EXAMPLE 16.9 Two Rounds of Golf Scores

golf

Here are the golf scores of 12 members of a college women’s golf team in two rounds of tournament play. (A golf score is the number of strokes required to complete the course, so that low scores are better.)

16-20

Player 1 2 3 4 5 6 7 8 9 10 11 12
Round 2 94 85 89 89 81 76 107 89 87 91 88 80
Round 1 89 90 87 95 86 81 102 105 83 88 91 79
Difference 5 −5 2 −6 −5 −5 5 −16 4 3 −3 1

Negative differences indicate better (lower) scores on the second round. We see that six of the 12 golfers improved their scores. We would like to test the hypotheses that in a large population of collegiate woman golfers

  • : scores have the same distribution in rounds 1 and 2
  • : scores are systematically lower or higher in round 2

A Normal quantile plot of the differences (Figure 16.8) shows some irregularity and a low outlier. We will use the Wilcoxon signed rank test.

image
Figure 16.8: FIGURE 16.8 Normal quantile plot of the differences in scores for two rounds of a golf tournament, Example 16.9.