nPropMoe: Simple random sample size for a proportion based on margin of error

Description

Calculates a simple random sample size based on a specified margin of error.

Usage

nPropMoe(moe.sw, e, alpha = 0.05, pU, N = Inf)

Value

numeric sample size

Arguments

moe.sw: switch for setting desired margin of error (1 = CI half-width on the proportion; 2 = CI half-width on a proportion divided by $p_{U}$ )
e: desired margin of error; either $e = z_{1 - α / 2} \sqrt{V (p_{s})}$ or $e = z_{1 - α / 2} C V (p_{s})$
alpha: 1 - (confidence level)
pU: population proportion
N: number of units in finite population

Author

Richard Valliant, Jill A. Dever, Frauke Kreuter

Details

The margin of error can be set as the half-width of a normal approximation confidence interval, $e = z_{1 - α / 2} \sqrt{V (p_{s})}$ , or as the half-width of a normal approximation confidence interval divided by the population proportion, $e = z_{1 - α / 2} C V (p_{s})$ . The type of margin of error is selected by the parameter moe.sw where moe.sw=1 sets $e = z_{1 - α / 2} \sqrt{V (p_{s})}$ and moe.sw=2 sets i.e., $e = \frac{z_{1 - α / 2} \sqrt{V (p_{s})}}{p_{U}}$ .

References

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 3). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

Examples

Run this code

# srs sample size so that half-width of a 95% CI is 0.01
# population is large and population proportion is 0.04
nPropMoe(moe.sw=1, e=0.01, alpha=0.05, pU=0.04, N=Inf)

# srswor sample size for a range of margins of error defined as
# half-width of a 95% CI
nPropMoe(moe.sw=1, e=seq(0.01,0.08,0.01), alpha=0.05, pU=0.5)

# srswor sample size for a range of margins of error defined as
# the proportion that the half-width of a 95% CI is of pU
nPropMoe(moe.sw=2, e=seq(0.05,0.1,0.2), alpha=0.05, pU=0.5)

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