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

Crawford, John R.; Garthwaite, Paul; Howell, David C. and Gray, Colin D. (2004). Inferential methods for comparing a single case with a control sample: modified t-tests versus mycroft et al.'s (2002) modified anova. Cognitive Neuropsychology, 21(7) pp. 750–755.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1080/02643290342000276
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Abstract

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.

Item Type: Journal Article
Copyright Holders: 2004 Taylor & Francis
ISSN: 0264-3294
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 19267
Depositing User: Colin Smith
Date Deposited: 21 Dec 2009 12:09
Last Modified: 25 Jul 2011 16:20
URI: http://oro.open.ac.uk/id/eprint/19267
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