References 455 TABLE 10.49 Outcome data for the Sorbinil Retinopathy Trial ($n = 481$) change in retinopathy level Better Worse Group 2+ Levels 1 Level No change 1 Level 2 Levels 3 Levels 4 Levels 5+ Levels Total Placebo 5 17 84 59 37 18 9 14 243 Sorbinil 4 21 97 50 22 16 14 14 238 but would take into account the ordinal nature of the change scores. 10.149 What test can be used to compare the two groups if this more efficient method is used? 10.150 Implement the test in Problem 10.149, and provide a $p$-value (two-tailed). 10.151 Reanalyze the data in Table 10.49 using the Wilcoxon rank sum test. 10.152 Compare your results in Problems 10.149 and 10.151. Which do you think is a better method of analysis?
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Consider the following competing hypotheses and accompanying sample data. (You may find it useful to reference the appropriate table: z table or t table) H0: p1 - p2 = 0.08 Ha: p1 - p2 ≠ 0.08 x1 = 127 n1 = 230 x2 = 138 n2 = 433 a. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic b. Find the p-value. 0.025 ≤ p-value < 0.05 0.05 ≤ p-value < 0.10 p-value ≥ 0.10 p-value < 0.01 0.01 ≤ p-value < 0.025
Madhur L.
Preliminary data analyses indicate that use of a paired t-test is reasonable. Perform each hypothesis test by using either the critical-value approach or the P-value approach. Glaucoma and Corneal Thickness. Glaucoma is a leading cause of blindness in the United States. N. Fhlers measured the corneal thickness of eight patients who had glaucoma in one eye but not in the other. The results of the study were published as the paper "On Corneal Thickness and Intraocular Pressure, II" (Acta Ophthalmology, Vol. 48, pp. 1107-1112). The following are the data on cornmeal thickness, in microns. At the $10 \%$ significance level, do the data provide sufficient evidence to conclude that mean corneal thickness is greater in normal eyes than in eyes with glaucoma?
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The Sorbinil Retinopathy Trial was conducted among 497 type I (insulin-dependent) diabetic patients who had little or no evidence of retinopathy at baseline [31]. Retinopathies are abnormalities of the retina that sometimes occur among diabetic patients and can result in substantial losses of vision in advanced stages. Patients were randomized to either Sorbinil, an aldose-reductase inhibitor, or placebo and were seen at 1 year and then every 9 months up to 48 months after randomization. In addition, all subjects had a final visit at the end of the trial (max $=56$ months). Sixteen of the patients provided no follow-up. The primary endpoint of the trial was based on change in retinopathy severity level from baseline to maximum follow-up (i.e., severity level at maximum follow-up - severity level at baseline). An ordinal grading scale was used to evaluate change: $2+$ levels better, 1 level better, no change, 1 level worse, ..., 5+ levels worse. The outcome data by treatment group are given in Table 10.49. The primary outcome for the study was worsening by 2 or more levels. What test can be used to compare the two treatment groups on the primary endpoint?
Shu N.
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