Boyd, Epstein and Martin have written Untangling the Causal Effects of Sex on Judging. The Abstract:
We enter the debate over the role of sex in judging by addressing the two predominant empirical questions it raises: whether male and female judges decide cases distinctly (individual effects) and whether the presence of a female judge on a panel causes her male colleagues to behave differently (panel effects). We do not, however, rely exclusively on the predominant statistical models - variants of standard regression analysis - to address them. Because these tools alone are ill-suited to the task at hand, we deploy a more appropriate methodology - non-parametric matching - which follows from a formal framework for causal inference.
Applying matching methods to sex discrimination suits resolved in the federal circuits between 1995 and 2002 yields two clear results. First, we observe substantial individual effects: The likelihood of a judge deciding in favor of the party alleging discrimination decreases by about 10 percentage points when the judge is a male. Likewise, we find that men are significantly more likely to rule in favor of the rights litigant when a woman serves on the panel. Both effects are so persistent and consistent that they may come as a surprise even to those scholars who have long posited the existence of gendered judging.