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Educational and Psychological Measurement
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Tests of Significance for Differences in Counts of Rare Events in Two Treatment Groups

Kritina L. Holden

Department of Psychiatry and Behavioral Sciences, University of Texas Medical School at Houston

John E. Overall

Department of Psychiatry and Behavioral Sciences, University of Texas Medical School at Houston

Counts of rare events tend to have Poisson or J-shaped distributions that render parametric assumptions questionable. Six different methods for testing the significance of the difference between location parameters for two such distributions are evaluated in this article. A binomial test for the difference between means is known to be the most powerful unbiased test when population distributions are truly Poisson; however, it appears extremely non-robust against departures from the distributional assumption. Robust enough to provide appropriate protection against Type I error, Student's t test was among the most powerful of the tests when applied to counts of rare events in two treatment groups. The Mann-Whitney sum of ranks test also provided superior alpha protection and power even where a large number of tied ranks occurred in the zero-count category of a J-shaped distribution. Finally, a 1 df chi-square test for linear shift in proportional representation across frequency categories of one group as opposed to the other was the most powerful of three chi-square tests that were evaluated.

Educational and Psychological Measurement, Vol. 47, No. 4, 881-892 (1987)
DOI: 10.1177/0013164487474003
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