SAMPLE DESIGN: HOW MANY WILL BE IN THE SAMPLE— ANALYTICAL OR EXPERIMENTAL STUDIES ?

# SAMPLE DESIGN: HOW MANY WILL BE IN THE SAMPLE— ANALYTICAL OR EXPERIMENTAL STUDIES ?

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## SAMPLE DESIGN: HOW MANY WILL BE IN THE SAMPLE— ANALYTICAL OR EXPERIMENTAL STUDIES ?

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1. SAMPLE DESIGN: HOW MANY WILL BE IN THE SAMPLE—ANALYTICAL OR EXPERIMENTAL STUDIES ? Lu Ann Aday, Ph.D.The University of Texas School of Public Health

2. CRITERIA: Analytical or Experimental Studies • Objective: • to test an hypothesis, i.e., provide “yes” or “no” answer re hypothesis • Framework: • power analysis

3. POWER ANALYSIS

4. POWER ANALYSIS • Type I error (α): Probability of rejecting Ho when it is true (there is no difference) • Confidence (1- α): Probability of not rejecting Ho when it is true • Type II error (β): Probability of not rejecting Ho when it is false (there is a difference) • Power (1- β): Probability of rejecting Ho when it is false

5. EFFECT SIZE • Definition: magnitude of hypothesized difference or effect expressed as standard deviation units • Formula: • Effect size = Δ/σ, where, Δ = hypothesized difference σ = standard deviation of difference

6. EFFECT SIZE • Example: Effect size = Δ/σ Δ/σ = 2 visits/2.5 visits Δ/σ = .80 • Magnitudes: If Effect Size,then, Effect Size < .50 small > .50-.79 medium > .80 large

7. STANDARD ERRORS • Standard Errors Associated with Confidence Intervals (Z1-α/2 ) 68 % = 1.00 90 % = 1.645 95 % = 1.96 99 % = 2.58 • Standard Errors Associated with Power (Z1-β) 70 % = .524 80 % = .842 90 % = 1.282 95 % = 1.645 99 % = 2.326

8. SAMPLE SIZE ESTIMATION: Group-Comparison (Two Groups)—Proportion

9. SAMPLE SIZE ESTIMATION: Group Comparison (Two Groups)—Mean

10. SAMPLE SIZE ESTIMATION: Case Control—Odds Ratio

11. SAMPLE SIZE ESTIMATION: Multivariate Analyses—Regression • Criteria: For logistic or linear regression, the required sample size for each model is 10 to 15 cases per variable entered into the model, including dummy variables • Example: n = no. of variables * 15 n = 20 * 15 n = 300

12. SUMMARY:Steps in Estimating Sample Size – Analytical or Experimental Studies • 1. Identify the major study hypotheses. • 2. Determine the statistical tests for the study hypotheses, such as a t-test, F-test, or chi-square test. • 3. Select the population or subgroups of interest (based on study hypotheses and design). • 4a. Indicate what you expect the hypothesized difference (Δ) to be. • 4b. Estimate the standard deviation (σ) of the difference. • 4c. Compute the effect size (Δ/σ).

13. SUMMARY:Steps in Estimating Sample Size – Analytical or Experimental Studies • 5. Decide on a tolerable level of error in rejecting the null hypothesis when it is true (alpha). • 6. Decide on a desired level of power for rejecting the null hypothesis when it is false (power). • 7. Compute sample size, based on study assumptions.

14. SAMPLE SIZE ESTIMATION: EXCEL SPREADSHEET • See EXCEL file with spreadsheet for computing sample sizes.

15. SAMPLE SIZE ESTIMATION: SOFTWARE • DSTPLAN • You can install DSTPLAN software to use for sample size computation: http://biostatistics.mdanderson.org/SoftwareDownload/SingleSoftware.aspx?Software_Id=41

16. REFERENCES • Lemeshow, S., Hosmer, D. W., Jr., Klar, J., & Lwanga, S. K. (1990). Adequacy of sample size in health studies. New York: Wiley. • Lipsey, M. W. (1990). Design sensitivity: Statistical power for experimental research. Newbury Park, CA: Sage.