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Estimation of the Box Correction for Degrees of Freedom from Sample Data in Randomized Block and Split-Plot Designs

Author

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  • Huynh Huynh
  • Leonard S. Feldt

Abstract

It has been suggested that when the variance assumptions of a repeated measures ANOVA are not met, the df of the mean square ratio should be adjusted by the sample estimate of the Box correction factor, É›. This procedure works well when É› is low, but the estimate is seriously biased when this is not the case. An alternate estimate is proposed which is shown by Monte Carlo methods to be less biased for moderately large É›.

Suggested Citation

  • Huynh Huynh & Leonard S. Feldt, 1976. "Estimation of the Box Correction for Degrees of Freedom from Sample Data in Randomized Block and Split-Plot Designs," Journal of Educational and Behavioral Statistics, , vol. 1(1), pages 69-82, March.
    • Handle: RePEc:sae:jedbes:v:1:y:1976:i:1:p:69-82
    DOI: 10.3102/10769986001001069
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    Cited by:

    1. Sylvan Wallenstein & Joseph Fleiss, 1979. "Repeated measurements analysis of variance when the correlations have a certain pattern," Psychometrika, Springer;The Psychometric Society, vol. 44(2), pages 229-233, June.
    2. Jain, Kriti & Bearden, J. Neil & Filipowicz, Allan, 2013. "Depression and forecast accuracy: Evidence from the 2010 FIFA World Cup," International Journal of Forecasting, Elsevier, vol. 29(1), pages 69-79.
    3. Patricia Mokhtarian & Francisco Samaniego & Robert Shumway & Neil Willits, 2002. "Revisiting the notion of induced traffic through a matched-pairs study," Transportation, Springer, vol. 29(2), pages 193-220, May.
    4. 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.
    5. Paula Fernández García & Guillermo Vallejo & Pablo Livacic-Rojas & Javier Herrero & Marcelino Cuesta, 2010. "Compative robustness of six tests in repeated measures designs with specified departures from sphericity," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(2), pages 289-301, February.
    6. Friedrich, Sarah & Brunner, Edgar & Pauly, Markus, 2017. "Permuting longitudinal data in spite of the dependencies," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 255-265.
    7. Steven Kachelmeier & Kristy Towry, 2005. "The Limitations of Experimental Design: A Case Study Involving Monetary Incentive Effects in Laboratory Markets," Experimental Economics, Springer;Economic Science Association, vol. 8(1), pages 21-33, April.
    8. Martin Spiess & Pascal Jordan & Mike Wendt, 2019. "Simplified Estimation and Testing in Unbalanced Repeated Measures Designs," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 212-235, March.
    9. Karen J. S. Bell & W. Grant Willis, 2016. "Teachers’ perceptions of bullying among youth," The Journal of Educational Research, Taylor & Francis Journals, vol. 109(2), pages 159-168, March.
    10. Dayanand Naik & Shantha Rao, 2001. "Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(1), pages 91-105.
    11. Friedrich, Sarah & Konietschke, Frank & Pauly, Markus, 2017. "A wild bootstrap approach for nonparametric repeated measurements," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 38-52.
    12. Eran Ben-Elia & Ido Erev & Yoram Shiftan, 2008. "The combined effect of information and experience on drivers’ route-choice behavior," Transportation, Springer, vol. 35(2), pages 165-177, March.
    13. A. Grieve, 1984. "Tests of sphericity of normal distributions and the analysis of repeated measures designs," Psychometrika, Springer;The Psychometric Society, vol. 49(2), pages 257-267, June.
    14. Wubben, Maarten J.J. & Cremer, David De & Dijk, Eric van, 2011. "The communication of anger and disappointment helps to establish cooperation through indirect reciprocity," Journal of Economic Psychology, Elsevier, vol. 32(3), pages 489-501, June.
    15. Robert Boik, 1981. "A priori tests in repeated measures designs: Effects of nonsphericity," Psychometrika, Springer;The Psychometric Society, vol. 46(3), pages 241-255, September.
    16. Zhang, Yahua & Round, David K., 2009. "The effects of China's airline mergers on prices," Journal of Air Transport Management, Elsevier, vol. 15(6), pages 315-323.

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