TY - JOUR

T1 - Comparing the overlapping of two independent confidence intervals with a single confidence interval for two normal population parameters

AU - Maghsoodloo, Saeed

AU - Huang, Ching Ying

PY - 2010/11/1

Y1 - 2010/11/1

N2 - Two overlapping confidence intervals have been used in the past to conduct statistical inferences about two population means and proportions. Several authors have examined the shortcomings of Overlap procedure and have determined that such a method distorts the significance level of testing the null hypothesis of two 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 formulas that may need refinement for small sample sizes, but accurate large sample information exists. Nevertheless, there are aspects of Overlap that have not been presented and compared against the standard statistical procedure. This article will present exact formulas for the maximum % overlap of two independent confidence intervals below which the null hypothesis of equality of two normal population means or variances must still be rejected 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. 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.

AB - Two overlapping confidence intervals have been used in the past to conduct statistical inferences about two population means and proportions. Several authors have examined the shortcomings of Overlap procedure and have determined that such a method distorts the significance level of testing the null hypothesis of two 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 formulas that may need refinement for small sample sizes, but accurate large sample information exists. Nevertheless, there are aspects of Overlap that have not been presented and compared against the standard statistical procedure. This article will present exact formulas for the maximum % overlap of two independent confidence intervals below which the null hypothesis of equality of two normal population means or variances must still be rejected 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. 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.

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U2 - 10.1016/j.jspi.2010.04.057

DO - 10.1016/j.jspi.2010.04.057

M3 - Article

AN - SCOPUS:77954030194

VL - 140

SP - 3295

EP - 3305

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 11

ER -