| A possible drawback of the ordinary correlation coefficient r is that r = 0 does not imply independence. We introduce a new correlation coefficient, closely related to (the square of) r, which however is zero if and only if the variables are independent and lies in the interval (0,1] otherwise. For 2x2 contingency tables, the two coefficients coincide. We discuss an orthogonal decomposition of the coefficient as a sum of ordinary correlations, asymptotic chi-square and small sample permutation tests of independence based on the coefficient, Frechet bounds, and the application to both categorical and continuous data. |