Comparing a single case with a control sample: refinements and extensions

Crawford and Garthwaite [Crawford, J. R. & Garthwaite, P. H. (2002). Investigation of the single case in neuropsychology: Confidence limits on the abnormality and test score differences. Neuropsychologia, 40, 1196-1208] have proposed an adjusted t-test, widely used in experimental neuropsychology, for comparing a single case with a control sample. This test does not assess whether the single-case score belongs in the population from which the control sample is drawn, but rather whether the mean of the distribution from which the case was drawn differs significantly from the mean of the control population. This approach is readily extended to more complex designs in which the analysis of variance is appropriate, and the single case is treated as belonging to a group of size one. The main qualification in using either this or Crawford and Howell's approach is that it makes the untestable assumption of homogeneity of variance between the two populations, but a simple adjustment either to the t-test or to the analysis of variance allows one to draw conclusions about the relation of the case itself to the control population.