K. J. Worsley - Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H۳A ۲K۶.
K. J. Friston - Wellcome Department of Cognitive Neurolugy, Institute of Neurology, Queen Square, London WCIN ۳BG, UK

A conjunction is defined in the brain mapping literature as the occurrence of the same event at the same location in two or more independent 3D brain images. The images are smooth isotropic 3D random fields of test statistics, and the event occurs when the image exceeds a fixed high threshold. We give a simple approximation to the probability of a conjunction accurring anywhere in fixed region, so that we can test for a local increase in mean of the images at the same unknown location in all images, a generalization of the split-t test. This is the corollary to a more general result on the expected Minkowski functional of the set of points where a conjunction occurs.