Symbolic Description of Factorial Models for Analysis of Variance

Wilkinson, G. N.; Rogers, C. E.

doi:10.2307/2346786

Cited by 714 publications

(486 citation statements)

References 8 publications

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“…Notation for factorial models is as in Wilkinson & Rogers (1973). Analyses of variance were used to examine the significance of fixed effects (Genus*Habit* Shade) at the plant (Block.…”

Section: Data Analysesmentioning

confidence: 99%

The architecture of New Zealand's divaricate shrubs in relation to light adaptation

Christian

Kelly

Turnbull

2006

New Zealand Journal of Botany

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The divaricating shoot habit is typified by a suite of architectural traits, quantified here using phylogenetic independent comparisons of three pairs of congeners, with or without the habit. We consider the hypothesis that the habit evolved as a structural photoprotection mechanism that maximises potential carbon fixation by minimising photoinhibition. Plants were grown in pots in full sun, or behind vertical screens transmitting c. 25, 52, or 73% sunlight. When shaded, all species shifted partitioning of biomass from stem thickening to leaf area expansion and occupied a larger crown volume for a given shoot biomass. Leaf numbers per stem length of divaricates and non-divaricates were greater in the lower and upper canopies, respectively, consistent with the view that in divaricates outer branches protect inner leaves. However, leaf numbers per stem length showed no response to variation in high light receipt. Divaricates showed some traits typical of plants adapted to sunny habitats: smaller effective leaf size, lesser fractional partitioning of biomass to leaves, and greater foliage densities. Other traits of divaricates were typical of plants adapted to shaded habitats: lesser stem diameters, stem biomass per unit stem length, leader dominance, leaf area index, ) would require a larger enhancement of net canopy photosynthesis than is likely to arise from avoidance of photoinhibition.

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“…Notation for factorial models is as in Wilkinson & Rogers (1973). Analyses of variance were used to examine the significance of fixed effects (Genus*Habit* Shade) at the plant (Block.…”

Section: Data Analysesmentioning

confidence: 99%

The architecture of New Zealand's divaricate shrubs in relation to light adaptation

Christian

Kelly

Turnbull

2006

New Zealand Journal of Botany

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“…All constrained components were used in reporting the results, and thus reduced-rank was not used because treatment effects were present on all axes, as judged by the relative magnitude of the eigenvalues of the constrained axes. The human model focused on the within-person tissue-dependent effects of isoflavone supplementation compared to placebo with the following model formula (Wilkinson & Rogers, 1973 Four different sets of significantly changed genes were used as dependent variables in the multivariate analysis; all significantly changed genes in 1) human PBMCs, 2) human WAT, 3)…”

Section: Resultsmentioning

confidence: 99%

A risk assessment-driven quantitative comparison of gene expression profiles in PBMCs and white adipose tissue of humans and rats after isoflavone supplementation

Velpen

Veer

Islam

et al. 2016

Food and Chemical Toxicology

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Quantitative insight into species differences in risk assessment is expected to reduce uncertainty and variability related to extrapolation from animals to humans. This paper explores quantification and comparison of gene expression data between tissues and species from intervention studies with isoflavones.Gene expression data from peripheral blood mononuclear cells (PBMCs) and white adipose tissue (WAT) after 8wk isoflavone interventions in postmenopausal women and ovariectomized F344 rats were used. A multivariate model was applied to quantify gene expression effects, which showed 3 to 5-fold larger effect sizes in rats compared to humans.For estrogen responsive genes, a 5-fold greater effect size was found in rats than in humans.For these genes, intertissue correlations (r=0.23 in humans, r=0.22 in rats) and interspecies correlation in WAT (r=0.31) were statistically significant. Effect sizes, intertissue and interspecies correlations for some groups of genes within energy metabolism, inflammation and cell cycle processes were significant, but weak.Quantification of gene expression data reveals differences between rats and women in effect magnitude after isoflavone supplementation. For risk assessment, quantification of gene expression data and subsequent calculation of intertissue and interspecies correlations within biological pathways will further strengthen knowledge on comparability between tissues and species.

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“…Here the experiments and analysis used an approach known as "factorial design" (Yates and Mather, 1963;Fisher, 1926;Hill and Lewicki, 2005;Wilkinson and Rogers, 1973;Benestad et al, 2010), where a factorial regression was used to assess which influence each of the choices in the model setup has on the forecasts. It is a technique that can analyse sets of factors which are considered to have potential effects on the outcome in experiments, where an analysis of variance (ANOVA; Wilks, 1995) provides estimates for error bars and the level of statistical significance.…”

Section: The Analysismentioning

confidence: 99%

The use of regression for assessing a seasonal forecast model experiment

Benestad¹,

Senan²,

Orsolini³

2016

Earth Syst. Dynam.

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Abstract. We show how factorial regression can be used to analyse numerical model experiments, testing the effect of different model settings. We analysed results from a coupled atmosphere-ocean model to explore how the different choices in the experimental set-up influence the seasonal predictions. These choices included a representation of the sea ice and the height of top of the atmosphere, and the results suggested that the simulated monthly mean air temperatures poleward of the mid-latitudes were highly sensitivity to the specification of the top of the atmosphere, interpreted as the presence or absence of a stratosphere. The seasonal forecasts for the midlatitudes to high latitudes were also sensitive to whether the model set-up included a dynamic or non-dynamic sea-ice representation, although this effect was somewhat less important than the role of the stratosphere. The air temperature in the tropics was insensitive to these choices.

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Symbolic Description of Factorial Models for Analysis of Variance

Cited by 714 publications

References 8 publications

The architecture of New Zealand's divaricate shrubs in relation to light adaptation

The architecture of New Zealand's divaricate shrubs in relation to light adaptation

A risk assessment-driven quantitative comparison of gene expression profiles in PBMCs and white adipose tissue of humans and rats after isoflavone supplementation

The use of regression for assessing a seasonal forecast model experiment

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