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slide12 - Chapter 12 Analysis of Variance Bin Wang 1 The F...

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Chapter 12: Analysis of Variance Bin Wang 1 The F Distribution Definition 1.1 (The F distribution) The F distribution is continuous and skewed to the right; assumes non-negative values. has two parameters: degrees of freedom for the numerator df 1 and degrees of freedom for the denominator df 2 . We denote an F distribution as F df 1 ,df 2 . Use the F table: for each level of significance, we have a separate F table. In each table, the F values are given for each pair of parameters df = ( df 1 , df 2 ). 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 + · · · - ( x ) 2 n , SSW = X x 2 - T 2 1 n 1 + T 2 2 n 2 + · · · , and T 1 = n 1 X i =1 x 1 i , T 2 = n 2 X i
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