Detecting Conjunctions Using Cluster Volumes

In brain mapping literatures, the experiment is repeated on several different subjects or for several different stimuli on the same subject, and the researcher is interested in the common points in the brain where ?activation? occurs in all test statistic images. The conjunction is thus defined as those points in the brain that show ?activation? in all images. We are interested in which parts of the conjunction are noise, and which show true activation in all test statistic images. Our main result is an approximate P-value for this in the case of the conjunction of two Gaussian or chi square test statistic images. The results are applied to a functional magnetic resonance experiment in pain perception.