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Mood (1, p. 394) discusses a test for the hypothesis that two samples come from populations having the same continuous cumulative frequency distributions. It consists of arranging the observations from the two samples in a single group in order of size and then comparing the numbers in the two samples above the median. This technique is extended to using several order statistics from the combined samples, and to the case of several samples. The test is non-parametric and might be a good substitute for the single variable of classification analysis of variance in cases of doubtful normality. The application of the test would be the same as in Mood (1, p. 398) except that there would be more than two rows in the table.
Frank J. Massey (Fri,) studied this question.