Transformação Box-Cox na homocedasticidade e normalidade uni e multivariada em experimentos de batata-doce

Abstract

Box-Cox transformation in homoscedasticity and normality univariate and multivariate in experiments evaluating sweet potatoViolating assumptions of normality and homoscedasticity of the residuals can be a complicating factor in the hypothesis tests and parameter estimation. When assumptions are not met, usually as a consequence of the measurement scale, the transformation of this scale can lead the suitability of the presuppositions. This study aimed to verify the effect of the Box-Cox transformation in the estimation of genetic parameters, homoscedasticity and univariate and multivariate normality of the residuals, based on eleven experiments with sweet potatoes. The experiments were carried out in a randomized block design between the years 2007 and 2011. The Box-Cox transformation was studied independently of the existence of homoscedasticity and normality of the residuals. The traits total and marketable root yield, average weight of marketable roots, vines productivity, soil insect resistance and shape of the roots were evaluated. No specific processing was ideal for each variable, and furthermore, processing data was not always necessary. The Box-Cox transformation has improved homoscedasticity and univariate and multivariate normality, however, not always these hypothesis are no longer rejected after the transformation. The Box-Cox transformation practically did not change the estimates of heritability and variation indexes and the conclusions of F test for treatment effect in most cases, however, it led to reductions in the estimates of environmental and genetic variation coefficient.

Comparison of Different Methods of Measuring Tree Volumes in the Municipality of Anapu, Pará, Brazil

“…This step was necessary to identify the lambda value (λ) that maximized the maximum likelihood estimator and minimized the residual of the factorial model to be used in the ANOVA. This transformation of the response variable (volume) was for the purpose of meeting the assumptions of homoscedasticity and normality of residuals (AZEVEDO et al, 2015). The means were compared using the Tukey multiple comparison test.…”

Transformação Box-Cox e modelagem dendrométrica de árvores isoladas no bioma Cerrado em Minas Gerais

“…Para transformação das variáveis é importante levar em consideração o método utilizado, uma vez que a transformação inadequada pode acarretar maiores problemas de normalidade, homocedasticidade e independência dos resíduos (Azevedo;Andrade Júnior;Fernandes, 2016). Portanto, pode ser utilizado o método de Box-Cox, no qual visa a obtenção de uma potência para que conjunto de dados transformados se aproximem de uma distribuição normal (Box;Cox, 1964).…”

Generalização do modelo AMMI para dados multiatributos

“…Ressalta-se que esses testes só são válidos se os pressupostos assumidos para os erros do modelo estiverem satisfeitos. Nos casos em que pressuposições da ANOVA não são satisfeitas, a família de transformações Box-Cox (Box e Cox, 1964) tem sido amplamente utilizada por produzir, com base na utilização de um valor λ que maximize o estimador de máxima verossimilhança e minimize o resíduo, uma transformação da variável resposta tal que as pressuposições de homocedasticidade e normalidade dos resíduos sejam simultaneamente satisfeitas (Azevedo et al, 2016).…”