Sample size for a Cronbach reliability confidence interval using an reliability estimate from a prior study

Computes the sample size required to estimate a Cronbach reliability with desired confidence interval precision in applications where an estimated Cronbach reliability from a prior study is available. The actual confidence interval width in the planned study will depend on the value of the estimated reliability in the planned study. An estimated Cronbach reliability from a prior study can be used to compute a lower prediction limit for the estimated reliability in the planned study, which is then used as a planning value in the sample size analysis. The probability that the prediction interval will have a width that is less than the desired width in the planned study is approximately 1 - alpha2.

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

Usage

size.ci.cronbach.prior(alpha1, alpha2, rel0, n0, r, w)

Arguments

alpha1: alpha level for 1-alpha1 confidence in the planned study
alpha2: alpha level for the 1-alpha2 prediction interval
rel0: estimated reliability in prior study
n0: sample size in prior study
r: number of measurements (items, raters, forms)
w: desired confidence interval width

Value

Returns the required sample size

Examples

size.ci.cronbach.prior(.05, .10, .86, 50, 5, .15)
#>  Sample size
#>           74

# Should return:
# Sample size
#          71