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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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