Analysis of means approach in advanced designs

Jayalath, Kalanka P.; Ng, Hon Keung Tony

doi:10.1002/asmb.2540

Cited by 3 publications

(2 citation statements)

References 23 publications

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“…(2018) [20], Kalanka P Jayalatha and Honkeung Tony Ng. (2020) [21], Kalanka P Jayalatha and Jacob Turner (2021) [22],…”

Section: Introductionmentioning

confidence: 99%

Extreme Value Charts and ANOM Based on Gumbel Distribution

Cheepuri

2022

IJMCR

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The quality is assessable by its feature is implicit with a probability model which follow Gumbel distribution. From each subgroups extreme values are used to construct extreme value charts and variable control charts. Probability model of the extreme order statistics and the size of each sub group are used in control chart constants. To find the decision lines of Gumbel distribution we implement a method of analysis of means (ANOM). The proposed ANOM decision lines are constructed for given number of subgroup within means category and between means category given by Ott (1967). These decision lines are illustrated by giving few examples.

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“…(2018) [20], Kalanka P Jayalatha and Honkeung Tony Ng. (2020) [21], Kalanka P Jayalatha and Jacob Turner (2021) [22],…”

Section: Introductionmentioning

confidence: 99%

Extreme Value Charts and ANOM Based on Gumbel Distribution

Cheepuri

2022

IJMCR

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“…Jayalath and Ng 18 suggest using ANOMQ procedure that uses the Studentized range

q

‐distribution for random factor ANOM analyses. Jayalath and Ng 19 further extend the ANOMQ for advanced designs such as mixed factor factorial, nested, and split‐plot designs. Jayalath and Turner 20 discuss recent developments on ANOM methods that are useful in practice and discussed logistical issues with post‐hoc testing.…”

Section: Introductionmentioning

confidence: 99%

A graphical alternative for multiple group comparisons in analysis of covariance

Jayalath

2022

Appl Stoch Models Bus & Ind

Self Cite

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Analysis of means (ANOM) is a graphical alternative for the analysis of variance (ANOVA) that was primarily developed for multiple mean comparisons. The ANOM is a simple graphical display that provides a visualization of statistically significant results and it allows validating their practical significance without deep statistics knowledge. The classical ANOM has been developed to analyze fixed mean effects, and its recent developments allow testing random and mixed effects. On the other hand, analysis of covariance (ANCOVA) is an extension of ANOVA that applies to test means in the presence of uncontrollable concomitant/nuisance variables. To effectively communicate the statistical findings from ANCOVA to a general audience on some public interest issue areas such as COVID-19, visualization of statistically significant results is a practical approach. This paper provides a graphical alternative for multiple group comparisons in ANCOVA as an extension of the ANOM. The proposed graphical alternative is validated and compared with the ANCOVA using a Monte Carlo simulation study. The simulation results indicated that the proposed method stands strong for practical ANCOVA problems. In addition, a COVID-19 application and two additional applications related to toxicology and business are used to exhibit the value of the proposed graphical procedure in practice.

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An improved statistical approach to compare means

Mahmood

Riaz

Iqbal³

et al. 2023

MATH

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<abstract><p>In many experiments, our interest lies in testing the significance of means from the grand mean of the study variable. Sometimes, an additional linearly related uncontrollable factor is also observed along with the main study variable, known as a covariate. For example, in Electrical Discharge Machining (EDM) problem, the effect of pulse current on the surface roughness (study variable) is affected by the machining time (covariate). Hence, covariate plays a vital role in testing means, and if ignored, it may lead to false decisions. Therefore, we have proposed a covariate-based approach to analyze the means in this study. This new approach capitalizes on the covariate effect to refine the traditional structure and rectify misleading decisions, especially when covariates are present. Moreover, we have investigated the impact of assumptions on the new approach, including normality, linearity, and homogeneity, by considering equal or unequal sample sizes. This study uses percentage type Ⅰ error and power as our performance indicators. The findings reveal that our proposal outperforms the traditional one and is more useful in reaching correct decisions. Finally, for practical considerations, we have covered two real applications based on experimental data related to the engineering and health sectors and illustrated the implementation of the study proposal.</p></abstract>

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Analysis of means approach in advanced designs

Cited by 3 publications

References 23 publications

Extreme Value Charts and ANOM Based on Gumbel Distribution

Extreme Value Charts and ANOM Based on Gumbel Distribution

A graphical alternative for multiple group comparisons in analysis of covariance

An improved statistical approach to compare means

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