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Abstract
Decisions about how to best analyze rare events need to be made in many investigations. For binary events, a normal approximation is often said to be satisfactory when the expected number of events is larger than 5 and the binomial proportion is not too close to zero or one. In most empirical research, the commonly employed large-sample method for determining a confidence interval or for testing a hypothesis for a parameter is based on its logarithmic transformed estimator. In this article, we investigate how much the logarithmic transformation improves the approximation of the distribution of a sample proportion to a normal distribution. We also investigate the performance of the arcsine square root transformation. We find that the success of a normal approximation has less to do with the size of the event rates than the values of np. Further, we find that the transformations do not substantially improve the normal approximation of the distribution of a sample proportion in computing coverage probabilities, that the untransformed results with continuity correction are just about as good as the first-order logarithmic transformation, and that the arcsine transformation is inferior to the logarithmic transformation.
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