Comparison of Sample Sizes to Estimate Proportions
Comparison of Sample Sizes to Estimate Proportions

Summary/Abstract: Sample size is the first requirement when the study starts. One should know the precision needed in order to have a consistent statistical analysis. The minimum number of data in the sample defines the error in estimating the parameters and therefore is related to the confidence interval. In medical area the frequency of an event (event rate, proportion) is often of great interest (have a look on the prevalence or incidence of a disease).There are different ways to estimate the confidence interval of a proportion. One use the approximation with a normal distribution, others compensate the lack of continuity by adding adjustments terms while others use the exact methods based on binomial distribution. Therefore if we have different ways of computing the confidence intervals which are related to the sample size we should take these into account. We have computed the sample size based on 4 confidence intervals: Wald, Wilson, Clopper-Pearson exact method, and finally the arcsin transformation. To compare the results, we have checked the precision on estimating the event rate by the probability of belonging to the range of acceptable proportions (similar to coverage probability). Finally we found that the simplest Wald method which is the most used in literature is practically the worse for extreme event rates but is robust in estimation for proportions close to 0.5.Clopper-Pearson and Arcsine are more trustful if we are to be sharp in computing the sample size. Wilson method is closed to Wald even if for confidence intervals it performs better.

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