A Robust Effect Size Index.

Area of Science:

• Statistics
• Behavioral Sciences
• Psychometrics

Background:

• Effect size indices are crucial for study design and reporting, offering unitless measures of association independent of sample size.
• Current effect size indices are often tied to specific parametric models or population parameters, limiting their generalizability.
• Existing estimators can be biased when parametric models are misspecified, such as with unknown heteroskedasticity.

Purpose of the Study:

• To propose a novel, robust effect size index based on M-estimators.
• To develop a generalizable, unitless effect size measure applicable across a wide range of statistical models.
• To provide tools for calculating statistical power and sample size based on the new index.

Main Methods:

• Developed a new effect size index using M-estimators.
• Demonstrated the index's relationship with existing measures (Cohen's d, standardized log odds ratio) under correct model specification.
• Utilized simulations to evaluate the bias and standard error of the proposed estimator in finite samples.

Main Results:

• The proposed effect size index is unitless and invariant across different statistical models.
• The new index functions as Cohen's d or standardized log odds ratio when parametric models are correctly specified.
• Existing estimators exhibit bias under incorrect model assumptions, a limitation addressed by the new index.

Conclusions:

• The proposed robust effect size index offers greater generalizability and uniformity across diverse statistical models.
• This invariance has the potential to significantly enhance the consistency and clarity of effect size communication within the behavioral sciences.
• The index facilitates standardized power and sample size calculations, aiding robust study design.