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Lesson #24 Multiple Comparisons

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When doing ANOVA, suppose we reject H 0 : 1 = 2 = 3 = … = k Next, we want to know which means differ. This does not protect the overall significance level, Do not perform a series of two-sample t-tests! which is the probability of making at least one Type I error in this series of comparisons.

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A good multiple comparison procedure protects this overall significance level. It is not “inflated”, as it would be with a series of simple t-tests, each performed at =.05. Many such procedures exist: - Scheffe’ (conservative) - Tukey (developed for pairwise comparisons) - Bonferroni (divide overall by # tests) - Duncan (liberal)

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Each procedure compares the difference of sample means to a “critical range”, or “minimum significant difference”, which depend on: We conclude that population means differ if their corresponding sample means differ by at least the minimum significant difference. - the procedure being used - the overall significance level, - k (the number of “treatments”) - sample sizes - MS ERROR

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