Comparing patients' predicted test scores from a regression equation with their obtained scores: A significance test and point estimate of abnormality with accompanying confidence limits

Crawford, John R. and Garthwaite, Paul (2006). Comparing patients' predicted test scores from a regression equation with their obtained scores: A significance test and point estimate of abnormality with accompanying confidence limits. Neuropsychology, 20(3) pp. 259–271.

DOI: https://doi.org/10.1037/0894-4105.20.3.259

Abstract

In contrast to the standard use of regression, in which an individual's score on the dependent variable is unknown, neuropsychologists are often interested in comparing a predicted score with a known obtained score. Existing inferential methods use the standard error for a new case (SN+1) to provide confidence limits on a predicted score and hence are tailored to the standard usage. However, SN+1 can be used to test whether the discrepancy between a patient's predicted and obtained scores was drawn from the distribution of discrepancies in a control population. This method simultaneously provides a point estimate of the percentage of the control population that would exhibit a larger discrepancy. A method for obtaining confidence limits on this percentage is also developed. These methods can be used with existing regression equations and are particularly useful when the sample used to generate a regression equation is modest in size. Monte Carlo simulations confirm the validity of the methods, and computer programs that implement them are described and made available.

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