The Analysis of Covariance

Db, DeLURY

doi:10.2307/3001562

Cited by 34 publications

(5 citation statements)

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“…The analysis of covariance is a very important statistical method in experimentation, especially for the agricultural sciences, but for various reasons it is not used in many occasions. It combines variance analysis with regression analysis in order to reduce the variability that can be explained by the covariate variable; it also adjusts treatment measures and estimates the effect of the independent variable (treatment) on the dependent variable with more precision (Wishart, 1936;DeLury, 1948).…”

Section: Analysis Of Covariance In the Agricultural Experimentationmentioning

confidence: 99%

Covariance analysis of sugarcane variety experiments (Saccharum spp.) in contrasting environments

Rodríguez¹,

Berres

Antunez³

et al. 2015

Weber, T., McPhee, M.J. And Anderssen, R.S. (Eds) MODSIM2015, 21st International Congress on Modelling and Simulation

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This contribution presents the results of a covariance analysis of experiments with sugarcane varieties (Saccharum spp.) in contrasting environments on a Vertisol soil type, both under normal soil conditions and in flooding conditions. The varieties of the used sugarcane were commercial varieties of the cuban sugarcane breeding program, C87-51, C1051-72, C120-78, C8612, C86-456 and C90-469. Plant cane and first ratoon cane, both at 12 months of age, were evaluated in a Randomized Complete Block Design (RCBD) with five replications. The first ratoon cane corresponds to a plant in its second season. It is formed during the first harvest of a plant, when the lower part of the plant is left uncut, such that ratoons can grow from the buds. First ratoon cane provides a faster maturing but delivers a less amount of yield. The dependent variable was the cane yield measured in tonnes (metric tons) per hectare (tcane. ha-1). As a covariate variable of the model the millable stalk number plot was chosen. The two variables were evaluated at the age of 12 months. The results demonstrate the usefulness of a covariance analysis in the presence of a quantitative variable, which affects the experimental units or plots. In particular, adjusted average values of agricultural performance and a correct ordering of the merit of these variables could be obtained. Thereby, a bias in the results is avoided, which might occur if the variety experiments are evaluated in contrasting environments. The covariance analysis minimizes the variability among experimental units by adjusting their values to a common value of the covariate. The use of the covariate reduced the mean square error in the analysis and increased the reliability of the experimental results. If the millable stalk number per plot were not measured, then the variation of the cane yield in dependence on the impact of the specific crop-plot combinations could not be determined and would be included in the error term (mean square error). The use of a covariate reduced the mean square error in the analysis and increased the significance of the experimental results in plant cane and in the first ratoon cycle. Under the effects of water excesses in the soil a marked reduction of the cane yield could be detected for all varieties. Thereby, the varieties C1051-73, C87-51 and C120-78 were affected most, and the other group integrated by C90-469, C86-12 and C86-456 in a significantly smaller proportion. This evidences that the latter group of varieties counts with a morphophysiology and biochemical mechanisms that make them adapt better to flooded soils. No marked difference between the first and second sugarcane cutting could be detected, except a decrease in the cane yield when the number of cuttings is increased. Therefore, similar results were obtained for the plant cane and in the first ratoon cycle, with only slight differences in the magnitudes.

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Section: Analysis Of Covariance In the Agricultural Experimentationmentioning

confidence: 99%

Covariance analysis of sugarcane variety experiments (Saccharum spp.) in contrasting environments

Rodríguez¹,

Berres

Antunez³

et al. 2015

Weber, T., McPhee, M.J. And Anderssen, R.S. (Eds) MODSIM2015, 21st International Congress on Modelling and Simulation

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“…The established way of proceeding (Fisher, 1934, p. 267;Wishart and Sanders, 1936, p, 55;Wishart, 1938Wishart, , 1950DeLury, 1948;Quenouille, 1952, section 8.5;Guenther, 1964,p. 159;Rao, 1965, section 4h) involves the quantities in the bottom lines of Table 4.…”

Section: A 2xexamplementioning

confidence: 99%

“…An analysis of variance of y is in Table 15, which confirms the large linear "times" effect as well as differences in effect between the drugs. The sums of squares and products for a covariance analysis are in Table 16; in view of the complete randomization described by Solandt et al (1943a) and by DeLury (1948), it is odd that the x-variate's mean squares for the two "times" components are the two x mean squares that are so much less than the others.…”

Section: Sexesmentioning

confidence: 99%

Covariance Analysis, Factorial Experiments and Marginality

Preece

1980

The Statistician

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The use of covariates introduces non-orthogonality into factorial analyses that would otherwise be orthogonal; in particular, non-orthogonality is induced between one treatment effect and another. Recent discussions on the general principles of non-orthogonal analyses and on the principle of marginality might therefore be thought relevant to factorial covariance analyses. The present paper examines these matters and tries to assesstheir importance in practice. Published analyses are re-examined and criticized, to illustrate the points at issue. Covariance analysis for split-plot experiments and for variates with missing values is not discussed.

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“…A statistical analysis was performed by methods like multiple comparison of the mean (Gabriel's and Dunnett's tests) 50 and correlation analysis. 51 In addition, an examination of the contribution of the atoms (represented by the stoichiometric coefficients) to HOMO and LUMO eigenvalues as well as IPs and EAs energy (as continuous variables) by means of the Analysis of Covariance method ANCOVA [52][53][54] was performed. ANCOVA calculations are more involved and time consuming than either technique alone.…”

Section: Methods and Technical Detailsmentioning

confidence: 99%

Assessment of quantum‐chemical methods for electronic properties and geometry of signaling biomolecules

Ferro

Bredow

2009

J Comput Chem

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A reasonable balance between accuracy and feasibility of quantum-chemical methods depends on the complexity of the molecular system and the scientific goals. Six series of indole-, naphthalene-, phenol-, benzoic-, phenoxy-, other auxin-derivatives, and a test set of similar organic molecules have been chosen for an assessment of 13 density functional and semi-empirical molecular orbital methods with respect to electronic and structural properties. The accuracy and precision of HOMO/LUMO calculations are determined by comparison with experimental ionization potentials and electron affinities. Further comparison was performed at atomic level by covariance analysis. The methods KMLYP, MSINDO, and PM3 are precise and accurate for the whole set of molecules. The method AM1 offers comparable accuracy with the exception of electron affinities of indole derivatives, where significant deviations from experiment were observed. Geometrical properties were best reproduced with the semi-empirical method MSINDO.

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The Analysis of Covariance

Cited by 34 publications

References 1 publication

Covariance analysis of sugarcane variety experiments (Saccharum spp.) in contrasting environments

Covariance analysis of sugarcane variety experiments (Saccharum spp.) in contrasting environments

Covariance Analysis, Factorial Experiments and Marginality

Assessment of quantum‐chemical methods for electronic properties and geometry of signaling biomolecules

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