Question 1083114: Ads for a baseball instructional video claimed it would improve the performances of young pitchers. To test this claim, 20 kids each threw 50 pitches before and after participation in the program, and the number of strikes was recorded. The accompanying table shows the number of strikes each player threw before and after the training. A test of paired differences failed to show that this training improves ability to throw strikes. Is there any evidence that the effectiveness of the video (Afterminus−Before) depends on the player's initial ability to throw strikes (Before)? Test an appropriate hypothesis. Use a significance level of 0.05.
Before,After
28,34
29,32
29,32
30,35
31,34
32,32
32,33
33,33
34,32
34,35
35,34
35,34
36,33
37,33
38,34
38,32
40,33
40,34
41,34
41,34
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 28,34===35,34 W
29,32===35,34 W
29,32===36,33 W
30,35===37,33 W
31,34===38,34 W
32,32===38,32 W
32,33===40,33 W
33,33===40,34 W
34,32===41,34 W
34,35===41,34 W
I used the Cox-Stuart test, which pairs the first half and the second half. If there were no difference between the initial value, there should be the same number of improvements vs. worsening. There is a clear difference between the two groups relative to the initial number of strikes. This is also good for comparing temperatures, for example, so 1901 is compared to 1951, 1920 to 1970, and so forth.
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