Mini 11 One-Way ANOVA

Mini 11 One-Way ANOVA Does a baseball player's salary depend on the position that he plays? The following data depict the 2005 season salaries (in millions of dollars) for players randomly selected from all players in their respective positions in the National Baseball League. The data is below. The statistical results are provided for you. 1. Complete the other steps of hypothesis testing, including the conclusion given the results below. a. State: i. H0: μ pitcher = μcatcher = μoutfielder = μ shortstop ii. H1: μ pitcher ≠ μcatcher ≠ μoutfielder≠ μshortstop b. Plan i. 1 nominal IV 3 ≤levels and 1 DV scale (ratio or interval) ii. Random selection: All positions and players were selected at random with different skill levels and experience playing baseball. iii. Normal distribution: all positions and players came from a normally distributed population with equal variances iv. Cut off 1. DF between = 4 − 1 = 3 2. DF within =( 20 − 1 ) , ( 19 − 1 ) , ( 18 − 1 ) , ( 17 − 1 )= 16 3. N = 20 ,K = 4 ,Cut off F ( 4,20 )= 3.10 c. Do: Salary Sum of Squares df Mean Square F Sig. Between Groups 5.458 3 1.819 .272 .845 Within Groups 107.063 16 6.691 Total 112.521 19 d. Conclude: i. Fail to reject null hypothesis, not statistically significant enough ii. F = 0.272 < 3.10 , P > 0.05 2. Given the results, is it appropriate to conduct a post-hoc test, and why or why not? What results in particular would you look for in the post-hoc analyses? a. No it wouldn’t because F = 0.272 is not statistically significant enough to conduct a post-hoc test, it wouldn’t be necessary to. Table: Baseball Salaries and Positions

Pitcher Catcher Outfielder Shortstop 0.600 0.650 1.350 0.322 6.050 3.000 7.750 8.250 3.000 0.750 0.575 0.445 0.750 3.133 3.100 3.400 1.600 0.324 2.325 0.318 Stat 95 Assignment: Comparing Three Means using One-Way ANOVA and Post- Hoc Tests Using SPSS Scenario : Dr. Olson is interested in the effects of three different methods for losing weight in long-distance truck-drivers. He tested a sample of 60 truck drivers. Participants were randomly assigned to one of three groups of 20 people each. Participants in the Diet-Only group followed a low-calorie diet but did not exercise. Participants in the Exercise-only group followed an exercise regimen but did not change their diet. Participants in the Diet + Exercise group followed both a low-calorie diet and an exercise regimen. Dr. Olson measured the number of pounds each individual lost after 6 months. Diet-Only Group Exercise-Only Group Diet+Exercise Group 5 9 15 7 10 18 10 8 20 10 11 22

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