Payne and Jones revisited: Estimating the abnormality of test score differences using a modified paired samples t-test

Crawford, J. R.; Howell, David C. and Garthwaite, Paul H. (1988). Payne and Jones revisited: Estimating the abnormality of test score differences using a modified paired samples t-test. Journal of Clinical and Experimental Neuropsychology, 20(6) pp. 898–905.

DOI: https://doi.org/10.1076/jcen.20.6.898.1112

Abstract

Payne and Jones (1957) presented a useful formula for estimating the abnormality of differences between an individual's scores on two tests. Extending earlier work by Sokal and Rohlf (1995) and Crawford and Howell tin press), we developed a modified paired samples t test as an alternative to this formula. Unlike the Payne and Jones formula, the new method treats data from a normative or control sample as sample statistics rather than as population parameters. Technically, the new method is more appropriate for any comparison of an individual's difference score against normative data. However, it is most useful when the normative data is derived from samples with modest Ns: in these circumstances the Payne and Jones method overestimates the abnormality of differences. We suggest that the modified t test can be a useful tool in clinical practice and in single-case research. A computer program is made available that automates the calculations involved and can be used to store relevant data for future use.

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