Permutation tests

fast_stat

Fast Stat is a set of command line programs dedicated to statistical analysis of MEG/EEG signals and their derivatives. Using permutation it generates the Ho distribution of your data and then compute the corresponding p values. This version reads LENA files. It generates LENA files readable in matlab or Muse. Matlab functions to read and to plot the results are provided. The documentation begins with a quick start guide for impatient users followed by methodological considerations. A complete description of all options is available in the second part of the manual.

The main goal of the permutation approach is to build the Ho distribution of your data. Thus almost no hypothesis (like normality of your data) are made. Moreover you will have the possibility to control for multiples comparisons.
Let us say that you have two populations of subjects A and B (See figure 1). You want to test the difference beetween population A and B using and difference of means (Σ = mean(A) − mean(B)).
Your Ho hypothesis is no difference between A and B. It means that we can exchange randomly a subject from population A for a subject of population B. We can permut subjets.
Thus building the distribution of Σ under Ho is fairly simple, we just have to compute a lot of values of Σ′ by selecting randomly subjects from population A or B for each computation. This step is at the heart of the permutation method.
At the end we will compare our true Σ value to the distribution of Σ′ values and then determine the corresponding p values.

:permutslide.png?400|

If your comparison beetween your two populations involve multiple dimensions (for example multiple sensors and multiple time steps), you will be confronted to the multiple hypothesis testing problem, i.e. you will multiply the risk of false positive by repeating testing at each time step on each sensor. One solution to overcome this point is to take max(Σ′) and build the associated distribution. You will place yourself in the worst case and thus theoritically and effectively control for the testing repetitions.
Here is a short description of the algorithm:

Load the signals for conditions A and B
Load the parameters
Compute true Σ between A and B
Draw a set of permutations according to the wanted number of permutations
Compute Σ′ for each permutation and compare it to Σ
When all permutations are done, output corresponding p value

:fast_stat.pdf|User Manual

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