SECTION 16.2 Summary

• The Wilcoxon signed rank test applies to matched pairs studies. It tests the null hypothesis that there is no systematic difference within pairs against alternatives that assert a systematic difference (either one-sided or two-sided).
• The test is based on the Wilcoxon signed rank statistic , which is the sum of the ranks of the positive (or negative) differences when we rank the absolute values of the differences. The matched pairs test and the sign test are alternative tests in this setting.
• The Wilcoxon signed rank test can also be used to test hypotheses about a population median by applying it to a single sample.
• -values for the signed rank test are based on the sampling distribution of when the null hypothesis is true. You can find -values from special tables, software, or a Normal approximation (with continuity correction).