Data transformation as an alternative to univariate analysis of variance

Abstract

In experiments, it is common to obtain various response variables that are subject to individual statistical analysis, leading to results for each characteristic. In order to propose an alternative analysis to deal with several characteristics at the same time, Fisher’s Discriminant Analysis was used in this work.  Through this analysis, multivariate data of various characteristics are transformed into a new univariate variable without information loss.  To illustrate the technique, we used data from na experiment of producing coffee seedlings in tubes, which evaluated the effect of two commercial substrates (A and B), and five substitution proportions (0, 20, 40, 60 and 80%) of the substrate for an organic compound. Seven quality characteristics of the seedlings were evaluated, and a new variable was obtained through the transformation of the original variables using Fisher’s Linear Discriminant function. The variance analysis of quality characteristics of individual seedlings detected significant diferences only in the replacing proportion of the substrate for organic fertilizer, and optimal proportions of 19 to 29% were estimated depending on the characteristic.  On the other hand, the variance analysis of the transformed data detected significant differences in substrate interaction x percentage replacement. These results show that using Fisher’s Discriminant Function to transform multivariate data into a new unidimensional variable can be considered a viable technique for evaluating experiments with various characteristics.