Crawford, J. R. and Garthwaite, P. H.
(2007).
*Cognitive Neuropsychology*, 24(4) pp. 343–372.

DOI (Digital Object Identifier) Link: | http://dx.doi.org/10.1080/02643290701290146 |
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Google Scholar: | Look up in Google Scholar |

## 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.

Item Type: | Journal Article |
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Copyright Holders: | 2007 Psychology Press |

ISSN: | 1464-0627 |

Academic Unit/Department: | Mathematics, Computing and Technology > Mathematics and Statistics Mathematics, Computing and Technology |

Item ID: | 15578 |

Depositing User: | Colin Smith |

Date Deposited: | 22 Apr 2009 15:57 |

Last Modified: | 15 Jan 2016 11:08 |

URI: | http://oro.open.ac.uk/id/eprint/15578 |

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