Introduction

Abstract

The word "statistics" derives from the collection and use of data to assist in the administration of a state (nation). The justice system is one of the fundamental pillars of a state, and is central to the political life of most countries. Ideas from probability and statistics have been used to try to model and improve methods of legal decision-making since the earliest days of our discipline in the 16th and 17th centuries. More recently, the debate over the Bayesian statistical paradigm, rooted in probability theory, as a model for legal reasoning has not subsided since being ignited by Finkelstein & Farley (1970); see Balding (1998) for a comment on a UK court judgment dealing directly with this issue.

Despite this interest in legal reasoning, in many respects the use of statistical inference to interpret data in the legal context is a relatively recent development. Statistical information has assisted in the enforcement of the Civil Rights Act, enacted in 1964 in the United States. Indeed, formal hypothesis testing comparing the racial composition of juries with the minority fraction of eligible members of the population was accepted by the US Supreme Court in the 1997 Castenda case. The data from that case, and related employment discrimination cases, are analyzed and discussed in Gastwirth (1988, Chapters 4--6) and Finkelstein & Levin (2000, Chapter 4). The tragedy of excessive birth defects in babies whose mothers used the drug thalidomide, which occurred in Germany and other parts of Europe, demonstrated the need for official surveillance of the effects of new drugs. When this surveillance fails, statisticians are called on to help evaluate the health-related studies in product liability cases. The US Federal Judicial Center has published an excellent reference manual on the current role of scientific evidence in courts, with a major emphasis on the role of statistics, which is freely downloadable over the internet (go to $\mathtt{http://www.fjc.gov/}$, and click on the "evidence" tab on the publications catalogue).

The court of law provides different challenges to statisticians than are demanded in other spheres of applied statistical work. All admissible evidence---not just "scientific" evidence---can play a role in the court's decision-making, for example evidence relating to possible motivations of the parties, and the time sequence of events. The concept of "admissibility" can cause further difficulties. Professional judgments by the statistician are inevitably required, concerning for example the alternative hypotheses that a court may wish to consider and hence require statistical assessment. Difficulties can arise when standard statistical conventions are not acceptable to the court (see the paper of Izenman). The papers in this issue concern both criminal and civil cases. In most legal systems the weight of evidence required to find an accused person guilty of a crime is greater than that needed to prevail in a civil case. The term "beyond a reasonable doubt" is often used for the criminal standard, and "preponderance of the evidence", or "balance of probabilities", for the civil standard. A statistical study that contributes to meeting the civil law standard might be insufficient in a criminal case.

The six papers in this issue deal with a range of legal settings and challenges to statistics. Foreman and co-authors from the UK Forensic Science Service review the interpretation of DNA evidence, an area which requires many judgments, for example about population genetic effects and about the appropriate hypotheses to consider. Complex genetic relationships among possible offenders provides a challenge which Bayesian networks are well suited to overcome, and this is an area of recent research reviewed by these authors.

Although glass evidence has been used for many years, issues concerning the quantification of this evidence have continued to evolve, in part because of the changing technology of glass manufacture and analysis techniques, but also in response to the increasing sophistication of courts in their handling of scientific evidence, reflected in an increasing role for likelihood ratios. Curran, a New Zealand statistician who has developed statistical techniques and software for glass and other forms of forensic evidence, discusses these developments.

For many years it has been assumed that fingerprints are unique to an individual, even an identical twin. However, fingerprint evidence has been used for over a century, and whether or not the basis for this claim meets modern scientific standards has been questioned. Specifically, in the mid-1990s the US Supreme Court changed the standards for admitting scientific evidence. Kaye, a leading legal scholar on the use of statistical and scientific evidence, describes and questions a study commissioned by the FBI to provide scientific support for the uniqueness claim. He highlights many apparent weaknesses of the study, in particular its failure to address the question of the quality of crime-scene fingerprints relative to those taken under ideal conditions. The lack of openness surrounding the study, and the fact that the FBI consulted a private contractor rather than researchers from the academic or voluntary sectors, are also causes for concern.

