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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Pelagatti, Matteo M. & Sen, Pranab K., 2013. "Rank tests for short memory stationarity," Journal of Econometrics, Elsevier, vol. 172(1), pages 90-105.
    7. 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.
    8. Al-Subaihi, Ali A., 2004. "Simulating Correlated Multivariate Pseudorandom Numbers," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 9(i04).
    9. 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.
    10. 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.
    11. Yen Lee & David Kaplan, 2018. "Generating Multivariate Ordinal Data via Entropy Principles," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 156-181, March.
    12. M Hashem Pesaran & Takashi Yamagata, 2012. "Testing CAPM with a Large Number of Assets," Discussion Papers 12/05, Department of Economics, University of York.
    13. Ory, David T, 2007. "Structural Equation Modeling of Relative Desired Travel Amounts," Institute of Transportation Studies, Working Paper Series qt8mj659fp, Institute of Transportation Studies, UC Davis.
    14. Beasley, T. Mark & Zumbo, Bruno D., 2003. "Comparison of aligned Friedman rank and parametric methods for testing interactions in split-plot designs," Computational Statistics & Data Analysis, Elsevier, vol. 42(4), pages 569-593, April.
    15. Jonas Månsson & Josefin Dahlander, 2011. "Social interaction impact on attitudes – Native Swedes’ attitudes towards labour immigrants and guest workers after hurricane Gudrun," Baltic Journal of Economics, Baltic International Centre for Economic Policy Studies, vol. 11(1), pages 51-64, July.
    16. Irmer, Julien Patrick & Klein, Andreas & Schermelleh-Engel, Karin, 2024. "A General Model-Implied Simulation-Based Power Estimation Method for Correctly and Misspecfied Models: Applications to Nonlinear and Linear Structural Equation Models," OSF Preprints pe5bj, Center for Open Science.
    17. Guangjian Zhang & Minami Hattori & Lauren A. Trichtinger, 2023. "Rotating Factors to Simplify Their Structural Paths," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 865-887, September.
    18. Fei Gu & Hao Wu, 2016. "Raw Data Maximum Likelihood Estimation for Common Principal Component Models: A State Space Approach," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 751-773, September.
    19. Pasquale Dolce & Cristina Davino & Domenico Vistocco, 2022. "Quantile composite-based path modeling: algorithms, properties and applications," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(4), pages 909-949, December.
    20. Peter Wludyka, 1999. "Two non-parametric, analysis-of-means-type tests for homogeneity of variances," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(2), pages 243-256.

    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.