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Abstract:
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A new hypothesis test, called the difference test, is presented for testing whether two normal populations have both equal means and equal standard deviations. First, a new parameterization scheme is presented that describes the difference in the populations in terms of a primary 'distance' parameter and a secondary 'orientation' parameter. The type I error and power properties for the difference test for various values of the primary and secondary parameters is then compared to those for four other tests: the likelihood ratio test, the Sukhatme test, the Welch t-test for the equality of means, and the F-test for the equality of variances. The distance test has favorable power properties for large sample sizes and also for small samples when the difference in the populations is due primarily to the difference in the means. A complete table of critical values is included.
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