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Tukey pocket test


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A simple slippage test (see test for equality of location) of the hypothesis that two samples have been drawn from the same distribution.

Suppose the largest observation is in sample 1. Tukey's test statistic, T, is calculated as follows: 1. If the smallest observation is in sample 1, T=0.2. Otherwise T is the sum of the number of observations in sample 1 that are larger than the largest observation in sample 2 and the number of observations in sample 2 that are smaller than the smallest observation in sample 1.Not only is the statistic easy to calculate, but its distribution is remarkably unaffected by the sample sizes. As a guide, T is significant at the 5% level if T > 7 the corresponding values for the 1% and 0.1% levels are 9 and 13, respectively. See test for equality of distribution.

1. If the smallest observation is in sample 1, T=0.

2. Otherwise T is the sum of the number of observations in sample 1 that are larger than the largest observation in sample 2 and the number of observations in sample 2 that are smaller than the smallest observation in sample 1.

Subjects: Probability and Statistics.


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