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The permutation test of the difference between two means is considered and compared with the ordinary t-test and Aspin-Welch test in cases where the two samples are from populations with different variances. Large-scale simulation was undertaken to generate and test many sets of data, and it is shown that for any given set of data, t-test and permutation test are in effect virtually identical. Further, some quantitative results on the sizes and power functions of the tests for various ratios of the population variances are given. The Aspin-Welch test is considered in the same way for certain samples sizes, and its usefulness and power quantitatively confirmed.
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