Nutritionists at George Washington University want to compare two different diets for a group of diabetic patients. Investigators plan to test the null hypothesis that the mean difference in blood glucose (mg/dL) for patients following Diet 1 will be the same as those patients following Diet 2. The research hypothesis states the mean difference in blood glucose will be different between the two diet groups. Investigators plan to draw their random sample of diabetic patients from the Washington DC area. Recruited patients will be randomly assigned to one of two diets. A fasting blood glucose test will be conducted on each patient at the beginning of the study and again 12 weeks later.

The biostatistician on the project wants to conduct a power analysis to determine the sample size needed to detect group differences. The standard deviation of blood glucose distribution for Diet Group 1 is reported to be 4.5 mg/dL; the standard deviation of blood glucose distribution for Diet Group 2 is reported to be to be 4.2 mg/dL. The biostatistician wants to estimate the number of subjects needed in each group (assuming equal sized groups) and decides to run an analysis for a two-sample t-Test at a significance level of 0.05 for a two-tailed test. In order to create a thorough recommendation for the study team, the analysis is run at four levels of power (80%, 85%, 90% and 95%).

Follow the instructions provided on Blackboard to complete Questions 1 and 2. A link to the online power calculator is also available on Blackboard.

1) Calculate the effect sizes and fill in the results in Table 2.1 (below) accordingly.

2) Carry over the effect sizes that you calculated in Table 2.1 and put them in the first column of Table 2.2 (below). Calculate the sample size estimations for each effect size and level of statistical power. Fill in the results accordingly.

3) Refer to Table 2.2 and describe what patterns you see in the sample size values. What happens to sample size as you read across a row (i.e. as statistical power changes)? What happens as you read down a column (i.e. as effect sizes change)?

4) Choose two cells from Table 2.2 (from two different columns and two different rows) and interpret those values. Remember that the purpose of this power analysis is to provide an estimate for the sample size of the study. So in your interpretation, it is the number in the cell that reflects how many people would need to be recruited per group given the power and the effect size (column and row respectively).