TY - JOUR

T1 - Analysis of means

T2 - a generalized approach using R

AU - Pallmann, Philip

AU - Hothorn, Ludwig A.

N1 - Funding Information: The work of the second author was supported by the German Research Foundation [DFG HO-1687/9].

PY - 2016/6/10

Y1 - 2016/6/10

N2 - 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.

AB - 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.

KW - ANOVA F-test

KW - control chart

KW - industrial quality assessment

KW - multiple contrast test

KW - multivariate t-distribution

UR - http://www.scopus.com/inward/record.url?scp=84958035390&partnerID=8YFLogxK

U2 - 10.1080/02664763.2015.1117584

DO - 10.1080/02664763.2015.1117584

M3 - Article

AN - SCOPUS:84958035390

VL - 43

SP - 1541

EP - 1560

JO - Journal of applied statistics

JF - Journal of applied statistics

SN - 0266-4763

IS - 8

ER -