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Mark S. Handcock, Martina Morris - Relative Distribution Methods in the Social Sciences

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 over growing inequality in earnings, racial differences 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 detailed comparisons of changes in the upper and lower tails of the distributions. Survey and census data contain a wealth of this distributional information, but the traditional methods of analysis leave most of it untapped.

This monograph presents a general framework for comparative distributional analysis. The methods are based on the relative distribution, a simple intuitive transformation that is also a complete nonparametric summary of the information required for scale-invariant distributional comparison. The relative distribution provides a graphical display that simplifies exploratory data analysis, a statistically valid basis for the development of hypothesis-driven summary measures, and location, shape, and covariate decompositions that identify the sources of distributional changes within and between groups.

The monograph is written for data analysts, methodologists, and those interested in measurement. It can serve as a supplementary text for a course on distributional methods or as a stand-alone text for an advanced methods course. The presentation alternates chapters on theory and methodological development with chapters providing an in-depth practical application.

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