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EQUIVALENT TEST STATISTIC
Within a RANDOMISATION SET, it is possible that two different STATISTICs may be inter-related in a manner which is provably monotonic irrespective of the data. In such a situation a RANDOMISATION TEST performed on either of these TEST STATISTICs will necessarily have the same outcome in terms of ALPHA. If one of the STATISTICs is of good descriptive validity whereas the other is simpler to compute, then a RANDOMISATION TEST upon the simpler STATISTIC may be used in place of a test upon the descriptively more valid one, with corresponding savings in amount of computation required. An example of such EQUIVALENT TEST STATISTICs occurs for the situation of comparison of levels of a single INTERVAL-SCALE variable between two groups. In this situation, the descriptively valid statistic, as defined for the PITMAN PERMUTATION TEST(1), is the difference of means, but simpler EQUIVALENT TEST STATISTICS include the mean for one designated group, or (most simply) the total of scores in one designated group.
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