The Degree of Dependence Between Multiple-Treatment Effect Sizes

Area of Science:

• Statistics
• Biostatistics
• Psychometrics

Background:

• Meta-analysis synthesizes results from multiple studies.
• Standardized mean difference (SMD) is a common effect size measure.
• Dependence between effect sizes in multiple-treatment studies requires careful consideration.

Purpose of the Study:

• To examine the dependence between SMD effect sizes in multiple-treatment meta-analyses.
• To simplify and explore the correlation formula for effect size dependence.
• To investigate the impact of group size ratios and effect size values on this dependence.

Main Methods:

• Utilized the correlation formula by Gleser and Olkin (1994).
• Simplified the formula under conditions of equal sample and effect sizes.
• Analyzed the influence of group size ratios on effect size correlation.

Main Results:

• The ratio of group sizes was found to be a more significant factor in effect size correlation than the magnitude of effect sizes.
• Smaller control group sizes and large effect sizes of the same sign correlated with stronger dependence.
• Ignoring effect size dependence decreased the precision of mean effect differences in meta-analyses.

Conclusions:

• Group size ratio is a critical factor influencing effect size dependence in meta-analysis.
• Accurate meta-analysis requires accounting for the dependence between effect sizes.
• Ignoring dependence leads to reduced precision, particularly when control groups are small relative to treatment groups.