Abstract
We present a unified statistical theory for assessing the significance of apparent signal observed in noisy difference images. The results are usable in a wide range of applications, including astrophysics, but are discussed with particular reference to images which represent changes in cerebral blood flow elicited by a specific cognitive or sensorimotor task. Our main result is an estimate of the p-value for local maxima of Gaussian, t, \chi^2 and F fields over search regions of any shape or size in any number of dimensions. This unifies the p-values for large search areas in 2-D (Friston et al., 1991), large search regions in 3-D (Worsley et al., 1992), and the usual uncorrected p-value at a single pixel or voxel.