Accurate Confidence and Bayesian Interval Estimation for Non-centrality Parameters and Effect Size Indices

Kaidi Kang (), Megan T. Jones, Kristan Armstrong, Suzanne Avery, Maureen McHugo, Stephan Heckers and Simon Vandekar ()
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Kaidi Kang: Vanderbilt University
Megan T. Jones: Vanderbilt University
Kristan Armstrong: Vanderbilt University Medical Center
Suzanne Avery: Vanderbilt University Medical Center
Maureen McHugo: Vanderbilt University Medical Center
Stephan Heckers: Vanderbilt University Medical Center
Simon Vandekar: Vanderbilt University

Psychometrika, 2023, vol. 88, issue 1, No 12, 253-273

Abstract: Abstract Reporting effect size index estimates with their confidence intervals (CIs) can be an excellent way to simultaneously communicate the strength and precision of the observed evidence. We recently proposed a robust effect size index (RESI) that is advantageous over common indices because it’s widely applicable to different types of data. Here, we use statistical theory and simulations to develop and evaluate RESI estimators and confidence/credible intervals that rely on different covariance estimators. Our results show (1) counter to intuition, the randomness of covariates reduces coverage for Chi-squared and F CIs; (2) when the variance of the estimators is estimated, the non-central Chi-squared and F CIs using the parametric and robust RESI estimators fail to cover the true effect size at the nominal level. Using the robust estimator along with the proposed nonparametric bootstrap or Bayesian (credible) intervals provides valid inference for the RESI, even when model assumptions may be violated. This work forms a unified effect size reporting procedure, such that effect sizes with confidence/credible intervals can be easily reported in an analysis of variance (ANOVA) table format.

Keywords: effect size; robust effect size index; confidence interval; credible interval; analysis of effect size; non-centrality parameter; bootstrap; bayesian bootstrap; non-central Chi-squared distribution; non-central F distribution (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11336-022-09899-x

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