Question

In Problem 6 you found a confidence interval for the difference from previously gathered data. In this problem you want to set the sample size for the two groups before conducting the study This will often be the case for clinical data where you want to make sure that, if a particular difference in two groups of the amount or level of a substance exists, your test will come back saying that such a difference exists. In other words, you want to make sure that your test has a certain level of power so that, if an important level of difference exists, your test does not come back with such a difference because the sample size is too small. Related to this is Type I error and Type II error. You want to keep the o (the Type I Error probability) and theB (the Type II error probability) at a certain level or below, to do this, you set the Power of the Test ( = 1-A) at a certain level. For example, you may say "I want to be able to conclude that there is a difference in the glucose level of at least 7 mg/dl for the two groups because anything less is not important-at the 5% significance level with 80% power. How big a sample size do I need?" Problem 7: (5 pts) A clinical dietician wants to compare two different diets, A and B, for diabetic patients, to see if they differ in terms of lower blood glucose. She plans to get a random sample of diabetic patients and randomly assign them to one of the two diets. At the end of the experiment, which lasts 6 weeks, a fasting blood glucose test will be conducted on each patient. She expects, with 95% probability that the average difference in blood glucose measure between the two groups will be about 8 mg/dl. Furthermore, she also assumes the standard deviation of blood glucose distribution for diet A to be 13 mg/dl and the standard deviation for diet B to be 15 mg/dl. The dietician wants to know the number of subjects needed in each group assuming equal sized groups How many persons should the dietician have in each group?

Answer 1

7. Analysis for Sample size calculation

We assume 2 different 1-sample t Test, as we have the standard deviation for both the groups

For first group - Power and Sample Size

1-Sample t Test

Testing mean = null (versus ≠ null)

Calculating power for mean = null + difference

α = 0.05 Assumed standard deviation = 13

Results

Difference	Sample Size	Target Power	Actual Power
8	23	0.8	0.805220

Sample size for first group will be 23

For second group - Power and Sample Size

1-Sample t Test

Testing mean = null (versus ≠ null)

Calculating power for mean = null + difference

α = 0.05 Assumed standard deviation = 15

Results

Difference	Sample Size	Target Power	Actual Power
8	30	0.8	0.806011

Sample size for second group will be 30