A Primary Tool For Measuring Nominal Association; a Survey on Proportional Reduction in Variance

Maman A. Djauhari ( Department of Mathematics, Institut Teknologi Bandung)

Jurnal Matematika & Sains
Vol 2, No 1 (1997)

Let Y and X be interval variables. Proportional reduction in variance (PRV) of Y given X is equal to the R2 or coefficient of determination of Y with respect to X. This phenomenon can be generalized to more than one explanatory variables. It describes the PRV from the marginal distribution to the conditional distribution of response Y. This paper deals with PRV as a primary tool for measuring nominal association. Several situations will be considered. It will be discussed its relationship with Goodman and Kruskal tau, proportional reduction in uncertainty (PRU) defined by Bui Quoc through Shannon entropy, canonical correlation through Bertier and Tenenhaus’s optimal coding, and also with RV coefficient.