STAT 4080 Experimental Design Homework # 5 Due: 2/23/17 Problem 1 (HW#4 Problem 1 continued): Four contrasts of interest: 1 1. Control versus the combined experimental groups, 1 4 (2 +3 +4 + 5 ) 1 1 2. Drug A versus drug B, 2 (2 +3 ) 2 (4 +5 ) 3. Low versus high dosage for drug A, 2 3 4. Low versus high dosage for drug B, 4 5 a. Use Holm's Stepdown procedure to test the significance of the four contrasts ( = .05). b. Compare the result with that of Bonferroni's procedure. Are these results different? If so, in what ways are they different? Problem 2: You have run an experiment with four groups and 11 subjects per group. An analysis of variance gives a significant result. You wish to test a contrast 1 1 ( + 3 + 4 ), so you calculate its test statistic = SSCMSE = 7.0. 3 2 a. Assume that you planned the experiment to test this contrast. What is the critical value at 0.05 level? Is it significant? b. Assume that you noticed this effect when you were looking through the data after completing the study. What is the critical value for the test at 0.05 level? Is it significant? c. Explain the discrepancy between the two answers. Why should a result be significant or not depend on WHEN you decide to look at it? Problem 3 (Helpless Non-constant variance): An experiment was run to determine whether or not the germination rate of the endangered species of Ohio plant Froelichia floridana is affected by storage temperature or storage methods. The two levels of the factor \"temperature\" were \"spring temperature, 14C-24C\" and \"summer temperature, 18C-27C. The two levels of the factors \"storage\" were \"stratified\" and \"unstratified\". Thus, there were four treatment combinations in total. Seeds were divided randomly into sets of 20 and the sets assigned at random to the treatments. Each stratified set of seeds was placed in a mesh bag, spread out to avoid overlapping, buried in tow inches of moist sand, and placed in a refrigeration unit for two weeks at 50F. The unstratified sets of seeds were kept in a paper envelop at room temperature. After the stratification period, each set of seeds was placed on a dish with 5 ml of distilled deionized water, and the dishes were put into one of two growth chambers for two weeks according to their assigned level of temperature. At the end of this period, each dish was scored for the number of germinated seeds. The resulting data are given below. Treatment combination Spring/stratified Spring/unstratified Summer/stratified Summer/unstratified Number of Germinating (Order of planting) 15(1), 0(28), 13(4), 0(27), 2(15), 3(14),7(39),17(20),19(13), 11(6) 9(22), 1(30), 2(21), 0(29), 0(2), 10(26), 2(35), 0(19), 3(40), 0(7) 7(23), 5(12), 4(31), 6(37), 5(10), 5(34), 7(8), 2(18), 6(9), 3(3) 1(36), 5(25), 6(38), 2(5), 2(33), 3(17), 5(24), 6(16), 1(32), 6(11) a. Analyze the residuals from this experiment. Are the basic analysis of variance assumptions satisfied? b. Evaluate the constant variance assumption on the one way model both graphically and by comparing sample variances. c. Plot ln against ln . and discuss whether or not a general power transformation might equalize the variances. (Again, only need to show the residual plots). d. Conduct Kruskal-Wallis Test using large sample approximation (use the original data). e. Conduct Kruskal-Wallis Test using EXACT -value (use the original data). f. Conduct a permutation test (use the original data)