Generalizing the Common Language Effect Size Indicator to Bivariate Normal Correlations

McGraw and Wong (1992) described an appealing index of effect size that requires no prior knowledge of statistics to understand. They termed this index the common language effect size indicator ( CL ): the probability that a score randomly sampled from 1 distribution will be larger than a randomly sampled score from a 2nd distribution. In extending this concept to a bivariate normal distribution, with correlation r, one may think again of randomly sampling 2 individuals; if the 1st individual has a higher score on the 1st variable than the 2nd individual, the CL R in this case is the probability that the 1st individual will also have a higher score on the 2nd variable. An equation for this probability is derived that permits converting any value of r into CL R , the common language effect size index for a bivariate correlation.