Confidence intervals and sample size calculations for the standardized mean difference effect size between two normal...

Area of Science:

• Social Sciences
• Statistical Methods
• Empirical Research

Background:

• Journal guidelines emphasize reporting effect sizes and confidence intervals.
• Accurate effect size estimation is crucial for advancing social science theory and practice.
• Existing methods for confidence intervals of standardized mean differences have limitations, particularly with unequal variances.

Purpose of the Study:

• To present an improved procedure for constructing confidence intervals of the standardized mean difference effect size.
• To offer a method that is theoretically justified and computationally simple.
• To provide a viable alternative to Cohen's d when population variances are unequal.

Main Methods:

• Developed a novel procedure for confidence interval construction for the standardized mean difference.
• Utilized simulation studies to compare the accuracy of the proposed intervals against existing methods.
• Delineated sample size procedures for precise interval estimation.

Main Results:

• The proposed confidence intervals demonstrated greater accuracy in achieving nominal coverage probability compared to existing methods.
• The new approach offers theoretical advantages and computational simplicity.
• Simulation results confirmed the superiority of the suggested method under unequal variance conditions.

Conclusions:

• The improved confidence interval procedure is a valuable tool for social science research, especially when assumptions of equal variances are violated.
• The method enhances the accuracy and applicability of effect size reporting.
• Supplementary programs facilitate the implementation of these advanced statistical techniques.