SECTION 16.1 Summary

• Nonparametric tests do not require any specific form for the distribution of the population from which our samples come.
• Rank tests are nonparametric tests based on the ranks of observations, their positions in the list ordered from smallest (rank 1) to largest. Tied observations receive the average of their ranks.
• The Wilcoxon rank sum test compares two distributions to assess whether one has systematically larger values than the other. The Wilcoxon test is based on the Wilcoxon rank sum statistic , which is the sum of the ranks of one of the samples. The Wilcoxon test can replace the two-sample test.
• -values for the Wilcoxon test are based on the sampling distribution of the rank sum statistic when the null hypothesis (no difference in distributions) is true. You can find -values from special tables, software, or a Normal approximation (with continuity correction).