Inferential methods for comparing a single case with a control sample: Modified t-tests versus Mycroft' et al.'s (2002) modified ANOVA

Mycroft, Mitchell, and Kay (2002) have criticised existing inferential methods (e.g., Crawford & Howell, 1998) for comparing a single case with a control sample and propose that such comparisons be made using a modified ANOVA. It is argued that the assumptions made by Mycroft et al. are questionable and, even if they held, would not invalidate Crawford and Howell's method. Crawford and Howell's null hypothesis is that the patient is an observation from the control population whereas Mycroft et al.'s null hypothesis is that the control population and a notional population of patients have a common mean. Even if one accepts Mycroft et al.'s conceptualisation, their arguments only have force if (1) the variance of a notional population of patients was larger than that of the control population, and (2) patients with impaired performance were balanced exactly by patients whose performance had been enhanced relative to controls. Furthermore, the modified ANOVA would have the undesirable consequence of reducing statistical power unnecessarily and it requires users to provide some estimate of the variance of a hypothetical population.