The paper “Quantitative Assessment of Glenohumeral Translation in Baseball Players” (The Amer. J. of Sports Med., 2004: 1711–1715) considered various aspects of shoulder motion for a sample of pitchers and another sample of position players [glenohumeral refers to the articulation between the humerus (ball) and the glenoid (socket)]. The authors kindly supplied the following data on anteroposterior translation (mm), a measure of the extent of anterior and posterior motion, both for the dominant arm and the nondominant arm.
Pos Dom Tr | Pos ND Tr | Pit Dom Tr | Pit ND Tr | |
1 | 30.31 | 32.54 | 27.63 | 24.33 |
2 | 44.86 | 40.95 | 30.57 | 26.36 |
3 | 22.09 | 23.48 | 32.62 | 30.62 |
4 | 31.26 | 31.11 | 39.79 | 33.74 |
5 | 28.07 | 28.75 | 28.50 | 29.84 |
6 | 31.93 | 29.32 | 26.70 | 26.71 |
7 | 34.68 | 34.79 | 30.34 | 26.45 |
8 | 29.10 | 28.87 | 28.69 | 21.49 |
9 | 25.51 | 27.59 | 31.19 | 20.82 |
Pos Dom Tr | Pos ND Tr | Pit Dom Tr | Pit ND Tr | |
10 | 22.49 | 21.01 | 36.00 | 21.75 |
11 | 28.74 | 30.31 | 31.58 | 28.32 |
12 | 27.89 | 27.92 | 32.55 | 27.22 |
13 | 28.48 | 27.85 | 29.56 | 28.86 |
14 | 25.60 | 24.95 | 28.64 | 28.58 |
15 | 20.21 | 21.59 | 28.58 | 27.15 |
16 | 33.77 | 32.48 | 31.99 | 29.46 |
17 | 32.59 | 32.48 | 27.16 | 21.26 |
18 | 32.60 | 31.61 | ||
19 | 29.30 | 27.46 | ||
29.4463 | 29.2137 | 30.7112 | 26.6447 | |
sd | 5.4655 | 4.7013 | 3.3310 | 3.6679 |
a. Estimate the true average difference in translation between dominant and nondominant arms for pitchers in a way that conveys information about reliability and precision, and interpret the resulting estimate.
b. Repeat (a) for position players.
c. The authors asserted that “pitchers have greater difference in side-to-side anteroposterior translation of their shoulders compared with position players.” Do you agree? Explain.
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Probability and Statistics for Engineering and the Sciences
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