Confidence interval for an average Cronbach alpha reliability

Computes the estimate, standard error, and confidence interval for an average Cronbach reliability coefficient from two or more studies.

For more details, see Chapter 2 of Bonett (2021, Volume 5).

Usage

meta.ave.cronbach(alpha, n, rel, r, bystudy = TRUE)

Arguments

alpha: alpha level for 1-alpha confidence
n: vector of sample sizes
rel: vector of sample reliabilities
r: number of measurements (e.g., items) used to compute each reliability
bystudy: logical to also return each study estimate (TRUE) or not

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

Estimate - estimated effect size
SE - standard error
LL - lower limit of the confidence interval
UL - upper limit of the confidence interval

References

Bonett DG (2010). “Varying coefficient meta-analytic methods for alpha reliability.” Psychological Methods, 15(4), 368–385. ISSN 1939-1463, doi:10.1037/a0020142 .

Bonett DG, Wright TA (2015). “Cronbach's alpha reliability: Interval estimation, hypothesis testing, and sample size planning.” Journal of Organizational Behavior, 36(1), 3–15. ISSN 08943796, doi:10.1002/job.1960 .

Bonett DG (2021). Statistical Methods for Psychologists, Vol 1-5, https://dgbonett.sites.ucsc.edu/.

Examples

n <- c(583, 470, 546, 680)
rel <- c(.91, .89, .90, .89)
meta.ave.cronbach(.05, n, rel, 10, bystudy = TRUE)
#>         Estimate      SE     LL     UL
#> Average   0.8975 0.00326 0.8911 0.9039
#> Study 1   0.9100 0.00557 0.8986 0.9204
#> Study 2   0.8900 0.00758 0.8744 0.9041
#> Study 3   0.9000 0.00639 0.8869 0.9119
#> Study 4   0.8900 0.00630 0.8771 0.9018

# Should return:
#         Estimate      SE     LL     UL
# Average   0.8975 0.00326 0.8911 0.9039
# Study 1   0.9100 0.00557 0.8986 0.9204
# Study 2   0.8900 0.00758 0.8744 0.9041
# Study 3   0.9000 0.00639 0.8869 0.9119
# Study 4   0.8900 0.00630 0.8771 0.9018