Chapter 27

Comparing two samples: the Wilcoxon rank sum test

1. Describe useful exploratory plots to generate before performing Wilcoxon’s Rank Sum Test, and interpret exploratory plots in this context.
2. Define the rank of a data value in a sample.
3. Explain the rationale for Wilcoxon’s Rank Sum Test for comparing two population distributions.
4. State Wilcoxon’s Rank Sum Test Statistic \(W\).
5. Given a (small) combined sample with the associated ranks, compute Wilcoxon’s Rank Sum Test Statistic.
6. State appropriate null and alternative hypotheses for Wilcoxon’s Rank Sum Test, given a claim about two populations.
7. Perform Wilcoxon’s Rank Sum Test using wilcox.test in R.
8. Interpret wilcox.test’s output for the Rank Sum Test.

Matched pairs: the Wilcoxon signed rank test

1. Describe useful exploratory plots to generate before performing Wilcoxon’s Signed Rank Test, and interpret exploratory plots in this context.
2. Explain the rationale for Wilcoxon’s Signed Rank Test for the median of a distribution.
3. State the assumption needed for Wilcoxon’s Signed Rank Test.
4. State Wilcoxon’s Signed Rank Test Statistic \(W^{+}\).
5. State appropriate null and alternative hypotheses for Wilcoxon’s Signed Rank Test, given a claim about a single population or two matched populations.
6. Perform Wilcoxon’s Signed Rank Test using wilcox.test in R.
7. Interpret wilcox.test’s output for the Signed Rank Test.