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Addendum to: Heterogeneity Coefficients for Mahalanobis' D as a Multivariate Effect Size
1a Department of Psychology , University of New Mexico.
Multivariate Behavioral Research
|April 24, 2018
Summary
This study revises heterogeneity coefficients for Mahalanobis' D, addressing potential overestimation issues. New indices (H2 and EPV2) are introduced and compared to the original ones using real-world data.
Area of Science:
- Multivariate statistics
- Psychometrics
- Data analysis
Background:
- Previous work introduced heterogeneity coefficients (H and EPV) for Mahalanobis' D, a multivariate effect size measure.
- The Gini coefficient formed the basis for these initial heterogeneity indices.
Purpose of the Study:
- To address limitations in the original heterogeneity coefficients (H and EPV) for Mahalanobis' D.
- To introduce revised coefficients (H2 and EPV2) that may offer more accurate heterogeneity estimation.
- To compare the performance of original and revised indices using empirical data.
Main Methods:
- Discussion of limitations in the previously proposed Gini-based heterogeneity coefficients.
- Development and description of two revised heterogeneity coefficients (H2 and EPV2).
- Application and comparison of original and revised indices on real-world datasets.
Main Results:
- The original heterogeneity coefficients (H and EPV) may overestimate heterogeneity in certain conditions.
- The revised coefficients (H2 and EPV2) are proposed as potentially more accurate measures.
- Illustrative examples demonstrate differences between the original and revised indices.
Conclusions:
- The revised heterogeneity coefficients (H2 and EPV2) offer an improvement over the original indices for Mahalanobis' D.
- Careful consideration of heterogeneity estimation methods is crucial in multivariate analysis.
- Empirical validation highlights the practical implications of revised statistical indices.