# Cronbach’s alpha hypothesis testing

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. |

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