uniform Sampling'), \n",
    "\t\tstroke = 1.25, size = 4, shape = 23) + \n",
    "\tgeom_point(data = normal, aes(x = 1:10, colour = 'Normal Sampling   '), \n",
    "\t\tstroke = 1.25, size = 6, shape = 23) + \n",
    "\tylab(\"Number of Reviews\") +\n",
    "\tscale_y_continuous(breaks = seq(from=0,to=3000,by=500)) +\n",
    "\tscale_x_discrete(breaks=observed$decimal, labels=xticklabs) +\n",
    "\ttheme_bw(base_size = 10) +\n",
    "\ttheme(\n",
    "\t\taxis.title.x=element_blank(),\n",
    "\t\tpanel.grid.major.x = element_blank(),\n",
    "\t\tlegend.direction=\"horizontal\", \n",
    "\t\tlegend.title = element_blank(),\n",
    "\t  \tlegend.position = c(0.5, 0.9),\n",
    "\t  \tpanel.grid.minor.y = element_blank(),\n",
    "\t  \taxis.text.x  = element_text(size=10),\n",
    "\t  ) + \n",
    "\tscale_colour_manual(values=c(\"#009688\", \"#FFB300\"))\n",
    "print(plot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results\n",
    "\n",
    "Obviously, \\*.0 is selected _far_ more often than you'd expect if scoring was unbiased. I think this is pretty strong evidence of statistical heaping!"
   ]
  }
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