LIVING BEYOND OUR MEANS - NEW METHODS FOR COMPARING DISTRIBUTIONS

This paper introduces the projection methods for describing and testin g the differences between pairs of continuous distributions, These met hods include the projection plot, the projection spline, and the iter- 1 test. The projection plot displays the difference between correspond ing quantiles against the average of the corresponding quantiles. It i s analogous to an empirical quantile-quantile plot that has been rotat ed 45 degrees. The projection spline is a knotted linear spline iterat ively fit to the projection plot so that all knots are associated with Significant changes in slope. It summarizes nonrandom deviations from linearity on the projection plot, allowing classification of the high est level of difference between two distributions as a difference in s hape, in spread, or in location. The iter-1 test compares the first it eration of the projection spline with the line y = 0, providing a glob al test of difference between two distributions that is more powerful in simulations than either the chi-square test of independence or the Kolmogorov-Smirnov test. These methods will enhance epidemiologic prac tice by making the comparison of full distributions an accessible tool for routine data analysis.