Cronbach’s alpha hypothesis testing

Expected Cronbach’s alpha:
Minimum acceptable Cronbach’s alpha:
Number of items (k):
Desired power (1 – β):
Significance level (α, two-sided):
Required sample size (n):

Approximate number of subjects required to test a Cronbach alpha coefficient with desired power.

For example: for an expected Cronbach alpha of 0.85 for a (sub-)scale of 5 items and a desired power of 0.9 (90%), 86 subjects are needed to demonstrate that this Cronbach alpha value is significantly different from a minimum acceptable Cronbach alpha value of 0.65 at a significance level of 0.05 (two-tailed significance).

Note: In most cases a one-sided hypothesis test will make more sense. For a one-tailed hypothesis test, multiply the desired significance level by two (e.g., 0.05 * 2 = 0.1) In the example above, for a one-tailed test the required sample size is 71 subjects.

References:
Bonett DG. Sample size requirements for testing and estimating coefficient alpha. J Educ Behav Stat. 2002;27(4):335-340.
Bonett DG, Wright TA. Cronbachs alpha reliability: Interval estimation, hypothesis testing, and sample size planning. J Organ Behav. 2015;36(1):3-15.


Calulator as Shiny app