Approximate is Better than “Exact” for Interval Estimation of Binomial Proportions
1998/05/01 by Alan Agresti, Brent A. Coull · 1 voice · 119 citations
Mathematics · #Statistics Education and Methodologies #Advanced Statistical Methods and Models #Statistical Methods and Bayesian Inference
paper · doi:10.1080/00031305.1998.10480550
Abstract
Abstract For interval estimation of a proportion, coverage probabilities tend to be too large for “exact” confidence intervals based on inverting the binomial test and too small for the interval based on inverting the Wald large-sample normal test (i.e., sample proportion ± z-score × estimated standard error). Wilson's suggestion of inverting the related score test with null rather than estimated standard error yields coverage 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 two “failures” to the sample. In elementary courses, with the score and adjusted Wald methods it is unnecessary to provide students with awkward sample size guidelines.
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