Confidence Limits, Power, and Sample Size Estimation in Statistical Analysis

1. Discussion 2 1/13/2014

2. Outline • Confidence limits • Power • One sample • Population variance known or unknown • Two sample • Population variance known or unknown • Sample size estimation • One sample (confidence interval) • Two sample (detect differences between two means) • How to read data in SAS

3. Questions?

4. Confidence Limits • If we take repeated samples of size n and construct confidence intervals we can expect (1 – α) x 100% of the intervals to contain the true population mean Example: n = 14, α = 0.05, and standard error of mean = 0.3279

5. Power • One sample – detect a difference between a mean and value previously known If you know population standard error If you don’t know population standard error

6. Power • Two sample – detect a difference between two means If sample size is different between group1 and group 2 If sample size is the same between group 1 and group 2 If the population variance is given to you, substitute it into the equation instead of the sample pooled variance

7. Sample Size Estimation • One sample – sample size to estimate a confidence interval of a mean Where Remember to do iterations when estimating sample size

8. Sample Size Estimation • Two sample – Sample size to detect differences between two means with a give α and power Where Remember to do iterations when estimating sample size

9. How to read data in SAS • Looked at correct and incorrect methods to read data in SAS using the data from Lab 1 Example 4