# 20: Power and sample size 3/28/07

## Review questions

1. List the factors that are needed in order to estimate a population mean with a given margin of error.
2. List the factors that are needed in order to detect a given difference in means.
3. List the factors that are need in order to estimate a proportion with a given margin of error.
4. List the factors that are needed in order to detect a difference in risk in a cohort study.
5. List the factors that are needed in order to detect a difference in risk in a case-control study.

## Exercises

(1)  Suppose you want to estimate a mean with a margin of error d. What additional information do you need to know before determining the sample size requirements of the study?

(2) You want to calculate a proportion so that the margin of error is .025 (2.5%). An educated guess of the proportion is  0.10. How large a sample is needed?

(3) You are looking for a mean difference of 5 and assume that the standard deviation of the variable is about 20. How many observations do you need to test the data for a difference with a = .05 (two-sided) and 1 - b = .8?

(4) A case-control study is looking to detect an odds ratio of 1.5. It uses a ratio 1:1 for cases: controls. The prevalence of exposure in the source population is 20%. How many cases and controls do you need to study assuming a = .05 (two-sided) and 1 - b = .8?

(5) Redo the sample size calculation for #4 now assuming an odds ratio of 2.0.

(6) You are planning a cohort study in which the expected incidence proportion in the exposed is 20% and the expected incidence proportion in the nonexposed is 10%. You want to test H0: RR = 1. Group sample sizes will be equal. How many people should you study?

Key to Odd Numbered Problems                              Key to Even Numbered Problems (may not be posted)