Ch 16 - ANOVA

Consequently several procedures have been developed

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Unformatted text preview: set of all pairwise comparisons among population means. In our previous Drug example, the possible pairwise comparisons are: Drug 1 with Drug 2, Drug 1 with Drug 3, and Drug 2 with Drug 3. To compare the pair of means we could … Compute a confidence interval for the difference between the two population means and see if 0 falls in the interval or not. Perform a test of hypotheses to assess if the two population means differ significantly. When many statistical tests are done there is an increased risk of making at least one type I error (erroneously rejecting a null hypothesis). Consequently, several procedures have been developed to control the overall family type I error rate or the overall family confidence level when inferences for a set (family) of multiple comparisons are done. Tukey’s procedure is one such procedure for the family of pairwise comparisons. If the family error rate is not a concern, Fisher’s procedure is used. Try It! Comparing 3 Drugs In the comparison of the three drugs, we rejected the null hypothesis at the 5% significance level. We follow with a multiple comparison procedure to determine which group means are significantly different from each other. SPSS multiple comparisons using Tukey's method and a family confidence level of 95%: Multiple Comparisons Dependent Variable: TIME Tukey HSD (I) DRUG 1 2 3 (J) DRUG 2 3 1 3 1 2 Mean Difference (I-J) -1.0800 1.4200 1.0800 2.5000* -1.4200 -2.5000* Std. Error .9485 .9485 .9485 .8659 .9485 .8659 Sig. .505 .318 .505 .027 .318 .027 95% Confidence Interval Lower Bound Upper Bound -3.5276 1.3676 -1.0276 3.8676 -1.3676 3.5276 .2657 4.7343 -3.8676 1.0276 -4.7343 -.2657 *. The mean difference is significant at the .05 level. a. Use the above output to report about the three pairwise comparisons: Does the confidence interval for 1 2 contain 0? ___Yes____ Does the confidence interval for 1 3 contain 0? ___Yes____ Does the confidence interval for 2 3 contain 0? ___No_...
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