### Abstract

Frequentist methods are available for comparison of a patient's test score ( or score difference) to a control or normative sample; these methods also provide a point estimate of the percentage of the population that would obtain a more extreme score ( or score difference) and, for some problems, an accompanying interval estimate ( i.e., confidence limits) on this percentage. In the present paper we develop a Bayesian approach to these problems. Despite the very different approaches, the Bayesian and frequentist methods yield equivalent point and interval estimates when ( a) a case's score is compared to that of a control sample, and ( b) when the raw ( i.e., unstandardized) difference between a case's scores on two tasks are compared to the differences in controls. In contrast, the two approaches differ with regard to point estimates of the abnormality of the difference between a case's standardized scores. The Bayesian method for standardized differences has the advantages that ( a) it can directly evaluate the probability that a control will obtain a more extreme difference score, ( b) it appropriately incorporates error in estimating the standard deviations of the tasks from which the patient's difference score is derived, and ( c) it provides a credible interval for the abnormality of the difference between an individual's standardized scores; this latter problem has failed to succumb to frequentist methods. Computer programs that implement the Bayesian methods are described and made available.

Original language | English |
---|---|

Pages (from-to) | 343-372 |

Number of pages | 30 |

Journal | Cognitive Neuropsychology |

Volume | 24 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2007 |

### Keywords

- monte-carlo-simulation
- test score differences
- subtest scatter
- WAIS-R
- statistical-methods
- dissociations
- abnormality
- deficit
- index
- power

### Cite this

*Cognitive Neuropsychology*,

*24*(4), 343-372. https://doi.org/10.1080/02643290701290146

**Comparison of a single case to a control or normative sample in neuropsychology : Development of a Bayesian approach.** / Crawford, John Robertson; Garthwaite, Paul H.

Research output: Contribution to journal › Article

*Cognitive Neuropsychology*, vol. 24, no. 4, pp. 343-372. https://doi.org/10.1080/02643290701290146

}

TY - JOUR

T1 - Comparison of a single case to a control or normative sample in neuropsychology

T2 - Development of a Bayesian approach

AU - Crawford, John Robertson

AU - Garthwaite, Paul H.

PY - 2007

Y1 - 2007

N2 - Frequentist methods are available for comparison of a patient's test score ( or score difference) to a control or normative sample; these methods also provide a point estimate of the percentage of the population that would obtain a more extreme score ( or score difference) and, for some problems, an accompanying interval estimate ( i.e., confidence limits) on this percentage. In the present paper we develop a Bayesian approach to these problems. Despite the very different approaches, the Bayesian and frequentist methods yield equivalent point and interval estimates when ( a) a case's score is compared to that of a control sample, and ( b) when the raw ( i.e., unstandardized) difference between a case's scores on two tasks are compared to the differences in controls. In contrast, the two approaches differ with regard to point estimates of the abnormality of the difference between a case's standardized scores. The Bayesian method for standardized differences has the advantages that ( a) it can directly evaluate the probability that a control will obtain a more extreme difference score, ( b) it appropriately incorporates error in estimating the standard deviations of the tasks from which the patient's difference score is derived, and ( c) it provides a credible interval for the abnormality of the difference between an individual's standardized scores; this latter problem has failed to succumb to frequentist methods. Computer programs that implement the Bayesian methods are described and made available.

AB - Frequentist methods are available for comparison of a patient's test score ( or score difference) to a control or normative sample; these methods also provide a point estimate of the percentage of the population that would obtain a more extreme score ( or score difference) and, for some problems, an accompanying interval estimate ( i.e., confidence limits) on this percentage. In the present paper we develop a Bayesian approach to these problems. Despite the very different approaches, the Bayesian and frequentist methods yield equivalent point and interval estimates when ( a) a case's score is compared to that of a control sample, and ( b) when the raw ( i.e., unstandardized) difference between a case's scores on two tasks are compared to the differences in controls. In contrast, the two approaches differ with regard to point estimates of the abnormality of the difference between a case's standardized scores. The Bayesian method for standardized differences has the advantages that ( a) it can directly evaluate the probability that a control will obtain a more extreme difference score, ( b) it appropriately incorporates error in estimating the standard deviations of the tasks from which the patient's difference score is derived, and ( c) it provides a credible interval for the abnormality of the difference between an individual's standardized scores; this latter problem has failed to succumb to frequentist methods. Computer programs that implement the Bayesian methods are described and made available.

KW - monte-carlo-simulation

KW - test score differences

KW - subtest scatter

KW - WAIS-R

KW - statistical-methods

KW - dissociations

KW - abnormality

KW - deficit

KW - index

KW - power

U2 - 10.1080/02643290701290146

DO - 10.1080/02643290701290146

M3 - Article

VL - 24

SP - 343

EP - 372

JO - Cognitive Neuropsychology

JF - Cognitive Neuropsychology

SN - 0264-3294

IS - 4

ER -