21_anova4

# 21_anova4 - Two-way ANOVA II Post-hoc comparisons two-way...

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Two-way ANOVA, II 9.07 4/29/2004 Post-hoc comparisons & two-way analysis of variance obt procedure equal • This is just like post-hoc testing for the one- way ANOVA Post-hoc testing As before, you can perform post-hoc tests whenever there’s a significant F – But don’t bother if it’s a main effect and has only two levels – you already know the answer We’ll just talk about the Tukey’s HSD – Requires that the n’s in all levels of a factor are Post-hoc testing for main effects 1

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just like what we did for one-way ANOVA n MS q HSD wn αα = α α q statistic based on alpha, df W k , the number of levels wn MS Is the mean square within groups. n I.E. how many numbers did you average to get each mean you are comparing? No The workbook helps. Post-hoc testing for main effects is is the Type I error rate (.05). Is a value from a table of the studentized range , and in the factor you are testing Is the number of people in each group. Our example from last time What effect do a workbook and coffee consumption have on exam performance? Both main effects and the interaction were significant Factor A (the workbook) had only two levels. post-hoc testing required. Factor B (the coffee) had three levels. We need to do post-hoc testing. Numbers from our example last time wn = 205.56 •q k df wn and k wn = 12 k = 3.77 for α Σ n B3 = 6 Σ n B2 = 6 Σ n B1 = 6 90, 85, 75 30, 40, 20 2 Cups of coffee (Factor B) 40, 60, 65 45, 50, 85 1 20, 45, 55 10, 30, 20 0 k sqrt(MS wn /n) m 3 = 56.7 m 2 = 57.5 m 1 =30 Level 3: 2 cups Level 2: 1 cup Level 1: 0 cups 27.5 0.9 26.7 •M S •n = 6 is a function of –d f –k = 3 So, from the table, q =0.05 x = 340 x = 345 x = 180 HSD for this example
m =83.33 m = 30 2 Cups of (Factor B) m = 55 m = 60 1 m = 40 m = 20 0 Yes No Workbook Confounded & unconfounded comparisons m =83.33 m = 30 2 Cups of (Factor B) m = 55 m = 60 1 m = 40 m = 20 0 Yes No Workbook there’s a confound . Post-hoc testing for the interaction Involves comparing cell means But we don’t compare every possible pair of cell means… coffee (Factor A) coffee (Factor A) Confounded comparison, because the cells differ along more than one factor. If there’s a difference, what’s the explanation? Is it because of factor A or B? We can’t tell, because Confounded & unconfounded comparisons m =83.33 m = 30 2 Cups of (Factor B) m = 55 m = 60 1 m = 40 m = 20 0 Yes No Workbook We can test these with post-hoc tests. (1) (2) k sqrt(MS wn /n) k wn and k, the number of compared adjusted comparisons (as coffee (Factor A) Unconfounded comparisons. The cells differ only in one factor. Tukey’s HSD for interactions

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21_anova4 - Two-way ANOVA II Post-hoc comparisons two-way...

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