A new nonparametric test for the equality of two populations is proposed. The test is a generalization of the Girone-Cifarelli test (see Girone (1964) and Cifarelli (1974, 1975)) which has been shown to be occasionally more powerful than other nonparametric tests, such as the Kolmogorov-Smirnov test. The test is based on a measure of dissimilarity between the sequences of ranks corresponding to the samples drawn from the two populations. The test can be adapted to verify the hypothesis of equality against one-sided and two-sided alternatives. Exact and asymptotic critical values of the test are provided. The asymptotic distribution of the test-statistic under H_0 shows an interesting link with brownian motion in [0,1].
Borroni, C. (2001). Some notes about nonparametric tests for the equality of two populations. TEST, 10(1), 147-159 [10.1007/BF02595829].
Some notes about nonparametric tests for the equality of two populations
BORRONI, CLAUDIO GIOVANNI
2001
Abstract
A new nonparametric test for the equality of two populations is proposed. The test is a generalization of the Girone-Cifarelli test (see Girone (1964) and Cifarelli (1974, 1975)) which has been shown to be occasionally more powerful than other nonparametric tests, such as the Kolmogorov-Smirnov test. The test is based on a measure of dissimilarity between the sequences of ranks corresponding to the samples drawn from the two populations. The test can be adapted to verify the hypothesis of equality against one-sided and two-sided alternatives. Exact and asymptotic critical values of the test are provided. The asymptotic distribution of the test-statistic under H_0 shows an interesting link with brownian motion in [0,1].
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