The standard two-variable chi-square test is typically consistent for all alternatives to independence, but effectively treats the data as nominal which may lead to loss of power for ordinal data. Alternatively, a test based on Kendall's tau does take ordinality into account, but only has power...

A possible drawback of the ordinary correlation coefficient p for two real random variables X and Y is that zero correlation does not imply independence. In this paper we introduce a new correlation coefficient p* which assumes values between zero and one, equalling zero iff the two variables...