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Analysis of means: a generalized approach using R

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  • Philip Pallmann
  • Ludwig A. Hothorn

Abstract

Papers on the analysis of means (ANOM) have been circulating in the quality control literature for decades, routinely describing it as a statistical stand-alone concept. Therefore, we clarify that ANOM should rather be regarded as a special case of a much more universal approach known as multiple contrast tests (MCTs). Perceiving ANOM as a grand-mean-type MCT paves the way for implementing it in the open-source software R. We give a brief tutorial on how to exploit R's versatility and introduce the R package ANOM for drawing the familiar decision charts. Beyond that, we illustrate two practical aspects of data analysis with ANOM: firstly, we compare merits and drawbacks of ANOM-type MCTs and ANOVA F -test and assess their respective statistical powers, and secondly, we show that the benefit of using critical values from multivariate t -distributions for ANOM instead of simple Bonferroni quantiles is oftentimes negligible.

Suggested Citation

  • Philip Pallmann & Ludwig A. Hothorn, 2016. "Analysis of means: a generalized approach using R," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(8), pages 1541-1560, June.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:8:p:1541-1560
    DOI: 10.1080/02664763.2015.1117584
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    References listed on IDEAS

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    1. Bretz, Frank, 2006. "An extension of the Williams trend test to general unbalanced linear models," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1735-1748, April.
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    4. Konietschke Frank & Bösiger Sandra & Brunner Edgar & Hothorn Ludwig A., 2013. "Are Multiple Contrast Tests Superior to the ANOVA?," The International Journal of Biostatistics, De Gruyter, vol. 9(1), pages 63-73, August.
    5. Esther Herberich & Johannes Sikorski & Torsten Hothorn, 2010. "A Robust Procedure for Comparing Multiple Means under Heteroscedasticity in Unbalanced Designs," PLOS ONE, Public Library of Science, vol. 5(3), pages 1-8, March.
    6. Peter Wludyka, 1999. "Two non-parametric, analysis-of-means-type tests for homogeneity of variances," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(2), pages 243-256.
    7. C. V. Rao & S. Hari Krishna, 1997. "A graphical method for testing the equality of several variances," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(3), pages 279-288.
    8. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
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