Cronbach’s alpha interval estimation

Expected Cronbach’s alpha:
Number of items (k):
Significance level (for 1 – α confidence interval):
Desired width of the confidence interval (w):
Required sample size (n):

Approximate number of subjects required to obtain a confidence interval of the desired width around a specified Cronbach alpha value.

Significance level (α) = 0.05 translates to a 95% confidence interval, α = 0.01 to a 99% confidence interval.

For example: for an expected Cronbach alpha of 0.80 for a (sub-)scale of 7 items, 147 subjects are needed to obtain a desired width of 0.1 for a 95% confidence interval (i.e., the value of Cronbach alpha is between 0.75 and 0.85).

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.

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