14.57 Rugby Injuries Knee injuries are a major problem for athletes in many contact sports. However, athletes who play certain positions are more prone to knee injuries than other players, and their injuries tend to be more severe. The preva- lence and patterns of knee injuries among women collegiate rugby players were investigated using a sample questionnaire, to which 42 rugby clubs responded. 21 A total of 76 knee injuries were classi- fied by type as well as the position (forward or back) of the player.

a. Use the MINITAB printout to determine whether there is a difference in the distribution of injury types for rugby backs and forwards. Have any of the assump- tions necessary for the chi-square test been violated? What effect will this have on the magnitude of the test statistic?

b. The investigators report a significant difference in the proportion of MCL tears for the two positions (P

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Type of Knee Injury Meniscal MCL ACL Patella PCL Position Tear Tear Tear Dislocation Tear Forward 13 14 7 3 Back 12 9 14 2 1 MINITAB output for Exercise 14.57 Chi-Square Test: Men Tear, MCL Tear, ACL Tear, Patella, PCL Tear Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts Men Tear MCL Tear ACL Tear Patella PCL Tear 13 12.50 0.020 14 11.50 7 3 1 Total 38 10.50 2.50 1.00 0.543 1.167 0.100 0.000 12 9 12.50 11.50 14 10.50 2 1 38 0.020 0.543 1.167 2.50 0.100 1.00 0.000 Total 25 23 21 5 76 Chi-Sq 3.660, DF = 4, P-value = 0.454 4 cells with expected counts less than 5.0