Herrnstein's Rank-Order Statistic, Rho

In order to determine discrimination performance is such a daily session we rank the peck rates counted in every trial. We then calculate the probability that a randomly selected positive exemplar will be ranked higher than a randomly selected negative exemplar by using the non-parametric Mann-Whitney U test. The resulting U value is then linearly transformed into Herrnstein's (Herrnstein et al, 1976; Herrnstein, 1979) rho measure of discrimination. It makes no assumptions about the underlying distributions of response rates. When rho is 0.5, discrimination is absent; and when rho is 1.0, discrimination is perfect. With 20 positive and 20 negative stimuli, a rho of 0.68 indicates that discrimination is significant at the 0.05 level.