Orthogonal Contrasts and the Generalized Inverse in Fixed Effects Analysis of Variance

1972 ◽  
Vol 26 (5) ◽  
pp. 32-34
Author(s):  
Walter H. Carter ◽  
Raymond H. Myers
Keyword(s):  
Analysis Of Variance ◽  
Fixed Effects ◽  
Generalized Inverse ◽  
Orthogonal Contrasts

scholarly journals Effect of the Age on the Evaluation of Horse Conformation and Movement

2016 ◽  
Vol 16 (3) ◽  
pp. 863-870 ◽  
Author(s):  
Janusz Wejer ◽  
Dorota Lewczuk
Keyword(s):  
Analysis Of Variance ◽  
Fixed Effects ◽  
Subjective Evaluation ◽  
Random Effect ◽  
Surprising Result ◽  
Age Classes ◽  
Phenotypic Correlations ◽  
Horse Breeding ◽  
Young Horses

AbstractThe evaluation of horse conformation is a changeable characteristic and knowledge of its character is essential in horse breeding. The effect of the age was investigated based on the analysis of a subjective evaluation of eight conformation and movement traits according to the 70 points scale of registered 857 Polish Trakehner. The analysis of variance included fixed effects of sex (mares and stallions), age (up to 1 year, yearlings, 2-year-old, 3-year-old and older) and the kind of breeder (private/national) and the random effect of the sire. The effect of the sire was statistically significant for all traits. The effect of the sex was significant only for the movement traits – the walk and canter in stallions reached higher notes. The effect of the kind of breeder was also statistically significant but only for the movement traits. The considered effect of the age was the most surprising result as it was statistically significant for all traits, but the only differences between age classes were found between very young horses (up to 1 year) and all other groups. The phenotypic correlations between traits suggest that traits such as overall impression, type, trunk and limbs (feet and legs) are overvalued in the youngest group of horses.

scholarly journals Specific residue: application of orthogonal contrasts when heteroscedasticity is present

2010 ◽  
Vol 67 (1) ◽  
pp. 117-125
Author(s):  
Maria Cristina Stolf Nogueira
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Analysis Of Variance ◽  
Residue Analysis ◽  
Sum Of Squares ◽  
Block Designs ◽  
Mean Square ◽  
Orthogonal Contrasts ◽  
Variance Homogeneity ◽  
Analyze Data

When experimental data are submitted to analysis of variance, the assumption of data homoscedasticity (variance homogeneity among treatments), associated to the adopted mathematical model must be satisfied. This verification is necessary to ensure the correct test for the analysis. In some cases, when data homoscedascity is not observed, errors may invalidate the analysis. An alternative to overcome this difficulty is the application of the specific residue analysis, which consists of the decomposition of the residual sum of squares in its components, in order to adequately test the correspondent orthogonal contrasts of interest between treatment means. Although the decomposition of the residual sum of squares is a seldom used procedure, it is useful for a better understanding of the residual mean square nature and to validate the tests to be applied. The objective of this review is to illustrate the specific residue application as a valid and adequate alternative to analyze data from experiments following completely randomized and randomized complete block designs in the presence of heteroscedasticity.

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