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MANOVA for Large Number of Treatments

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Statistical Modeling and Simulation for Experimental Design and Machine Learning Applications (SimStat 2019)

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

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Abstract

The performance of Wilks’ likelihood ratio test statistic \(\Lambda \) is evaluated when the number of populations in a MANOVA model is allowed to increase, where the sample size and dimension are kept fixed. For simplicity, only one-way MANOVA model under homoscedasticity is considered, although for both balanced and unbalanced cases. Apart from the usual normality assumption, the error vectors in the model are also allowed to follow a t distribution, in order to assess the statistic for its robustness to normality. Whereas the statistic is found to be accurate under normality assumption, for both size and power, a serious size distortion and discernably low power are witnessed for t distribution for an increasing number of populations, even for large sample size. Finally, as a special case, the univariate \( \operatorname {\mathrm {F}}\) statistic for ANOVA model is also evaluated and compared with two of its recent modifications typically introduced for a large number of populations.

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Acknowledgements

The authors would like to thank Professor Jürgen Pilz and co-editors for the kind invitation to contribute a paper and processing it. The research of Professor S. Ejaz Ahmed was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Brock University, St. Catharines, ON, Canada

    S. Ejaz Ahmed

  2. Department of Statistics, Uppsala University, Uppsala, Sweden

    M. Rauf Ahmad

Authors
  1. S. Ejaz Ahmed
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  2. M. Rauf Ahmad
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Correspondence to M. Rauf Ahmad .

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Editors and Affiliations

  1. Department of Statistics, University of Klagenfurt, Klagenfurt, Austria

    Jürgen Pilz

  2. Department of Stochastic Simulation, St. Petersburg State University, St. Petersburg, Russia

    Viatcheslav B. Melas

  3. Department of Artificial Intelligence and Human Interfaces, Paris Lodron University Salzburg, Salzburg, Austria

    Arne Bathke

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Ahmed, S.E., Ahmad, M.R. (2023). MANOVA for Large Number of Treatments. In: Pilz, J., Melas, V.B., Bathke, A. (eds) Statistical Modeling and Simulation for Experimental Design and Machine Learning Applications. SimStat 2019. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-40055-1_2

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