Testing for a deficit in single-case studies: Effects of departures from normality

In neuropsychological single-case research inferences concerning a patient's cognitive status are often based on referring the patient's test score to those obtained from a modestly sized control sample. Two methods of testing for a deficit (z and a method proposed by Crawford and Howell [Crawford, J. R. & Howell, D. C. (1998). Comparing an individual's test score against norms derived from small samples. The Clinical Neuropsychologist, 12, 482–486]) both assume the control distribution is normal but this assumption will often be violated in practice. Monte Carlo simulation was employed to study the effects of leptokurtosis and the combination of skew and leptokurtosis on the Type I error rates for these two methods. For Crawford and Howell's method, leptokurtosis produced only a modest inflation of the Type I error rate when the control sample N was small-to-modest in size and error rates were lower than the specified rates at larger N. In contrast, the combination of leptokurtosis and skew produced marked inflation of error rates for small Ns. With a specified error rate of 5%, actual error rates as high as 14.31% and 9.96% were observed for z and Crawford and Howell's method respectively. Potential solutions to the problem of non-normal data are evaluated.