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

John Robertson Crawford, P. H. Garthwaite

Research output: Contribution to journalArticle

56 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)259-271
Number of pages12
JournalNeuropsychology
Volume20
DOIs
Publication statusPublished - 2006

Keywords

  • neuropsychological assessment
  • regression equations
  • single-case methods
  • TRUAX RELIABLE CHANGE
  • CLINICAL NEUROPSYCHOLOGY
  • CLASSICAL APPROACH
  • STANDARD ERROR
  • WAIS-R
  • INDEX
  • PERFORMANCE
  • JACOBSON

Cite this

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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 (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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N2 - 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.

AB - 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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KW - regression equations

KW - single-case methods

KW - TRUAX RELIABLE CHANGE

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KW - CLASSICAL APPROACH

KW - STANDARD ERROR

KW - WAIS-R

KW - INDEX

KW - PERFORMANCE

KW - JACOBSON

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