Good practice of legal statistics depends on a foundation of good statistical science. Causal inference from statistical data depends both on understanding of substantive causal processes and adequate principles of statistical inference. The paper makes a case that Bayesian reasoning is needed for statistical studies of employment discrimination. A model based on Bayesian principles is developed in detail and is used to show that any statistical estimate of the effects of employment discrimination must be adjusted from sources of knowledge outside the statistician's data. Econometric analyses, which suggest otherwise, are analyzed and criticized.

This paper reviews Daniels' saddlepoint approximation to the distribution of the mean of a random sample, and the many aspects of second order asymptotic inference that have been developed from it. These include Barndorff-Nielsen's approximation to the distribution of the maximum likelihood estimate, Bartlett factors for the likelihood ratio statistic and approximations to predictive and conditional likelihood. The emphasis is on statistical applications of the saddlepoint method. The intention is to provide fairly broad coverage of the literature and to indicate possibilities for future development. An annotated bibliography is included.

Linear models are widely used in many branches of empirical inquiry. The classical analysis of linear models, however, is based on a number of technical assumptions whose failure to apply to the data at hand can result in poor performance of the classical techniques. Two methods of dealing with this that have gained some acceptance are the data-analytic and model expansion approaches, in which graphical and numerical methods are employed to detect the ways in which the data do not meet the classical assumptions, and either the data are modified appropriately before the classical techniques are applied (data-analytic) or the model is broadened to take account of the departures discovered (model expansion). Another approach involves the use of robust methods, which are intended to be sufficiently insensitive to deviations from the classical assumptions that the data may be analyzed without modification or additional (explicit) modeling. In this article a comparison is made between the data-analytic, model expansion and robust approaches to linear models analysis, and the application of one type of robust methods, those based on $R$-estimators (which use the logic of rank tests to motivate inference on the raw data scale), to problems of estimation, testing and confidence and multiple comparison procedures in the general linear model is reviewed.