Median Test

Origins of the Median Test

The median of a set of scores is a measure of their central tendency defined as the value below which 50% of the scores fall. If the number of scores is odd, the median is the centermost score when they are ranked from the lowest to the highest. If the number of scores is even, the median is the average of the two centermost scores when they are ranked from the lowest to the highest.

The median test is employed to test the null hypothesis that the scores obtained by two independent groups are drawn from populations with [Page 1043]the same median. The first step is to find the overall median of the combined data (i.e., without regard to group membership). The scores within each group are then categorized in terms of whether they fall above or below the overall median. If the null hypothesis is true, then roughly half of the scores in each group should fall above the overall median and half should fall below the overall median. If the null hypothesis is false, the proportions in question would be expected to be different. Table 1 shows the outcome in a schematic form. This is simply an example of a 2 × 2 contingency table.

Source: Adapted from Siegel, S. (1956). Nonparametric statistics for the behavioral sciences (p. 111). New York, NY: McGraw-Hill. Copyright by the McGraw-Hill Book Company, Inc.

The median test was first described by Dutch biologist Jacob Westenberg in 1948. He referred to the earlier writings of Ronald A. Fisher on the analysis of 2 × 2 contingency tables and advocated the use of the Fisher exact probability test (described later in this entry) to analyze data of the sort shown in Table 1. Westenberg’s initial account assumed that the two groups being compared contained the same number of cases (so that the total number of cases was by definition an even number), but in 1950, he published a more general account allowing for unequal sample sizes. The same year, a U.S. statistician, Alexander M. Mood, independently derived the median test. He proposed that the Fisher exact probability test should be used to analyze the resulting contingency table if either group contained 10 cases or fewer, but that for larger samples, Karl Pearson’s chi-square test could be used instead. One of Mood’s colleagues, George W. Brown, demonstrated how the median test could be extended to encompass designs involving more than two groups. In this case, Pearson’s chi-square test would have to be used.

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