Comparison of Threshold Rules for a Normal Approximation to a Binomial Distribution

A commonly used rule for determining if a Binomial(n, p) distribution may be reasonably approximated by a normal distribution is whether or not np and n(1 – p) are at least some constant, such as 10. Two competing rules, one based on the binomial variance and the other based on the coefficient of variation, are considered when constructing confidence intervals and performing hypothesis testing, both using and not using a continuity correction. Under one criterion the rule based on the coefficient of variation is found to be the best in terms of coverage probabilities, and under another criterion the rule based on the binomial variance is found to be the best.