A Measure of Concordance When There are Many Traits

Abst rac t: We consider two populations, each of which contains at least one object. On each ob-ject there are several traits measured. We obtain a simple nonparametric measure of concordance to as-sess the degree of positive relationship between the two populations, and in this measure the different traits can be weighted. We consider two cases, one in which each population has one object and the other case in which each population includes more than one object. Using the one to one correspond-ing common variables, our formula gives a similarity measure which ranges between 0 and 1 with increas-ing similarity from 0 to 1. We perform a simula-tion to assess the sensitivity of the measure to the changes in the weights. When the respective vari-ables are widely spread out, the score obtained from the transformed values appears to be the better mea-surement. 1. In t roduct ion Statisticians routinely calculate the correlation be-tween two groups when the measurements are sim-ilar, both continuous and discrete variables (e.g., weight and sex). Pearson (1896) presented mathe-matical formula of correlation estimation and many papers have been published since then on the sam