Law, Probability and Risk - Advance Access

Using the Peters-Belson method in equal employment opportunity personnel evaluations

Sinclair, M. D., Pan, Q. — 2009-06-12

The Peters–Belson method has been used as an alternative approach to standard linear regression analysis to examine potential wage discrimination as it also accounts for any differences in the qualifications of the applicants. To apply the Peters–Belson method, one first conducts a regression analysis on the favoured class and applies the resulting model to the non-favoured class to identify whether this class would have received a different rate of pay if they had been treated the same as their favoured counterparts. Since this method was recently extended to explore disparities in the personnel selections via logistic regression, we will examine the general properties of this method as compared to standard regression analysis. The effects of the demographic mix and size of the applicant pool, the difference in the distribution of the qualifications and the employer's evaluation criteria on the estimated disparity will be examined. Some of the philosophical and legal issues from selected court cases surrounding the use of these two techniques will also be discussed.

Are blacks egregious speeding violators at extraordinary rates in New Jersey?

Kadane, J. B., Lamberth, J. — 2009-06-12

In 1996, a New Jersey Court found that the New Jersey State Police engaged in targeting black motorists on the New Jersey Turnpike (NJT), intensifying the debate around racial profiling. Two recent articles have claimed that the standard of comparison for determining racial profiling was incorrect because either the measurements utilized to make that determination or the standard used in Soto were wrong. The present article concludes that the measures used in the Soto case were valid and reliable. It presents two experiments that show that the suggestion that blacks are stopped at about the correct rate on the NJT because they egregiously violate speed laws much more frequently than do whites is erroneous. The data are consistent with the use of racially informed traffic stops as a pretext for drug searches on the southern end of NJT.

Is the civil 'higher standard of proof ' a coherent concept?

McBride, E. — 2009-05-14

The standard of proof used in criminal cases is that of proof ‘beyond reasonable doubt’, whereas in civil cases it is that of the ‘balance of probabilities’. It is commonly accepted that these standards are coherent ones but a problem arises where criminal conduct has to be proved in civil proceedings: which standard of proof should be used then? The courts have attempted to resolve this problem by rejecting the use of a third, intermediate standard of proof for such cases, while at the same time requiring a ‘higher standard’ of proof in them. This article argues that consideration of this enhanced standard of proof demonstrates a problem with the concept and questions whether it is a coherent one, with reference to the various interpretations of the ‘higher standard’ commonly proposed to account for legal decision making. In particular, a critique is presented of two recent decisions of the House of Lords, purporting to settle the issue definitively.

Response to Professor Haug

Kadane, J. B. — 2009-03-16

Revisiting the p-value: a comparison of statistical evidence in clinical and legal medical decision making

Zou, K. H., DeTora, L. M., Haker, S. J., Mulkern, R. V. — 2009-03-16

While the use of p-values in evidence-based medicine (EBM) is consistent and well-defined, the application of statistical information in health law varies greatly. A comparative literature review of clinical and legal medical decision making using Medline (Pub Med) and LexisNexis reveals large disparities in the mode and frequency with which statistical evidence is used in EBM when compared with health law. We present the historical background of the p-value in the statistical literature and legal case law, including several medical malpractice cases, and then compare the use of the p-value as statistical evidence in health law and clinical research. We suggest that health law may consider the establishment of statistical criteria for appropriate applications.

Calculating remittiturs

Kadane, J. B. — 2009-03-04

This note reviews several methods proposed for calculating the amount of an appropriate remittitur using a sample of ‘comparable’ cases. It recommends a simple quantile estimate.

Invited Comment on Calculating Remittiturs

Haug, M. G. — 2009-03-04

How accurate are the power calculations relied on by the SEC in its regulatory deliberations?

Bura, E., Gastwirth, J. L. — 2009-03-04

In two related decisions in Chamber of Commerce of the United States of America v. Securities and Exchange Commission (SEC), the District of Columbia Federal Court of Appeals ruled that the SEC had not fully complied with some provisions of the Administrative Procedures Act when it required that the boards of investment companies managing mutual funds have at least 75% of their membership and the Chairman be independent directors. In preparation for renewed rule making, the Office of Economic Analysis of the SEC prepared a Power Study to respond to an industry-sponsored report claiming that the returns of funds with independent boards and chairs are not superior to funds with boards dominated by management. The Power Study concluded that the available studies on the effectiveness of independent board members do not have sufficient statistical power to detect a meaningful difference in the returns of the two types of funds. This paper demonstrates that the method used by the SEC in their power calculation is not correct, unless a very restrictive condition that rarely occurs in practice holds. When the appropriate power formulas are used, the expected power of studies of the same size as the ones examined by the SEC is actually lower than the corresponding results of the SEC. Thus, the results in the paper actually strengthen the argument that the SEC is advocating. The relevance of both the SEC and the industry studies to the main issue in the case is also questioned in the discussion.

A science of evidence: contributions from law and probability

Schum, D. A. — 2009-03-04

Presented in this paper are arguments that studies of evidence in the fields of law and probability constitute a science of evidence when they are examined in light of five criteria for scientific activity. Three examples of studies from law and probability are presented to justify this argument. Examples from law include a method for classifying recurrent forms and combinations of evidence regardless of their substance or content, studies identifying credibility attributes for different forms of evidence and studies of complex argument construction in which new lines of inquiry and evidence are generated or discovered. Examples from probability include various views among probabilists about what the weight or force of evidence means and how it should be assessed, several examples of how important subtleties or complexities in evidential reasoning can be captured for study and analysis and one example of how alternative theories about the meaning of complex combinations of events can be tested empirically. All evidence has three major credentials: relevance, credibility and inferential force or weight. The law and probability studies cited in this paper concern all these credentials.