Effect sizes of the differences between means without assuming variance equality and between a mean and a constant

Area of Science:

• Statistics
• Biostatistics
• Psychometrics

Background:

• Standardized mean differences (SMDs) are crucial for meta-analysis and power analysis.
• Common SMDs like Cohen's d and Hedges' d rely on the assumption of equal variances, which is often violated in real-world data.
• This fragility limits the accuracy of traditional effect size calculations.

Purpose of the Study:

• To introduce a novel effect size measure for comparing means that does not assume equal variances.
• To provide an unbiased estimator for effect sizes comparing a mean to a known constant.
• To enhance the reliability of statistical analyses in the presence of heterogeneous variances.

Main Methods:

• Developed a new effect size metric derived from Welch's t-tests.
• Formulated an unbiased estimator for mean-constant effect size.
• Implemented calculations for effect size, variance, and confidence intervals.

Main Results:

• The proposed effect size accurately reflects differences between means even when variances are unequal.
• The new metric provides a more robust alternative to traditional SMDs under heterogeneity.
• An R package is available for practical application of these methods.

Conclusions:

• The novel effect size measure offers a more accurate and reliable approach for statistical analyses with unequal variances.
• This methodology improves the precision of meta-analysis and power calculations.
• The provided R package facilitates the adoption of these advanced statistical tools.