Abstract

RUBIA, José Moral de la. A measure of variation for qualitative data with any type of distribution. Psychol. av. discip. [online]. 2022, vol.16, n.2, pp.63-76.  Epub Sep 19, 2023. ISSN 1900-2386.  https://doi.org/10.21500/19002386.5642.

There are many measures of variation for nominal data, but they are little known, when this type of data is common in health and social science research. Among these measures, the Gibbs-Poston’s qualitative variation index (QVI), the Freeman’s variation ratio (VR), the Wilcox’s variation ratio from the mode (VRMod), the Shannon’s relative entropy (ERel), and the Kvalseth’s standard deviation from the mode (SDM) stand out. The objective of this article is to propose a modification of the variation ratio that overcomes the limitation to unimodal distributions of Freeman and Wilcox formulas; also describe the behavior pattern of the six indices. This new index is named the universal variation ratio (UVR), since it is valid for any type of distribution with qualitative data. It is observed that RV, UVR, RVMod and DEM quickly approach 0 when there is a very defined mode with proximity to the distribution of a constant random variable. On the contrary, ERel and QVI quickly approach 1 when there are multiple modes or proximity to a uniform distribution with a unique mode. It is concluded that, among six indices, SDM and UVR are the best measures.

Keywords : qualitative variation; nominal scale of measurement; qualitative variable; variability measures; descriptive statistics..

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