Section 14.3 Summary

1. A distribution is symmetric if a line (axis of symmetry) splits the image in half so that one side is the mirror image of the other. A data set is symmetric when its corresponding boxplot has whiskers of approximately equal length, and the median line is situated approximately in the center of the box.
2. The Wilcoxon signed rank test takes the magnitude of the data into account by ranking the data values. The Wilcoxon signed rank test can be applied to matched-pair data from two dependent samples. The hypotheses for the Wilcoxon signed rank test for the population median of the differences are the same as those for the corresponding sign test.
3. The Wilcoxon signed rank test for a single population median is comparable to the sign test for the population median. The hypotheses are the same, there are small-sample and large-samples cases, and the test statistic depends on the form of the hypotheses.