A new class of statistics for detecting association between two variables is proposed. The statistics improve on traditional correlation coefficients by being sensitive to U-shaped and other non-linear relationships between the variables. If both variables are one dimensional, they can be simply defined in terms of ranks, so that their null distributions can in principle be tabulated. Asymptotic discrimination of order n<sup>-1/2</sup> is obtained for any alternative of a continuous functional relationship between the variables. Power against trend alternatives is investigated by simulation.