Crawford, John R.; Garthwaite, Paul H. and Howell, David C.
On comparing a single case with a control sample: an alternative perspective.
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Corballis [Corballis, M. C. (2009). Comparing a single case with a control sample: Refinements and extensions. Neuropsychologia] offers an interesting position paper on statistical inference in single-case studies. The following points arise: (1) Testing whether we can reject the null hypothesis that a patient's score is an observation from the population of control scores can be a legitimate aim for single-case researchers, not just clinicians. (2) Counter to the claim made by Corballis [Corballis, M. C. (2009). Comparing a single case with a control sample: Refinements and extensions. Neuropsychologia], Crawford and Howell's [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] method does test whether we can reject the above null hypothesis. (3) In all but the most unusual of circumstances Crawford and Howell's method can also safely be used to test whether the mean of a notional patient population is lower than that of a control population, should neuropsychologists wish to construe the test in this way. (4) In contrast, the method proposed by Corballis is not legitimate for either of these purposes because it fails to allow for uncertainty over the control mean (as a result Type I errors will not be under control). (5) The use of a mixed ANOVA design to compare a case to controls (with or without the adjustment proposed by Corballis) is beset with problems but these can be overcome using alternative methods.
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