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Some changes to Chapter 7

# Some changes to Chapter 7 - Chapter 7 The Two-Way Layout...

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Chapter 7 The Two-Way Layout Some Changes to pages 9 – 12: 7.4 One-sided Comparisons of Treatments with Control Based on Friedman Rank Sums (Nemenyi, Wilcoxon – Wilcox, Miller) Used after rejecting the null hypothesis of no difference between treatment effects. Compares each treatment with a control group (call it treatment 1). Hypotheses of interest are Ho: τ u = τ 1 vs. Ha: τ u > τ 1 for all u = 2, 3, …, k with decision Rule: Decide τ u > τ 1 if (R u – R 1 ) ≥ r* α . Or Ha: τ u > τ 1 for all u = 2, 3, …,k with decision rule τ 1 < τ u if (R 1 – R u ) ≥ r* α . Example: Use the hydrobromide data of the example on page 3 (copied below) to test whether any of the hydrobromides produce a higher average number of hours of sleep per night that does the “no hypnotic,” i.e., treatment A. Patient A B C D 1 0.6 (1) 1.3 (2) 2.5 (4) 2.1 (3) 2 1.1 (1.5) 1.1 (1.5) 5.7 (3) 5.8 (4) 3 2.5 (1) 6.2 (2) 8 (3) 8.2 (4) 4 2.8 (1) 3.6 (2) 4.4 (4) 4.3 (3) 5 2.9 (1) 4.9 (2) 6.3 (3) 6.4 (4) 6 3.0 (2) 1.4 (1) 3.8 (3) 4.4 (4) R j (7.5) (10.5) (20) (22) We are interested in testing Ho: τ u = τ 1 vs. Ha: τ u > τ 1 , for all u = 2, 3, 4 simultaneously. From Table A25, with n = 6, k = 4 and α = 0.0404, we find Hence we will decide τ u > τ 1 if R u – R 1 ≥ 10. Show that, from the observed data we have R 1 = 7.5, R 2 = 10.5, R 3 = 20 and R 4 = 22 and hence Hence we decide that Treatments C and D are better than control (Treatment A), the others are not different from the control.

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