Comparing Robust Measures of Association Estimated Via a Smoother.

A classic problem is comparing Pearson's correlation corresponding to two independent groups. The article examines a generalization where the goal is to compare the groups based on a robust variation of explanatory power used in conjunction with a particular nonparametric regression method that allows curvature. If the nonparametric regression estimator is replaced by the ordinary least squares estimator, and if explanatory power is measured with the usual variance, and if the regression line is straight, the approach used here reduces to comparing Pearson's correlation. For reasons summarized in the article, Cleveland's (1979) lowess estimator is used. It is found that a modified percentile bootstrap method controls Type I error probabilities reasonably well in simulations. Even when the regression line is straight, the power of the method compares well to a variation that fits a (straight) robust regression line to the data. And even under normality, using Pearson's correlation was found to provide little or no advantage in terms of power. [ABSTRACT FROM AUTHOR]