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

Two overlapping confidence intervals have been used in many sources in the past 30 years to conduct statistical inferences about two normal population means (microx and microy). Several authors have examined the shortcomings of Overlap procedure in the past 13 years and have determined that such a method completely distorts the significance level of testing the null hypothesis H0: microx = micro y and reduces the statistical power of the test. Nearly all results for small sample sizes in Overlap literature have been obtained either by simulation or by somewhat inaccurate formulas, and only large-sample (or known-variance) exact information has been provided. Nevertheless, there are many aspects of Overlap that have not yet been presented in the literature and compared against the standard statistical procedure. This paper will present exact formulas for the % overlap, ranging in the interval (0, 61.3626%] for a 0.05-level test, that two independent confidence intervals (CIs) can have, but the null hypothesis of equality of two population means must still be rejected at a pre-assigned level of significance a for sample sizes = 2.