Inferential methods for comparing two single cases

Abstract

In neuropsychological single-case studies, it is not uncommon for researchers to compare the scores of two single cases. Classical (and Bayesian) statistical methods are developed for such problems, which, unlike existing methods, refer the scores of the two single cases to a control sample. These methods allow researchers to compare two cases' scores, with or without allowing for the effects of covariates. The methods provide a hypothesis test (one- or two-tailed), point and interval estimates of the effect size of the difference, and point and interval estimates of the percentage of pairs of controls that will exhibit larger differences than the cases. Monte Carlo simulations demonstrate that the statistical theory underlying the methods is sound and that the methods are robust in the face of departures from normality. The methods have been implemented in computer programs, and these are described and made available (to download, go to http://www.abdn.ac.uk/~psy086/dept/Compare_Two_Cases.htm).

Keywords:

• Single-case methods
• Bayesian statistics
• Dissociations
• Neuropsychological methods
• Credible limits
• Multiple indicators

Notes

¹ As a reviewer pointed out, when raw scores are converted to scaled scores, some information is lost as, commonly, more than one raw score can be converted to the same scaled score. However, the practice is ubiquitous in neuropsychology, not least because it allows the neuropsychologist to refer a case's scores to normative values.