IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v37y2012i1p137-156.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998610396897
    Download Restriction: no
    File URL: https://libkey.io/10.3102/1076998610396897?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Doole, Graeme J. & Romera, Alvaro J. & Leslie, Jennifer E. & Chapman, David F. & Pinxterhuis, Ina (J.B.). & Kemp, Peter D., 2021. "Economic assessment of plantain (Plantago lanceolata) uptake in the New Zealand dairy sector," Agricultural Systems, Elsevier, vol. 187(C).
    2. Headrick, Todd C. & Sheng, Yanyan & Hodis, Flaviu-Adrian, 2007. "Numerical Computing and Graphics for the Power Method Transformation Using Mathematica," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i03).
    3. Yuan, Ke-Hai & Chan, Wai, 2008. "Structural equation modeling with near singular covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4842-4858, June.
    4. Pesaran, M. Hashem & Yamagata, Takashi, 2012. "Testing CAPM with a Large Number of Assets," IZA Discussion Papers 6469, Institute of Labor Economics (IZA).
    5. Schinckus, Christophe, 2015. "The valuation of social impact bonds: An introductory perspective with the Peterborough SIB," Research in International Business and Finance, Elsevier, vol. 35(C), pages 104-110.
    6. Max Auerswald & Morten Moshagen, 2015. "Generating Correlated, Non-normally Distributed Data Using a Non-linear Structural Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 920-937, December.
    7. Mohan D. Pant & Todd C. Headrick, 2017. "Simulating Uniform- and Triangular- Based Double Power Method Distributions," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(1), pages 1-1.
    8. Mahul, Olivier, 2002. "Hedging Price Risk in the Presence of Crop Yield and Revenue Insurance," 2002 International Congress, August 28-31, 2002, Zaragoza, Spain 24881, European Association of Agricultural Economists.
    9. Löhndorf, Nils, 2016. "An empirical analysis of scenario generation methods for stochastic optimization," European Journal of Operational Research, Elsevier, vol. 255(1), pages 121-132.
    10. Shaobo Jin & Fan Yang-Wallentin, 2017. "Asymptotic Robustness Study of the Polychoric Correlation Estimation," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 67-85, March.
    11. Schinckus, Christophe, 2018. "The valuation of social impact bonds: An introductory perspective with the Peterborough SIB," Research in International Business and Finance, Elsevier, vol. 45(C), pages 1-6.
    12. Foss, Tron & Jöreskog, Karl G. & Olsson, Ulf H., 2011. "Testing structural equation models: The effect of kurtosis," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2263-2275, July.
    13. Pelagatti, Matteo M. & Sen, Pranab K., 2013. "Rank tests for short memory stationarity," Journal of Econometrics, Elsevier, vol. 172(1), pages 90-105.
    14. Nicolas Depraetere & Martina Vandebroek, 2014. "Order selection in finite mixtures of linear regressions," Statistical Papers, Springer, vol. 55(3), pages 871-911, August.
    15. Emanuela Raffinetti & Pier Alda Ferrari, 2021. "A dependence measure flow tree through Monte Carlo simulations," Quality & Quantity: International Journal of Methodology, Springer, vol. 55(2), pages 467-496, April.
    16. Al-Subaihi, Ali A., 2004. "Simulating Correlated Multivariate Pseudorandom Numbers," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 9(i04).
    17. Ringle, Christian M. & Götz, Oliver & Wetzels, Martin & Wilson, Bradley, 2009. "On the Use of Formative Measurement Specifications in Structural Equation Modeling: A Monte Carlo Simulation Study to Compare Covariance-Based and Partial Least Squares Model Estimation Methodologies," MPRA Paper 15390, University Library of Munich, Germany.
    18. Ke-Hai Yuan & Yubin Tian & Hirokazu Yanagihara, 2015. "Empirical Correction to the Likelihood Ratio Statistic for Structural Equation Modeling with Many Variables," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 379-405, June.
    19. David Ory & Patricia Mokhtarian, 2010. "The impact of non-normality, sample size and estimation technique on goodness-of-fit measures in structural equation modeling: evidence from ten empirical models of travel behavior," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(3), pages 427-445, April.
    20. Africa Borges del Rosal & Concepción San Luis & Alfonso Sánchez-Bruno, 2003. "Dominance Statistics: A Simulation Study on the d Statistic," Quality & Quantity: International Journal of Methodology, Springer, vol. 37(3), pages 303-316, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:jedbes:v:37:y:2012:i:1:p:137-156. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.