The Generalized ANOVA: A Classic Song Sung with Modern Lyrics

  • Hui ZhangEmail author
  • Xin Tu


The widely used analysis of variance (ANOVA) suffers from a series of flaws that not only raise questions about conclusions drawn from its use, but also undercut its many potential applications to modern clinical and observational research. In this paper, we propose a generalized ANOVA model to address the limitations of this popular approach so that it can be applied to many immediate as well as potential applications ranging from an age-old technical issue in applying ANOVA to cutting-edge methodological challenges. By integrating the classic theory of U-statistics, we develop distribution-free inference for this new class of models to address missing data for longitudinal clinical trials and cohort studies.


Count response Missing data Overdispersion 



The authors sincerely thank Dr. W. Jack Hall and Ms. Cheryl Bliss-Clark at the University of Rochester for their help to improve the presentation of the manuscript. This paper was also supported by the ASA Best Student Paper Award and ENAR Distinguished Student Paper Award to be presented at the 2009 JSM in Washington and 2010 ENAR Spring Meeting in New Orleans, respectively.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Feinberg School of MedicineNorth Western University ChicagoILUSA
  2. 2.Division of Biostatistics and BioinformaticsUC San Diego School of MedicineCAUSA

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