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A simple recommendation for the analysis of matching data.
Psychological Methods  (IF10.929),  Pub Date : 2022-01-27, DOI: 10.1037/met0000474
Douglas W. Levine

The matching paradigm can take a number of forms and has been used in many areas of psychology. When participants are asked to match or order sets of objects, researchers must correctly account for the number of matches expected purely by chance. Not accounting for the expected chance matches can lead to incorrectly drawing conclusions based on one's data. This study demonstrated that the z test can be an appropriate and easy test to use in the analysis of matching data from studies that require pairs of objects to be matched with each other. This article proves that in a matching paradigm the expected number of chance matches is 1.0 and the associated variance is also 1.0. The z test is shown to maintain the Type I error close to the nominal significance level when the null hypothesis is true and the sample size is at least 80 or 110. To attain power of .80, a sample size larger than 80 may be needed depending upon the effect size associated with the area of interest and the hypothesized alternative probability distribution.