APPROXIMATE IS BETTER THAN EXACT FOR INTERVAL ESTIMATION OF BINOMIAL PROPORTIONS

For interval estimation of a proportion, coverage probabilities tend t o be too large for ''exact'' confidence intervals based on inverting t he binomial test and too small for the interval based on inverting the Wald large-sample normal test (i.e., sample proportion +/- z-score x estimated standard error). Wilson's suggestion of inverting the relate d score test with null rather than estimated standard error yields cov erage probabilities close to nominal confidence levels, even for very small sample sizes. The 95% score interval has similar behavior as the adjusted Wald interval obtained after adding two ''successes'' and tw o ''failures'' to the sample. In elementary courses, with the score an d adjusted Wald methods it is unnecessary to provide students with awk ward sample size guidelines.