Genetic scaling for ordinal variables

This book aims to propose a method to quantify ordinal variables through the optimization of an objective function. There are various methods for quantifying (scaling) ordinal sta-tistical variables, but if the researcher wishes to make comparisons between two or more groups regarding the same feature, he should optimize the differences between their distributions, whether they concern assessments, attitudes, opinions, or other features. To do this, he needs to optimize linear forms and quadratic forms sub-ject to linear constraints of inequality and quadratic constraints of equality. This book suggests a solution to the problem, i.e. the use of ge-netic algorithms. If genetic algorithms are used there’s no need for information about the gradient of the objective function and it’s impossible to get relative and non-absolute extremes. This paper also implements the rules for deciding whether average evalua-tions are equal or not. The next section of this book is intended to apply the above technique in order to quantify the ordinal statistical variables. This method is subjected to clearly-defined objective rules and is, therefore, freed from the researcher’s will, thus being more relia-ble and more consistent than other methods of quantification that are already present in the literature. The method used to compare average evaluations expressed at a qualitative ordinal level is de-scribed in the first part of this paper. Besides, the method itself is validated by comparing the opinions that have been expressed by a sample of university graduates about the effectiveness of uni-versity education in terms of job exploitability; in particular, the interviewed people have been divided according to the different Faculties they attended as students, and to their current job condi-tion. A broad Appendix is given at the end of this book, including the MATLAB® code expressly written to perform this method.