Key result
Novel two-way ANOVA procedures control type-I error and achieve high power for analyzing cholesterol data.
Why the study?
Two-way ANOVA models typically assess homogeneity of effects, but incorporating prior knowledge of monotone orderings in factors like age and gender requires more powerful and computationally intensive tests.
A novel statistical approach for two-way ANOVA with ordered effects provides high power and robustness, demonstrated through application to cholesterol data.
May aid analysis of ordered effects in cholesterol data; leaves open validation before wider use.
Two-way ANOVA models are usually employed to see the homogeneity of row (column) effects. In various medical and psychological studies, prior information that these effects follow monotone orderings may be available; for example, the effects of the factors ‘Age’ and ‘Gender’ on low-density lipoprotein are observed to be monotonic with respect to both factors. Integrating this information yields computationally intensive yet powerful tests. Here we develop powerful procedures for testing simultaneous trends and constructing simultaneous confidence intervals for ordered effects in a two-way heteroscedastic additive ANOVA model. The likelihood ratio test and two union-intersection type tests are developed. For comparing various treatments, the reporting of confidence intervals for successive differences in effects that lead to the rejection of the null hypothesis is of interest. The proposed tests control type-I error rates, achieve high power, and remain robust under departures from normality. They also allow the construction of simultaneous confidence intervals. The test procedures developed here are implemented on cholesterol data of the patients classified according to age and gender and are seen to detect even small increments in effects of the factors. An ‘R’ software package has been developed to implement the proposed tests.
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Dey et al. (2026) studied Cholesterol. Statistical procedures for testing simultaneous trends in a two-way ANOVA was evaluated on Type-I error rates and power. The proposed statistical procedures for testing simultaneous trends in a two-way ANOVA controlled type-I error rates, achieved high power, and detected small increments in effects on cholesterol data.