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Chapter 12: Analysis of Variance Bin Wang 1 One-Way ANOVA Test Example 1.1 (Example 12-2) Fifteen fourth-grade students were randomly assigned to three groups to experiment with three different methods of teaching arithmetic. At the end of the semester, the same test was given to all 15 students. The table gives the scores of students in the three groups. Method I Method II Method III 48 55 84 73 85 68 51 70 95 65 69 74 87 90 67 2 One-Way ANOVA Data: Treatments treatment 1 treatment 2 ··· treatment k x 11 x 21 ··· x k 1 x 11 x 22 ··· x k 2 . . . . . . . . . . . . x 1 n 1 x 2 n 2 ··· x kn k Hypotheses: H 0 : μ 1 = μ 2 = ··· = μ k ; H 1 : not all means are equal (at least two of the means are not equal). Test statistic: F = V ariance between samples V ariance within samples = MSB MSW , where MSB = SSB k - 1 and MSW = SSW n - k , 1
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and SSB = ± T 2 1 n 1 + T 2 2 n 2 + ··· ² - ( x ) 2 n , SSW = X x 2 - ± T 2 1 n 1 + T 2 2 n 2 + ··· ² , and T 1 = n 1 X i =1 x 1 i , T
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slide12 - Chapter 12: Analysis of Variance Bin Wang 1...

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