The basic logic of the Wilcoxon signed rank test is that if about half the data values fall above the hypothesized median, and about half fall below, the null hypothesis should not be rejected.

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The Wilcoxon signed rank test is a non-parametric statistical test used to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ. It is based on the ranks of the differences between pairs of observations, with the logic that if the median difference between pairs of observations is zero (or some hypothesized value), then about half of the differences should be positive and about half should be negative, assuming the distribution of differences is symmetric. If this is the case, it suggests that the median of the population from which the samples are drawn is likely consistent with the hypothesized median, leading to a failure to reject the null hypothesis.

The Basic Logic of the Wilcoxon Signed Rank Test Is