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These pages give you a little insight into how the statistics in LIMO MEEG work. These are not tutorials, but instead, expose the code and results used to test the various statistical functions.

General Linear Model stuff

• limo_test_glm.m tests that all the 'basic' stats using Ordinary Least Squares (OLS) work; any change to the base code limo_glm.m is tested against this.
• limo_test_irls.m validates the weighting schemes against matlab robust fit, revealing similar performances, although much faster.
• limo_test_wglm.m validates weighting schemes compared to OLS, that is the Weighted Least Squares (WLS) and Iterative Reweighted Least Squares (IRLS) return the same error rates given null ERP or Gaussian data as input.
• limo_test_glmboot.m validates the null results by computing the cell-wise type 1 error rate and the family-wise type 1 error rates for maximum statistics and spatial-temporal clustering. Given some LIMO processed data as input, it checks the corresponding null - data are partitioned with one set used to create the null distribution and the other set used for testing.

Extensive simulations were performed showing that weighting schemes provide good control over the type 1 error rate (see Weighting Scheme Comparison and Bootstrapping under the null)

Robust statistics

First-level analyses are performed using either Ordinary Least Squares or Weighted Least Squares. In this latter case, outlying trials are weighted down. Simulations show that our method weights down trials with different dynamics, here in red, those trials with low weights, compared to the 'good' (high weights) trials in black.

Example of how WLS differs from standard weighting - instead of point-wise amplitude differences, it separate trials with different dynamics.

Second-level analyses are performed using robust approaches. Here, those functions are tested against ground truth examples - see limo_test_robuststats.m.