Median test

In statistics, Mood's median test is a special case of Pearson's chi-squared test. It is a nonparametric test that tests the null hypothesis that the medians of the populations from which two samples are drawn are identical. The data in each sample are assigned to two groups, one consisting of data whose values are higher than the median value in the two groups combined, and the other consisting of data whose values are at the median or below. A Pearson's chi-squared test is then used to determine whether the observed frequencies in each group differ from expected frequencies derived from a distribution combining the two groups.

The test has low power (efficiency) for moderate to large sample sizes, and is largely regarded as obsolete. The Wilcoxon–Mann–Whitney U two-sample test should be considered instead. Siegel & Castellan (1988, p. 124) suggest that there is no alternative to the median test when one or more observations are "off the scale." The relevant difference between the two tests is that the median test only considers the position of each observation relative to the overall median, whereas the Wilcoxon–Mann–Whitney test takes the ranks of each observation into account. Thus the latter test is usually the more powerful of the two.

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See also

• Sign test - a paired alternative to the median test.

References

• Corder, G.W., Foreman, D.I. (2009).Nonparametric Statistics for Non-Statisticians: A Step-by-Step Approach Wiley, ISBN 9780470454619
• Siegel, S., & Castellan, N. J. Jr. (1988, 2nd ed.). Nonparametric statistics for the behavioral sciences. New York: McGraw–Hill.
• Friedlin, B. & Gastwirth, J. L. (2000). Should the median test be retired from general use? The American Statistician, 54, 161–164.