Izenman's contribution to the issue highlights a clash between scientific and legal cultures. Once a defendant has been convicted of drug possession, the issue arises as to whether the severity of the sentence should depend on the amount of the drugs seized and, if so, how accurately this needs to be measured, given that exhaustive testing is infeasible. If the seizure includes many containers, it would seem natural to statisticians to estimate drug quantity via a random sampling of the containers followed by testing of a sample of the contents of the chosen containers. However, this practice may not suffice to establish the amount of drugs to the criminal evidence standard that, a recent US Supreme Court judgment seems to imply, is required in such cases.

The right of an individual or corporation to profit from their creative products underlies intellectual property law. As world trade increases, the different systems protecting the value of such products adopted by the nations of the world are becoming harmonized. Basmann and Slottje describe a case in which another company without authorization used the insignia of a sports team. The sales of the team's official merchandise were diminished and the authors developed a regression model to estimate the lost profit (damages). Their discussion of the trial testimony illustrates that statisticians testifying in court need to be very careful to accurately describe the underlying statistical concept. The misinterpretation of the $p$-value of a test as a "posterior" probability of the hypothesis being true is all too common in legal opinions.

Gastwirth, Miao and Zheng discuss the types of statistical data and techniques used in employment discrimination cases concerned with the potential use of a non-job related requirement to reduce the employment or promotion prospects of minority groups. While the basic data often is a simple two by two table when several years of data are involved, the issue of when it is proper to combine the yearly tables arises. In order to demonstrate that a job-requirement is appropriate, typically employers show it is correlated to an important aspect of the job, e.g., yearly performance evaluations. Psychologists have used the expectancy concept, that is the probability that an applicant at a certain percentile on a pre-employment exam will be an "above average" employee, to illustrate the productivity gain of requiring prospective employees to pass the exam. The authors introduce a notion of productivity gain, derived from the expectancy curve, and illustrate its use on data from an actual case.

While the papers in this issue illustrate the uses of statistical reasoning in important areas of the law, they are far from exhaustive. In particular, the proper design of quality control sampling for checking compliance with environmental regulations has not received adequate attention. For instance, due to concern that chemicals used in de-icing roadways increased leaching of nitrogen and heavy metals into the country's water supply, in 2002 Finland introduced a system of using 200 monitoring points to check the ground water quality of 100 aquifers. Statistical input will be needed in order that the samples are taken often enough to detect an increase in harmful chemicals to ensure the safety of drinking water. Similarly, a French institute has raised concerns about residues of medicines in surface and groundwater both on the aquatic environment and humans (see $\mathtt{http://www.cemagref.fr}$). An environmental group in Italy found microbiological contamination in 78.5\% of samples from 18 rivers, including the Arno, Po and Tiber (see $\mathtt{http://www.legambiente.it}$).

Environmental protection often interacts with free trade and other economic issues as regulations are subject to cost-benefit analyses. Several Eastern European and Central Asian countries recently agreed to protect various ecosytems. The framework adopted can be found at $\mathtt{http://www.kyiv-}$ $\mathtt{2003.info/main/index.php?mode=5}$. The Mediterranean nations agreed to reduce industrial pollution substantially by 2010. Recommendations and agreements are available at $\mathtt{http://www.}$ $\mathtt{unepmap.gr}$.

Environmental issues seem likely to continue to raise interesting statistical questions, and require the input of statistical experts. Other regulatory issues, especially those related to international trade, will also provide new problems to challenge statisticians, as well as experts from other disciplines.

Balding, D.J. (1998). Court condemns Bayes. Royal Statistical Society News, {\bf 25}(8), 1--2.

Finkelstein, M.O. & Fairley, W.B. (1970). A Bayesian approach to identification and evidence. Harvard Law Review, {\bf 83}, 489--517.

Finkelstein, M.O. & Levin, B. (2000). Statistics for Lawyers. New York: Springer.

Gastwirth J.L. (1988). Statistical Reasoning in Law and Public Policy. San Diego: Academic Press.