Methods of testing for a deficit in single-case studies: Evaluation of statistical power by Monte Carlo simulation

Testing for the presence of a deficit by comparing a case to controls is a fundamental feature of many neuropsychological single-case studies. Monte Carlo simulation was employed to study the statistical power of two competing approaches to this task. The power to detect a large deficit was low to moderate for a method proposed by Crawford and Howell (1998; ranging from 44% to 63%) but was extremely low for a method proposed by Mycroft, Mitchell, and Kay (2002; ranging from 1% to 13%). The effects of departures from normality were examined, as was the effect of varying degrees of measurement error in the scores of controls and the single case. Measurement error produced a moderate reduction in power when present in both controls and the case; the effect of differentially greater measurement error for the single case depended on the initial level of power. When Mycroft et al.'s method was used to test for the presence of a classical dissociation, it produced very high Type I error rates (ranging from 20.7% to 49.3%); in contrast, the rates for criteria proposed by Crawford and Garthwaite (2005b) were low (ranging from 1.3% to 6.7%). The broader implications of these results for single-case research are discussed.