Box-Cox transformation in homoscedasticity and normality univariate and multivariate in experiments evaluating sweet potato

ABSTRACT:

Violating assumptions of normality and homoscedasticity 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, 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, branches productivity, soil insect resistance and shape of the roots were evaluated. No specific processing was ideal for each variable, and furthermore, processing datawas 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.

Keywords:
Ipomoea batatas; genetic parameters; homogeneity of variance; analysis of variance.