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 = = .99
Where n = 100, & N = 300
n/N = 100/300 = .333
fpc = = .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., = .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
Sample n: P1= .50; P2= .50
Sample n: P1= .80; P2= .20
100 80 71
250
152
124
500
217
165
750
254
185
1,000
278
198
2,500
333
224
5,000
357
234
10,000
370
240
25,000
378
244
50,000
381
245
100,000
383
1,000,000
384
246
100,000,000

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 = >
medium =
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 =
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. SAMPLE SIZE ADJUSTMENTS: Computations to Adjust n
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

12. WEIGHTING THE DATA: Adjusting for Disproportionate Sampling
STRATA/
WEIGHT
African American
Hispanic
TOTAL
POPULATION (N)
90, (90%)
10, (10%)
100,000 (100%)
SAMPLE
(n/N)
1/100 = 900
(81.8%)
1/50 = 200
(18.2%)
1,100
(100%)
EXPANSION WEIGHT (N/n)
100/1 * 900 = 90,000
(90%)
50/1 * 200 = 10,000
(10%)
RELATIVE WEIGHT
(Total N/Total n= 100,000/1,100 =90.9)
100/90.9 * 900 = (90%)
50/90.9 *200 = 110

13. WEIGHTING THE DATA: Adjusting for Nonresponse &/or Noncoverage
STRATA/
WEIGHT
African American
(RR=720/900=.80)
Hispanic
(RR=140/200 =.70)
RESPONSE RATE WEIGHT
(Applied to Relative Weight)
720 * (100/90.9)/.80=
720 * 1.1/.80=
720 * 1.375=
990
140 * (50/90.9)/.70=
140 * .55/.70=
140 * .786=
110
POST-STRATIFICATION WEIGHT
Population (%)
Sample (%)
Weight
Poor Nonpoor
5% %
3% %
15% %
5% %

14. SURVEY ERRORS: Deciding How Many Will Be in the Sample
Systematic Errors
Variable Errors
Noncoverage
bias
Unit nonresponse bias
Weighting errors
Standard errors
Design effects
Solutions to Errors
Construct
and apply
poststratification
weights.
Construct and apply
nonresponse
Construct and apply disproportionate sampling weights (when applicable).
Compute the sample size required to have a desired level of precision or power in addressing the study objectives.
Apply adjustments to increase the sample size as needed.
When using complex, especially cluster sample, designs, incorporate design effects in estimating the required sample size, and in analyzing the data.

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:
Dillman, Don A. (2000). Mail and Internet Surveys: The Tailored Design Method. Second Edition. New York: John Wiley & Sons, Inc.