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Unformatted text preview: Stat 665 (Spring 2011) Kaizar Solutions 3 Exercises 40 points total 1. (a) Yes No Jamar 186 172 Kosta 90 73 (b) Marginal OR: 186 * 73 90 * 172 = 0 . 877 Conditional OR, 3-pointer: 1 . 157 Conditional OR, other: 7 . 461 (c) plotvals 0.0 0.5 1.0 1.5 risk of made = Yes Jamar Kosta Three Other M M (d) This is an example of Simpsons Paradox because the marginal odds ratio favors Kosta in shooting accuracy, whereas the conditional odds ratios favor Jamar in both three- point shots and other shots. This example contains the two things needed for Simpsons Paradox to occur: 1 The number of three-point shots is related to player (Jamar attempts many more three-point shots) The number of three-point shots is related to the number of made shots (three-point shots are much less successful) (e) Mantel-Haenszel X-squared = 9.334, df = 1, p-value = 0.002249 Because the p-value is so small, I reject the null hypothesis and conclude that there is an association between player and shots made, for at least one type of shot. (f) Of course, the choice depends on the type of player the team needs most. However, I would choose Jamar, since he is a more successful shot, regardless of the type of shot made. I.e., the conditional odds ratios both favor Jamar....
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