Aim: We want to compare the performance of the 2 sample t-test and the Wilcoxon test...

 

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Aim: We want to compare the performance of the 2 sample t-test and the Wilcoxon test in this exercise. We fix the (nominal) level of these tests at a=5%. This will be achieved through simulations using the following scenario. We want to assess the effect of a blood-pressure lowering medication in a specific population. Imagine a study where 200 patients are assigned to either a placebo or the test drug. Each arm of the study has 100 patients. We focus on the diastolic blood pressure and assume that its distribution is normal with mean = 80 and a standard deviation of 10 in the placebo group. We will also assume that the distribution of diastolic blood pressure in the treated group is normal with mean =80-8 where & represents the reduction in diastolic blood pressure or the treatment effect. The same standard deviation as in the placebo group, a-10, can be used. a. Carry out simulations similar to those done in Exercise 3b, with d= 0, 2, 4, 6, 8 and 10. The main difference is that we now have tests based on 2 different samples. Tabulate and plot the same simulation-based estimates of the power functions (as functions of 8) for each test, as was carried out in Exercise 3c. [See eLearning for Stata code] b. Which test seems to have an advantage when the distribution is indeed normal in both groups? We now consider that the distribution of diastolic blood pressure in the treated group is a "contaminated" normal. Approximately 97% of observations come from the same normal distribution as before and the remainder are sampled from a distribution with a larger mean and variance N(130, y) where y=20-20. Outliers are likely to arise in the treated group since about 3% of the observations are sampled from a different population. c. Repeat part (a) using the data. d. Does the t-test maintain its nominal significance level of 5%? Which test seems to have an advantage now? A note on the Wilcoxon 2 sample test: this test is commonly used as an alternative to the 2 sample t-test, when it is thought that the assumption of normality does not hold. It is based on the ranks of the observations. Aim: We want to compare the performance of the 2 sample t-test and the Wilcoxon test in this exercise. We fix the (nominal) level of these tests at a=5%. This will be achieved through simulations using the following scenario. We want to assess the effect of a blood-pressure lowering medication in a specific population. Imagine a study where 200 patients are assigned to either a placebo or the test drug. Each arm of the study has 100 patients. We focus on the diastolic blood pressure and assume that its distribution is normal with mean = 80 and a standard deviation of 10 in the placebo group. We will also assume that the distribution of diastolic blood pressure in the treated group is normal with mean =80-8 where & represents the reduction in diastolic blood pressure or the treatment effect. The same standard deviation as in the placebo group, a-10, can be used. a. Carry out simulations similar to those done in Exercise 3b, with d= 0, 2, 4, 6, 8 and 10. The main difference is that we now have tests based on 2 different samples. Tabulate and plot the same simulation-based estimates of the power functions (as functions of 8) for each test, as was carried out in Exercise 3c. [See eLearning for Stata code] b. Which test seems to have an advantage when the distribution is indeed normal in both groups? We now consider that the distribution of diastolic blood pressure in the treated group is a "contaminated" normal. Approximately 97% of observations come from the same normal distribution as before and the remainder are sampled from a distribution with a larger mean and variance N(130, y) where y=20-20. Outliers are likely to arise in the treated group since about 3% of the observations are sampled from a different population. c. Repeat part (a) using the data. d. Does the t-test maintain its nominal significance level of 5%? Which test seems to have an advantage now? A note on the Wilcoxon 2 sample test: this test is commonly used as an alternative to the 2 sample t-test, when it is thought that the assumption of normality does not hold. It is based on the ranks of the observations.

Answer rating: 100% (QA)

a To carry out simulations similar to Exercise 3b we need to perform the following steps 1 Define the parameters Mean of the control group 80 Standard deviation of the control group 10 Mean of the tre... View the full answer