Nonparametric Models for ANOVA and ANCOVA: A Review

Michael G. Akritas, Edgar Brunner

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Citations (Scopus)

Abstract

This chapter discusses the nonparametric models, hypotheses, and test statistics for analysis of variance (ANOVA) and analysis of covariance (ANCOVA) designs, with independent and dependent ordinal data. This chapter presents the nonparametric models for two-way ANOVA and one-way ANCOVA. These are the simplest designs where all features of the nonparametric modeling can be appreciated. An important advantage of the nonparametric models is that these hypotheses and the procedures for analyzing them are unchanged by monotone transformations in the response. Decomposition for two-way ANCOVA that displays the covariate adjusted main effects and interactions of the two factors are easily obtained by replacing the single index. The nonparametric hypothesis of no interaction is equivalent to the statement that the mean of any transformation of the response can be decomposed in an additive fashion.

Original languageEnglish (US)
Title of host publicationRecent Advances and Trends in Nonparametric Statistics
PublisherElsevier Inc.
Pages79-91
Number of pages13
ISBN (Print)9780444513786
DOIs
StatePublished - Jan 1 2003

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Analysis of Covariance
Nonparametric Model
Analysis of variance
Nonparametric Hypotheses
Ordinal Data
Main Effect
Dependent Data
Interaction
Test Statistic
Covariates
Monotone
Decompose
Modeling
Review
Design

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Akritas, M. G., & Brunner, E. (2003). Nonparametric Models for ANOVA and ANCOVA: A Review. In Recent Advances and Trends in Nonparametric Statistics (pp. 79-91). Elsevier Inc.. https://doi.org/10.1016/B978-044451378-6/50006-5
Akritas, Michael G. ; Brunner, Edgar. / Nonparametric Models for ANOVA and ANCOVA : A Review. Recent Advances and Trends in Nonparametric Statistics. Elsevier Inc., 2003. pp. 79-91
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Akritas, MG & Brunner, E 2003, Nonparametric Models for ANOVA and ANCOVA: A Review. in Recent Advances and Trends in Nonparametric Statistics. Elsevier Inc., pp. 79-91. https://doi.org/10.1016/B978-044451378-6/50006-5

Nonparametric Models for ANOVA and ANCOVA : A Review. / Akritas, Michael G.; Brunner, Edgar.

Recent Advances and Trends in Nonparametric Statistics. Elsevier Inc., 2003. p. 79-91.

Research output: Chapter in Book/Report/Conference proceedingChapter

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Akritas MG, Brunner E. Nonparametric Models for ANOVA and ANCOVA: A Review. In Recent Advances and Trends in Nonparametric Statistics. Elsevier Inc. 2003. p. 79-91 https://doi.org/10.1016/B978-044451378-6/50006-5