title: 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.
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 (s-subN+1) to provide confidence limits on a predicted score and hence are tailored to the standard usage. However, s-subN+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.
authors.affiliation: School of Psychology, University of Aberdeen, Aberdeen, United Kingdom. j.crawford@abdn.ac.uk
authors.forename: John R
authors.initials: JR
authors.lastname: Crawford
authors.forename: Paul H
authors.initials: PH
authors.lastname: Garthwaite
mesh_terms: D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D006801:Humans; D009010:Monte Carlo Method; D009483:Neuropsychological Tests / Q000706:statistics & numerical data*; D011237:Predictive Value of Tests; D011594:Psychometrics; D012044:Regression Analysis; D012680:Sensitivity and Specificity; D014894:Weights and Measures