A measure of one-dimensional asymmetry for qualitative variables

Abstract

This methodological investigation aims to define a concept of asymmetry for qualitative variables, quantify it, and show its validity. A panel of five expert judges and Monte Carlo simulations were used. The statistic Mean Difference in Frequency (MDF) between pairs of categories ordered by frequency homogeneity was defined. The MDF statistic showed a behavior adjusted to expectations with different variants of the binomial distribution. The correlation between the mean skewness score of the judges and MDF was very high. To obtain interpretive guiding cutoffs, 20,000 samples of sizes 20, 40, 100, 200, 500, and 1000 were simulated, drawn from a binomial distribution. It is concluded that MDF is validity to measure asymmetry in qualitative variables.