Better Estimates of Confidence Intervals for Very Low Error Rate Population

In the estimation of error rates for populations, whose error rate is quite small, the usual assumption of normality can lead to erroneous results. The confidence interval that is actually calculated for any given probability will have too low a lower bound, and not a high enough upper bound. Thus, the user may be misled into too optimistic a view of the population being sampled. This article discusses the nature of the problem and provides graphs from which the more accurate interval can be read. The final section of the paper deals with the related problem of confidence intervals when the observed error rate is zero. Tables are provided which facilitates the developing of confidence statements for such samples.