Overlapping Confidence Intervals Versus One Confidence Interval: Comparing the Overlapping of Two Independent Confidence Intervals with a Single ... Interval for Two Normal Population Parameters

Two overlapping confidence intervals have been used in the past to conduct statistical inferences about two normal population means. Several authors have examined the shortcomings of Overlap procedure and have determined that such a method distorts the significance level of testing the equality of two normal population means and reduces the statistical power of the test. Nearly all results for small samples in Overlap literature have been obtained either by simulation or by inaccurate formulas. This book will present exact formulas for the % overlap that two independent confidence intervals can have, but the null hypothesis of equality of two population means or variances must be rejected at a level of significance for any sample sizes. Further, the impact of Overlap on the power of testing the null hypothesis of equality of two normal variances will be assessed, which has never been considered in Overlap literature. Finally, the noncentral t distribution is used to assess the Overlap impact on type II error probability when testing equality of means for sample sizes larger than 1.