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Unformatted text preview: 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 : 1 = 2 = = 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 and SSB = T 2 1 n 1 + T 2 2 n 2 + - (...
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- Fall '09