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

## Review questions

- List the factors that are needed in order to estimate a population mean
with a given margin of error.
- List the factors that are needed in order to detect a given difference in
means.
- List the factors that are need in order to estimate a proportion with a
given margin of error.
- List the factors that are needed in order to detect a difference in risk
in a cohort study.
- 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 *H*_{0}: *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)