Prediction limits for sample value of Cronbach reliability in a future study

Computes approximate one-sided or two-sided prediction limits for the estimated Cronbach reliability in a future study with a planned sample size of n. The prediction interval uses a Cronbach reliability estimate from a prior study.

The size.ci.cronbach and size.ci.cronbach2 functions require a planning value of the expected sample value of Cronbach's reliability in the planned study. A one-sided lower prediction limit for the sample value of Cronbach's reliability in the planned study can be used in the size.ci.cronbach and size.ci.cronbach2 functions to obtain conservatively large sample size requirements. This strategy for specifying a reliability planning value is useful in applications where the population Cronbach reliability in the prior study is assumed to be very similar to the population Cronbach reliability in the planned study.

Usage

pi.cronbach(alpha, rel, r, n0, n, type)

Arguments

alpha

alpha value for 1-alpha confidence

rel

estimated Cronbach reliability from prior study

r

number of measurements (e.g., items, raters, etc.)

n0

sample size used to estimate reliability in prior study

n

planned sample size of future study

type

set to 1 for two-sided prediction interval
set to 2 for one-sided upper prediction limit
set to 3 for one-sided lower prediction limit

Value

Returns one-sided or two-sided prediction limit(s) of an estimated Cronbach reliability in a future study

Examples

pi.cronbach(.1, .852, 5, 100, 150, 1)
#>      LL     UL
#>  0.7923 0.8945

# Should return:
#       LL     UL
#   0.7944 0.8956
 
pi.cronbach(.1, .852, 5, 100, 150, 3)
#>      LL
#>  0.8073

# Should return:
#      LL
#  0.8092