SAMPLE DESIGN: HOW MANY WILL BE IN THE SAMPLE— SAMPLE SIZE ADJUSTMENTS ?

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

2. SAMPLE SIZE ADJUSTMENT: Based on Population Size • Finite population correction (fpc) • Formula: (1-n/N), where, • n = sample size • N = population size • Meaning: mirrors the extent to which the sample (n) represents a small or large proportion of the population (N)

3. SAMPLE SIZE ADJUSTMENT: Based on Population Size • Finite population correction (fpc) • Examples • Where n = 100, & N = 10,000 • n/N = 100/10,000 = .01 • fpc = 1 - .01 = .99 • Where n = 100, & N = 300 • n/N = 100/300 = .333 • fpc = 1 - .333 = .667

4. SAMPLE SIZE ADJUSTMENT: Based on Population Size • Adjustment to Standard Error (SE) based on finite population correction (fpc) • Formula: • SE = sqrt [(1-n/N) * s2/n] • Implications: • The higher the proportion a sample represents of the population (n/N) (e.g., 100/300=.333), then the lower the fpc (e.g., 1-.333 = .667) and the Standard Error (SE) of estimates based on the sample. • Therefore, fewer cases are needed in the sample because of its greater precision (lower Standard Errors).

5. SAMPLE SIZE ADJUSTMENT: Based on Population Size • Formula for Sample Size Adjustment based on fpc: • nadj = n/(1 + (n-1)/N), where, n = computed sample n N = size of Population • Example: • nadj = 384/(1 + (384-1)/100) 384/(1 + (383)/100) 384/4.83 80

6. SAMPLE SIZE ADJUSTMENT: Based on Population Size

7. SAMPLE SIZE ADJUSTMENT:Design Effect • Variances: • Deff = varcs/varsrs, where, Deff = design effect varcs = variance for complex (cluster) sample varsrs = variance for simple random sample If Deff,then, Deff none = 1.0 low = > 1.0-1.3 medium = 1.4-1.9 high = > 2.0

8. SAMPLE SIZE ADJUSTMENT:Design Effect • Formula: • Deff = 1 + (b-1) roh, where, Deff = design effect b = cluster size roh = rate of homogeneity (intra-cluster correlation) none = 0 low = < .10 medium = .11-.19 high = > .20

9. SAMPLE SIZE ADJUSTMENT:Proportion Eligible • Formula: • Pe = ne/n, where, ne = number in sample that meet eligibility criteria n = sample size

10. SAMPLE SIZE ADJUSTMENT:Response Rate • Formula: • RR = nc/ ne, where, RR = response rate nc = number of completed interviews ne = number in sample that meet eligibility criteria

11. Criteria Population size (N) Design effect (Deff) Proportion eligible (Pe) Response rate (RR) Example (Estimate) n/(1 + (n-1)/N) = 80 nadj * Deff = 80 * 1.3 = 104 nadj/Pe = 104/.90 = 115 nadj/RR= 115/.80 =144 SAMPLE SIZE ADJUSTMENTS:Computations to Adjust n

12. WEIGHTING THE DATA:Adjusting for Disproportionate Sampling

13. WEIGHTING THE DATA:Adjusting for Nonresponse &/or Noncoverage

14. SURVEY ERRORS: Deciding How Many Will Be in the Sample

15. REFERENCES • Bennett, S., Woods, T., Liyanage, W.M., & Smith, D.L. (1991). A simplified general method for cluster-sample surveys of health in developing countries. World Health Statistics Quarterly 44: 98-106. • Dillman, Don A. (2000). Mail and Internet Surveys: The Tailored Design Method. Second Edition. New York: John Wiley & Sons, Inc.