Chapter 13 Outline Section 3

Chapter 13 Outline Section 3 - III. Multiple Comparison...

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III. Multiple Comparison Procedures: Fisher’s LSD (least significant difference) A. The ANOVA procedure tells us only that not all means are equal. It does not tell us which mean pairs are not equal. B. We must use follow-up procedures to compare all pairwise means to see where the actual differences lie. (If the null is not rejected in the ANOVA procedure, MC procedures are not necessary)
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C. Hypothesis set for each pairwise comparison: H o : μ i = μ j H a : μ i μ j 1. Test Statistic is: j i X X - = = sample mean difference 2. Critical Difference = LSD = + j i n n MSE t 1 1 2 / α where 2 / t has df = k n T - 3. Rejection Rule: Reject the null hypothesis if the sample mean difference is greater than the critical difference; that is, reject if j i X X - > LSD. 4. There are k(k-1)/2 possible pairwise comparisons.
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D. Our example: H o : μ 1 = μ 2 = μ 3 H 1 : not all μ ’s are equal Remember: Source of Sum of Mean Variation Squares DF Square F
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Chapter 13 Outline Section 3 - III. Multiple Comparison...

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