In social science research, differences among groups or changes over
time are a common focus of study. While means and variances are
typically the basis for statistical methods used in this research, the
underlying social theory often implies properties of distributions that
are not well captured by these summary measures. Examples include the
current controversies regarding growing inequality in earnings, racial
diferences in test scores, socio-economic correlates of birth outcomes,
and the impact of smoking on survival and health. The distributional
differences that animate the debates in these fields are complex. They
comprise the usual mean-shifts and changes in variance, but also more
subtle comparisons of changes in the upper and lower tails of
distributions. Survey and census data on such attributes contain a
wealth of distributional information, but traditional methods of data
analysis leave much of this information untapped. In this monograph, we
present methods for full comparative distributional analysis. The
methods are based on the relative distribution, a nonparametric complete
summary of the information required for scale--invariant comparisons
between two distributions. The relative distribution provides a general
integrated framework for analysis. It offers a graphical component that
simplifies exploratory data analysis and display, a statistically valid
basis for the development of hypothesis-driven summary measures, and the
potential for decomposition that enables one to examine complex
hypotheses regarding the origins of distributional changes within and
between groups. The monograph is written for data analysts and those
interested in measurement, and it can serve as a textbook for a course
on distributional methods. The presentation is application oriented,
