New proposals to estimate unbiased selection gain and coefficient of variation in traits evaluated using score scales

Abstract

In plant breeding, several multicategorical variables are evaluated using score scales that are treated as interval scales. However, statistics that use ratio operations, such as the experimental CV and the selection gain, are only appropriate for ratio scales data. Thus, this work aimed to propose strategies to mitigate the inconveniences faced in the data analysis of score scales, especially those involving CV and selection gain obtained from different scales. This work proposes the following strategies: (i) the use of a standard score scale with the properties of a ratio scale (ascending scale with 0 as the point of origin); (ii) the conversion of the scores from different scales into a common ratio scale; (iii) the adjustment of the data from an interval scale to a ratio scale using the Delta Scale (Scale δui), and (iv) the use of unbiased estimator for CV and selection gain in score scales data. The proposed strategies resulted in unbiased estimates of CV and selection gain from data of different score scales. These strategies have the potential to be used in the meta-analysis of data within and between plant breeding programs.