# nWilson: Calculate a simple random sample size for estimating a... In PracTools: Tools for Designing and Weighting Survey Samples

## Description

Calculate a simple random sample size for estimating a proportion using the Wilson method.

## Usage

 `1` ```nWilson(moe.sw, alpha = 0.05, pU, e) ```

## 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 `pU`) `alpha` 1 - (confidence level) `pU` population proportion `e` desired margin of error; either the value of CI half-width or the value of the half-width divided by `pU`

## Details

Calculate a simple random sample size using the Wilson (1927) method. A margin of error can be set as the CI half-width on the proportion (`moe.sw=1`) or as the CI half-width as a proportion of the population value p_U (`moe.sw=2`).

## Value

 `n.sam` numeric sample size `"CI lower limit"` lower limit of Wilson confidence interval with computed sample size `"CI upper limit"` upper limit of Wilson confidence interval with computed sample size `"length of CI"` length of Wilson confidence interval with computed sample size

## Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

## References

Valliant, R., Dever, J., Kreuter,F. (2013, chap. 3). Practical Tools for Designing and Weighting Survey Samples. New York: Springer.

Wilson, E.B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22, 209-212.

`nCont`, `nLogOdds`, `nProp`, `nPropMoe`
 ```1 2 3``` ```# srs sample size using Wilson method so that half-width of a 95% CI # is 0.01. Population proportion is 0.04 nWilson(moe.sw = 1, pU = 0.04, e = 0.01) ```