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Reliability & Agreement · ALPHA-1S

Sample Size for Hypothesis Test of Cronbach Alpha

Plan the number of participants needed to test whether a multi-item scale has a specified Cronbach alpha reliability.

1. Information obtained from previous studies or literature

Use a defensible minimum reliability from prior evidence or the protocol.

2. Information decided by the researcher

The implemented method uses a two-sided critical value.

Defaults to 10%. Enter 0 if no adjustment is required.

3. Results

Enter the planning assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A researcher develops a depression screening scale and wants to test whether its Cronbach alpha exceeds the minimum acceptable internal-consistency value.

Formula and methodological note

This calculator uses the preserved published approximation documented in the calculator specification. It assumes the selected reliability or agreement model, independent subjects, the stated number of items or ratings, and defensible planning values.

Sample size is rounded upward before the dropout/non-response adjustment, which is also rounded upward. The method does not replace design-specific review for clustered samples, multiple raters beyond the stated model, missing ratings, weighted kappa, ordinal outcomes, or alternative ICC definitions.

Method references

  1. Bonett DG. Sample size requirements for testing and estimating coefficient alpha. J Educ Behav Stat. 2002;27(4):335–340.
  2. Bonett DG, Wright TA. Sample size requirements for estimating Pearson, Kendall and Spearman correlations. Psychometrika. 2000;65(1):23–28.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Hypothesis Test of Cronbach Alpha (ALPHA-1S).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. http://127.0.0.1:4321/tools/sample-size/reliability-agreement/cronbach-alpha/.