7.10. Nonparametric Statistical Analysis of FMRI Data

These are notes by B. Douglas Ward, written in the Good Ol’ Days.

7.10.1. Abstract

Parametric statistical analysis programs such as 3dttest and 3dANOVA assume that the underlying populations (of voxel intensities) have a normal (or near normal) distribution. There are two reasons why one might prefer to use a nonparametric statistical analysis: 1) The population in question may differ significantly from the normal distribution. 2) Nonparametric statistical analysis techniques are usually less sensitive to the presence of “outliers”, i.e., they are more robust. Therefore, to provide the user with this option, the current distribution of AFNI includes four nonparametric analysis programs: 3dMannWhitney, 3dWilcoxon, 3dKruskalWallis, and 3dFriedman. This set of programs is intended to provide the capability to perfom nonparametric statistical analysis of FMRI data, roughly corresponding to the present (* well, note that “present” here is in the 90s) capability to perform parametric statistical analysis.

Section 1 describes Program 3dMannWhitney, for the comparison of two treatments (two samples). This program performs the Wilcoxon-Mann-Whitney rank-sum test on two groups of 3D datasets, voxel-by-voxel, to determine if the two samples are from the same population. Program otuput includes an estimate fo the treatment effect, as well as the normalized Wilcoxon rank-sum statistic, for each voxel.

Section 2 describes Program 3dWilcoxon, for the paired comparison of two treatments. This program performs the Wilcoxon signed-rank test for pairs of 3D datasets. Output includes an estimate for the treatment effect, and the normalized Wilcoxon signed-rank statistic, for each voxel.

Section 3 describes Program 3dKruskalWallis, for comparing mulitple treatments. This program performs the Kruskal-Wallis test to determin if any of k treatments (k groups of 3D datasets) are statistically different, on a voxel-by-voxel basis. Output includes the index of the best (highest ranking) treatment, as well as the Kruskal-Wallis chi-square statistic, for each voxel.

Section 4 describes Program 3DFriedman, which compares blocked multiple treatments. This program performs the Friedman test for randomized block designs, on a voxel-by-voxel basis. Output includes the index of the best (highest ranking) treatment, as well as the Friedman chi-square statistic, for each voxel.

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7.10.2. ... Full Enlightenment

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