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Robust Means Modeling

Author

Listed:
  • Weihua Fan

    (University of Houston)

  • Gregory R. Hancock

    (University of Maryland, College Park)

Abstract

This study proposes robust means modeling (RMM) approaches for hypothesis testing of mean differences for between-subjects designs in order to control the biasing effects of nonnormality and variance inequality. Drawing from structural equation modeling (SEM), the RMM approaches make no assumption of variance homogeneity and employ robust estimation/rescaling strategies in order to alleviate reliance on normality. A Monte Carlo simulation is conducted to compare the Type I error rate and the power of the proposed six RMM test statistics to five analysis of variance (ANOVA)-based statistics, the latter of which have also employed trimmed means and Winsorized variances to enhance robustness. Various simulation factors manipulated include variance inequality, sample-size pairings with group variances, degree of nonnormality, alpha level for hypothesis tests, and effect size. Results show that the proposed RMM methods are indeed superior to the traditional ANOVA-based methods.

Suggested Citation

  • Weihua Fan & Gregory R. Hancock, 2012. "Robust Means Modeling," Journal of Educational and Behavioral Statistics, , vol. 37(1), pages 137-156, February.
    • Handle: RePEc:sae:jedbes:v:37:y:2012:i:1:p:137-156
    DOI: 10.3102/1076998610396897
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    References listed on IDEAS

    as
    1. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    2. Masanori Ichikawa & Sadanori Konishi, 1995. "Application of the bootstrap methods in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 60(1), pages 77-93, March.
    3. H. Keselman & Rhonda Kowalchuk & Lisa Lix, 1998. "Robust nonorthogonal analyses revisited: An update based on trimmed means," Psychometrika, Springer;The Psychometric Society, vol. 63(2), pages 145-163, June.
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