Details
| Original language | English |
|---|---|
| Pages (from-to) | 1541-1560 |
| Number of pages | 20 |
| Journal | Journal of applied statistics |
| Volume | 43 |
| Issue number | 8 |
| Early online date | 12 Feb 2016 |
| Publication status | E-pub ahead of print - 12 Feb 2016 |
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.
Keywords
- ANOVA F-test, control chart, industrial quality assessment, multiple contrast test, multivariate t-distribution
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Journal of applied statistics, Vol. 43, No. 8, 12.02.2016, p. 1541-1560.
Research output: Contribution to journal › Article › Research › peer review
}
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 - 2016/2/12
Y1 - 2016/2/12
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 -