Pallmann, Philip Steffen and Hothorn, Ludwig A. (2016) Analysis of means : a generalized approach using R. Journal of Applied Statistics, 43 (8). pp. 1541-1560. ISSN 0266-4763
JApplStat_Pallmann_Hothorn_Penultimate.pdf - Accepted Version
Available under License Creative Commons Attribution.
Download (464kB)
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 opensource software R. We give a brief tutorial on how to exploit R's versatility and introduce R package ANOM for drawing the familiar decision charts. Beyond that, we illustrate two practical aspects of data analysis with ANOM: rstly, 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 benet of using critical values from multivariate t-distributions for ANOM instead of simple Bonferroni quantiles is oftentimes negligible.