Testing for ordered alternatives in heteroscedastic ANOVA under normality

Mondal, Anjana; Pauly, Markus; Kumar, Somesh

doi:10.1007/s00362-022-01366-0

Cited by 5 publications

(4 citation statements)

References 32 publications

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“…The classical F -test for three-way ANOVA is performed using standard test functions available in the R library based on the method of Bao and Ananda. − The assumption of normality of all data sets is verified using the quantile–quantile (Q–Q) plot. , WSD data consists of horizontal and vertical wear scar diameters (HSD and VSD) for each of the three stationary bottom balls. The Pearson correlation coefficient is calculated between HSD and VSD values. , A recently developed LRT is used to determine the ordering among the effects of various oil concentrations on WSD values (Supporting Information S1.6) …”

Section: Methodsmentioning

confidence: 99%

“…Some statistical tests are used to test for the significance of effects of oil concentrations on WSD values. A recently developed “Likelihood ratio test (LRT)” by Mondal et al is used to find the trends in effects on WSD values by using different levels of oil concentrations . All computations are carried out using the statistical software “R” .…”

Section: Introductionmentioning

confidence: 99%

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TiO₂ Nanoparticles Coated with Nitrogen-Doped Amorphous Carbon as Lubricant Additives in Engine Oil

Srivastava,

Ranjan,

Muthusamy

et al. 2023

ACS Appl. Nano Mater.

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Nanoparticle-dispersed lubricants reduce friction and wear of tribo-pairs by providing nanoscale polishing and asperity filling mechanisms. But these particles also have an adverse effect on the lubrication due to the agglomeration and poor interaction with the tribo-interface. Herein, we explore the effect of surface modification of TiO2 nanoparticles on the tribological properties of commercial engine oil. Surface modifications of TiO2 nanoparticles are done by coating layers of amorphous carbon and nitrogen-doped amorphous carbon. Investigations of the tribological properties of surface-modified TiO2 nanoparticle-dispersed oils show improved performance due to high dispersibility in engine oil. There is a decrease in the coefficient of friction by ∼35% and the wear scar diameter by ∼27% when compared to the base oil. Both a surface roughness reduction of ∼85% and a wear depth profile reduction of ∼88% are due to the nanoscale polishing mechanism at the tribo-interface by nanoparticles. To gain insights of the effects of oil concentration and ball types on the wear scar diameter, a statistical approach is employed. The analysis of variance test yields that the different oil concentrations have a significant effect on the wear scar diameter. The trends obtained from this statistical test are consistent with the experimental results. This novel approach opens up exploring advanced methods of statistical analysis for tribological applications.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

TiO₂ Nanoparticles Coated with Nitrogen-Doped Amorphous Carbon as Lubricant Additives in Engine Oil

Srivastava,

Ranjan,

Muthusamy

et al. 2023

ACS Appl. Nano Mater.

View full text Add to dashboard Cite

show abstract

“…For testing multiple contrasts in randomized dose-response studies with correlated multiple primary endpoints, Hasler and Hothorn (2012) considered a Williams-type approach. Mondal et al (2022) proposed several test procedures for testing the homogeneity of treatment effects against ordered alternatives in a one-way ANOVA model with unknown and unequal error variances. Mondal et al (2023) considered the problem of testing the equality of row effects against their ordered alternatives in a two-way additive ANOVA model when errors follow normal distributions.…”

Section: Introductionmentioning

confidence: 99%

“…Mondal et al. (2022) proposed several test procedures for testing the homogeneity of treatment effects against ordered alternatives in a one‐way ANOVA model with unknown and unequal error variances. Mondal et al.…”

Section: Introductionmentioning

confidence: 99%

Bootstrap tests for simultaneous monotone ordering of effects in a two‐way ANOVA

Dey,

Mondal,

Kumar

2024

Biometrical J

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In a two‐way additive analysis of variance (ANOVA) model, we consider the problem of testing for homogeneity of both row and column effects against their simultaneous ordering. The error variances are assumed to be heterogeneous with unbalanced samples in each cell. Two simultaneous test procedures are developed—the first one using the likelihood ratio test (LRT) statistics of two independent hypotheses and another based on the consecutive pairwise differences of estimators of effects. The parametric bootstrap (PB) approach is used to find critical points of both the tests and the asymptotic accuracy of the bootstrap is established. An extensive simulation study shows that the proposed tests achieve the nominal size and have very good power performance. The robustness of the tests is also analyzed under deviation from normality. An “R” package is developed and shared on “GitHub” for ease of implementation of users. The proposed tests are illustrated using a real data set on the mortality due to alcoholic liver disease and it is shown that age and gender have a significant impact on the increasing incidence of mortality.

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Testing against ordered alternatives in one-way ANOVA model with exponential errors

Mondal,

Pauly,

Kumar

2024

Ann Inst Stat Math

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Testing for ordered alternatives in heteroscedastic ANOVA under normality

Cited by 5 publications

References 32 publications

TiO₂ Nanoparticles Coated with Nitrogen-Doped Amorphous Carbon as Lubricant Additives in Engine Oil

TiO₂ Nanoparticles Coated with Nitrogen-Doped Amorphous Carbon as Lubricant Additives in Engine Oil

Bootstrap tests for simultaneous monotone ordering of effects in a two‐way ANOVA

Testing against ordered alternatives in one-way ANOVA model with exponential errors

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Testing for ordered alternatives in heteroscedastic ANOVA under normality

Cited by 5 publications

References 32 publications

TiO2 Nanoparticles Coated with Nitrogen-Doped Amorphous Carbon as Lubricant Additives in Engine Oil

TiO2 Nanoparticles Coated with Nitrogen-Doped Amorphous Carbon as Lubricant Additives in Engine Oil

Bootstrap tests for simultaneous monotone ordering of effects in a two‐way ANOVA

Testing against ordered alternatives in one-way ANOVA model with exponential errors

Contact Info

Product

Resources

About

TiO₂ Nanoparticles Coated with Nitrogen-Doped Amorphous Carbon as Lubricant Additives in Engine Oil

TiO₂ Nanoparticles Coated with Nitrogen-Doped Amorphous Carbon as Lubricant Additives in Engine Oil