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Most sports injuries are immediate and obvious, like a broken leg. However, some can be more subtle, like the neurological damage that may occur when soccer players repeatedly head a soccer ball. To examine effects of repeated heading, McAllister et al. (2013) examined a group of football and ice hockey players and a group of athletes in noncontact sports before and shortly after the season. The dependent variable was performance on a conceptual thinking task. Following are hypothetical data from an independent-measures study similar to the one by McAllister et al. The researchers measured conceptual thinking for contact and noncontact athletes at the beginning of their first season and for separate groups of athletes at the end of their second seasorn Factor A: Factor B: Time Sport Before the First Season After the Second Seasonn n 20 n20 Contact T= 180 SS = 380 n 20 T = 80 SS 390 n = 20 Noncontact T= 180 T 160 SS = 350 SS400 ZX2 6,360 Use a two-factor ANOVA with α = .05 to evaluate the main effects and interaction. Source df MS Between treatments Ax B Within treatments Total 80 180 80 1,520 1,860 80 180 80 20 4.000 9.000 4.000 76 79

F Distribution Numerator Degrees of Freedom-4 Denominator Degrees of Freedom 64 0.0 1.0 2.03.0 4.0 5.0 6.07.0 8.0 9.0 10.0 11.0 12.0 ДАЛ Use the Distributions tool to find the critical F values. (Use three decimal places.) F-criticalA- F-criticals F-criticalAXB 0.253 0.253 0.253 Is there a main effect for Factor A? Is there a main effect for Factor B? Is there an interaction? Calculate the effect size (n2) for the main effects and the interaction. (Use three decimal places.) nB AXB Briefly describe the outcome of the study. For the noncontact athletes, there is of the second season, but the contact athletes show noticeably difference between the beginning of the first season and the enc scores after the second season.

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