Estimation of the number of "true" null hypotheses in multivariate analysis of neuroimaging data.

The repeated testing of a null univariate hypothesis in each of many sites (either regions of interest or voxels) is a common approach to the statistical analysis of brain functional images. Procedures, such as the Bonferroni, are available to maintain the Type I error of the set of tests at a specified level. An initial assumption of these methods is a "global null hypothesis," i.e., the statistics computed on each site are assumed to be generated by null distributions. This framework may be too conservative when a significant proportion of the sites is affected by the experimental manipulation. This report presents the development of a rigorous statistical procedure for use with a previously reported graphical method, the P plot, for estimation of the number of "true" null hypotheses in the set. This estimate can then be used to sharpen existing multiple comparison procedures. Performance of the P plot method in the multiple comparison problem is investigated in simulation studies and in the analysis of autoradiographic data.