and limitations of existing approaches to measuring discrimination across these domains and suggest how approaches prevalent in one domain might usefully be employed in others.

Even a cursory review of the literature on labor markets, education, housing, criminal justice, and health care reveals that it is quite common for researchers to employ statistical models when addressing questions of racial discrimination (see Table 4-1). Given the range of domains we examine, we do not attempt to be exhaustive in our presentation. Instead, we provide examples from individual studies in particular domains to illustrate particular methodological issues. Our intent is to summarize what we see as the most important challenges that arise in using statistical models to study racial differences in outcomes. And although we make frequent use of labor market concepts as concrete examples throughout this chapter, the fundamental statistical issues underlie the measurement of discrimination in all domains.

It should be noted that the style of exposition in this chapter is more mathematical than that in the rest of the report. This mathematical presentation is necessary to make clear what statistical decompositions of racial differences measure. It is also needed for precision regarding the role of models as descriptions of the ways in which outcomes are determined in the presence of discrimination, the role of models and assumptions in drawing causal inferences regarding discrimination from observational data, the nature of the biases that arise when those assumptions are violated, and the ways in which alternative study designs can reduce those biases.

STATISTICAL ANALYSIS FOR RESEARCH AND LITIGATION

Before we proceed, a caveat is in order. This chapter attempts to illuminate state-of-the-art statistical methods that should be used by academic researchers attempting to detect the existence and magnitude of racial discrimination in a wide variety of domains. Statistical proof of racial discrimination may often be sought in other contexts in which the same degree of attention to methodological detail may be valued differently. In particular, courts are often called upon to decide discrimination cases in circumstances that are far less congenial to the detailed and sustained analysis of the academic researcher. Litigants often press for expert testimony based on something far short of state-of-the-art statistical practices that academic researchers might employ. In some instances, a straightforward analysis of the available data may appear to make a compelling case, but many outside the courts would argue for more details and alternative analyses to buttress the arguments.

In a paper commissioned for this panel, Nelson and Bennett (2003) investigate the courts’ use of statistics to make decisions in cases alleging



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