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Computations using analysis of covariance

Authors

  • Timothy J. Barrett

    Corresponding author
    1. Canadian Rivers Institute, Department of Biology, University of New Brunswick, Saint John, NB, Canada
    2. Department of Mathematics and Statistics, University of Prince Edward Island, Charlottetown, PE, Canada
    • Canadian Rivers Institute, Department of Biology, University of New Brunswick, Saint John, NB, Canada
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Abstract

Although analysis of covariance (ANCOVA) was introduced long ago, it is not well understood by many researchers and is frequently misused. ANCOVA is an extension of analysis of variance (ANOVA) with the inclusion of one or more covariates. Its benefits compared to ANOVA include (1) increased power and (2) a reduction in biases caused by differences in experimental units [the covariate(s)] among groups. ANCOVA can be presented using an adjusted means procedure (testing for differences in means adjusted for the covariate), but the procedure can be easily understood using a multiple linear regression method using indicator variables to represent groups. Statistical software packages use general linear models to perform ANCOVA which are identical to the multiple linear regression models. Failure to meet assumptions of ANCOVA can lead to misinterpretation of results. Failing to meet the assumption of parallel group regression slopes is common in many data sets and methods are available to analyze these data sets (e.g., the Johnson–Neyman technique). Although ANCOVA is robust to violations of some assumptions (e.g., normality and equality of variances) when sample sizes are equal, many nonparametric tests based on ranks are available as nonparametric alternatives to ANCOVA. WIREs Comp Stat 2011 3 260–268 DOI: 10.1002/wics.165

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