Sample size for a proportion confidence interval using an estimated proportion from a prior study

Computes the sample size required to estimate a population proportion with desired confidence interval precision in applications where an estimated proportion from a prior study is available. The actual confidence interval width in the planned study will depend on the value of the estimated proportion in the planned study. An estimated proportion from a prior study is used to predict the value of the estimated proportion in the planned study, and the predicted proportion estimate is then used as a planning value in the sample size computation. The probability that the prediction interval in the planned study will have a width that is less than the desired width is approximately 1 - alpha2.

This sample size approach assumes that the population proportion in the prior study is very similar to the population proportion in the planned study. If an estimated proportion from a prior study is not available the researcher must use expert opinion to guess the value of the proportion that will be observed in the planned study. The size.ci.prop function uses a proportion planning value that is based on expert opinion regarding the likely value of the proportion estimate that will be observed in the planned study.

For more details, see Section 1.16 of Bonett (2021, Volume 3)

Usage

size.ci.prop.prior(alpha1, alpha2, p0, n0, w)

Arguments

alpha1: alpha level for 1-alpha1 confidence in the planned study
alpha2: alpha level for the 1-alpha2 prediction interval
p0: estimated proportion in prior study
n0: sample size in prior study
w: desired confidence interval width

Value

Returns the required sample size

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

size.ci.prop.prior(.05, .10, .78, 50, .1)
#>  Sample size
#>          384

# Should return:
# Sample size
#         384