Confidence Limits and Sample Size
When selecting a sample size, one can consider that a higher number of individuals surveyed from a target group yields a tighter measurement, a lower number yields a looser range of confidence limits. The confidence limits may need to be corrected if, according to Lauer and Asher (1988), "the sample size starts to approach the population size" or if "the variable under scrutiny is known to have a much [original emphasis] smaller or larger occurrence than 50% in the whole population" (p. 59). For smaller populations, Singleton (1988) said the standard error or confidence interval should be multiplied by a correction factor equal to sqrt(1 - f), where "f" is the sampling fraction, or proportion of the population included in the sample.
Lauer and Asher (1988) give a table of correction factors for confidence limits where sample size is an important part of population size (p. 60) and also a table of correction factors for where the percentage incidence of the parameter in the population is not 50% (p. 61).
Tables for Calculating Confidence Limits vs. Sample Size
Correction Factors for Confidence Limits When Sample Size (n) Is an Important Part of Population Size (N >= 100)
|
Sample percentage of population |
Correction factor |
|
5% |
.98 |
|
10% |
.95 |
|
15% |
.92 |
|
20% |
.89 |
|
25% |
.87 |
|
30% |
.84 |
|
35% |
.81 |
|
40% |
.78 |
|
45% |
.74 |
|
50% |
.71 |
|
55% |
.67 |
|
60% |
.63 |
|
65% |
.59 |
|
70% |
.55 |
(For n over 70% of N, take all of N)
From Lauer and Asher (1988, p. 60)
Correction Factors for Rare and Common Percentage of Variables
|
Percentage incidence |
Correction factor |
|
50% |
none |
|
40% or 60% |
.98 |
|
35% or 65% |
.95 |
|
30% or 70% |
.92 |
|
25% or 75% |
.87 |
|
20% or 80% |
.80 |
|
15% or 85% |
.71 |
|
10% or 90% |
.60 |
|
5% or 95% |
.44 |
|
2.5% or 97.5% |
.31 |
From Lauer and Asher (1988, p. 61)
For more information on sampling statistical concepts and calculations, please see the Introduction to Statistics unit.