Analysis of Means Using Ranks

Bakir, Saad T.

doi:10.1080/03610918908812789

Cited by 24 publications

(23 citation statements)

References 9 publications

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“…ANOM-type data analysis may also be carried out nonparametrically e.g., with ranks as inputs (ANOMR) Bakir (1989Bakir ( , 1994 or as a randomization test based on permutations (PANOM). Nonparametric MCTs are discussed by Konietschke et al (2012); they express the hypotheses in terms of relative effects, which in turn are estimated based on global rankings.…”

Section: Nonparametric Anommentioning

confidence: 99%

Analysis of means: a generalized approach using R

Pallmann

Hothorn

2016

Journal of Applied Statistics

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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: 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.

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Section: Nonparametric Anommentioning

confidence: 99%

Analysis of means: a generalized approach using R

Pallmann

Hothorn

2016

Journal of Applied Statistics

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“…After Ott 4 introduced ANOM, many authors, including References 5-11 contributed to the later development of the ANOM procedure. For instance, heteroscedastic ANOM (HANOM) 12 can be used for mean testings in the presence of heteroscedastic data.…”

Section: Introductionmentioning

confidence: 99%

Analysis of means approach in advanced designs

Jayalath

2020

Appl Stoch Models Bus & Ind

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Analysis of means (ANOM), similar to Shewhart control chart that exhibits individual mean effects on a graphical display, is an attractive alternative mean testing procedure for the analysis of variance (ANOVA). The procedure is primarily used to analyze experimental data from designs with only fixed effects. Recently introduced, the ANOM procedure based on the q‐distribution (ANOMQ procedure) generalizes the ANOM approach to random effects models. This article reveals that the application of ANOM and ANOMQ procedures in advanced designs such as hierarchically nested and split‐plot designs with fixed, random, and mixed effects enhances the data visualization aspect in graphical testing. Data from two real‐world experiments are used to illustrate the proposed procedure; furthermore, these experiments exhibit the ANOM procedures' visualization ability compared with ANOVA from the point of view of the practitioner.

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“…This is equivalent to the multiple comparisons of means and variances. Standard statistical methods for such comparisons include multiple hypothesis tests (Carroll and Schneider, 1985), ANalysis Of Means (ANOM) chart (Ott, 1967), ANalysis Of Means for Variance (ANOMV) chart (Nelson et al, 2005), ANOM using Ranks (ANOMR) chart (Bakir, 1989), ANOMR-type test for homogeneity of Variances (ANOMRV) chart (Bakir, 2010), etc. Multiple hypothesis tests, such as the F-test in ANOVA and Levene's test, give conclusions on whether different groups have the same mean and variance, respectively.…”

Section: Introductionmentioning

confidence: 99%

Quality-driven workforce performance evaluation based on robust regression and ANOMR/ANOMRV chart

2013

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The integration of quality improvement and manufacturing system management has emerged as a promising research topic in recent years. Since operators' performance variation can be reflected in product quality, workforce performance evaluation should be conducted with quality-based metrics to improve product quality as well as manufacturing system productivity. In this article, a methodology incorporating regression modeling and multiple comparisons is proposed to aid the performance evaluation. The effects of other impacting factors that contribute to operators' performance variation are quantified with a robust zero-inflated Poisson regression model. The model coefficients are analyzed with multiple hypothesis tests to identify underperforming machines. Two statistical charts used in multiple comparisons are adopted for identifying underperforming operators. A case study with data from a real-world production system and a simulation experiment are presented to demonstrate the proposed methodology.

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Analysis of Means Using Ranks

Cited by 24 publications

References 9 publications

Analysis of means: a generalized approach using R

Analysis of means: a generalized approach using R

Analysis of means approach in advanced designs

Quality-driven workforce performance evaluation based on robust regression and ANOMR/ANOMRV chart

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