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Evaluating the Normal Approximation to the Binomial Test

Queens College of CUNY

Patricia P. Ramsey

Fordham University

The normal approximation to the binomial test with and without a continuity correction is evaluated in terms of control of Type I errors and power. The normal approximations are evaluated as robust for a given sample size, N, and at a given level if the true Type I error rate never exceeds 1.5 . The uncorrected normal test is found to be less robust than is implied by the currently applied guidelines. The most stringent currently used guideline of requiring ²10 is adequate at = .05 but must be increased to ² 35 at = .01. The corrected test is shown to be robust but not conservative. Both tests are shown to have substantial power loss in comparison to the exact binomial test.

Key Words: binomial test • normal approximation • robustness • power

Journal of Educational and Behavioral Statistics, Vol. 13, No. 2, 173-182 (1988)
DOI: 10.3102/10769986013002173


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