Abstract: Functional magnetic resonance imaging studies answer questions about activation effects in populations of subjects. To begin with, this involves appropriate modeling of the fMRI data at the within-subject level. This is followed by extending the model to multiple subjects. There have been several attempts toward this extension, all of which have focused on inference on a single effect of interest (e.g., fMRI response for one type of working memory). However, the existing literature does not seem to say much about the relevant inferential procedures when multiple effects are of interest (e.g., response for four different types of working memory). In particular, the within subject dependence of one activation effect on another is an important issue with a multivariate repeated measures model. While most standard statistical methods regard such correlation as a nuisance, to be adjusted for and then ignored, we develop two simple and intuitive tests to make inference on the existence of such correlation. We demonstrate use of these tests by application to an fMRI study of attention switching. These tests are different not only from conventional tests for sphericity but also, more importantly, from the likelihood ratio test (LRT) of the relevant hypothesis. We also discuss what prompts us to look for tests different from the LRT.
Key words and phrases: Attention switching, functional magnetic resonance imaging, likelihood ratio test, mixed model.