EXAMPLE 16.10 Software Results for Golf Scores

Here are the two-sided -values for the Wilcoxon signed rank test for the golf score data from several statistical programs:

All lead to the same practical conclusion: these data give no evidence for a systematic change in scores between rounds. However, the -values reported differ a bit from program to program. The reason for the variations is that the programs use slightly different versions of the approximate calculations needed when ties are present. The exact result depends on which of these variations the programmer chooses to use.

For these data, the matched pairs test gives with . Once again, and lead to the same conclusion.