http://lpr.oxfordjournals.org Law, Probability and Risk - RSS feed of articles 1470-840X Law, Probability and Risk 1470-8396 http://lpr.oxfordjournals.org/cgi/content/short/mgn001v1?rss=1 The degree of deference courts give to the interpretation of a statute made by the government agency administering it arises in a variety of legal contexts. This spring the U.S. Supreme Court decided a case concerning the interpretation of a formula used to determine whether the educational funds available to the school districts of a state are ‘equalized’. A state with an ‘equalized’ school system receives most of the federal money given to school districts in the state to compensate them for the real estate tax revenue lost due to the presence of a large federal facility in the district. The main issue concerned the calculation of the percentiles used to determine the school districts, called local educational agencies (LEAs) as the formula uses the 5th and 95th percentiles. In order for the funding of education in a state to be ‘equalized’, the disparity (D) or ratio of the difference between the per-pupil expenditures of the LEAs at these two percentiles to the fifth percentile needs to be less than or equal to one-fourth. After arranging the LEAs in increasing order of their per-pupil expenditures, the government calculated the percentiles by weighting the LEAs by the number of students and found that New Mexico had an ‘equalized’ system. When the LEA per-pupil expenditure data are not weighted, however, the disparity measure exceeds 0.25. Two impacted LEAs interpreted the law as specifying the unweighted calculation and sued the Department of Education as they would receive substantially more money if the entire federal payment went to the impacted LEAs. The Court found that the statute was ambiguous and that the government's interpretation was permissible. The opinion also gave four other ‘interpretations’, including the one offered by the plaintiffs, that it would also deem permissible. Both the majority and the dissenting opinions are summarized. The results of two informal surveys of statisticians who read and interpreted the formula are reported. Most favoured the ‘unweighted’ calculation and none agreed that the wording of the statute was consistent with all five interpretations the Court would allow. From the opinion and transcript, it appears that the Court might have believed that the government's approach was an ‘approximation’ to what the disparity would be if it were calculated from data on each pupil, had such data been available. Using data from a classic school segregation case, where the disparity between schools with predominantly minority students was 0.70, we formed a ‘state’ with 22 LEAs by randomly aggregating five schools to each state. In 10 000 randomly formed ‘states’, the largest disparity calculated from the LEA-wide data was 0.38, just over one-half the true disparity. Three-fourths of these state systems had disparity measures less than 0.25 and would be deemed ‘equalized’ even though the overall disparity was nearly three times as large. Since using district-wide expenditure data substantially underestimates the value of the disparity calculated on school-wide data, it is likely to underestimate the disparity between students even more. This result applies to the interpretations of both parties. If the purpose of the Federal Impact Aid Act is to ensure that students in schools affected by a federal presence receive an adequate education, Congress needs to modify the formula. Currently, a state with only a few impacted LEAs can be ‘equalized’ even if all of them are at the low end of the distribution and are ‘deleted’ from the current calculation.

]]> 2008-05-23 info:doi/10.1093/lpr/mgn001 Oxford University Press 2008-05-23 Article http://lpr.oxfordjournals.org/cgi/content/short/mgm042v1?rss=1 In the fight against blood doping, the interpretation of the measured levels of blood markers is based on either population-derived reference ranges or the previous test history of the individual under scrutiny. In this report, we demonstrate how an empirical hierarchical Bayesian model can be used to unify both approaches. The aim is to allow anti-doping organizations to bring reliable evidence of blood manipulation in front of a disciplinary panel. Before any tests are performed on an individual, population distributions constitute the priors of a Bayesian network that may depend on heterogeneous factors such as gender, ethnic origin and age. Inferences from the results of a new test are then drawn iteratively. A decision rule can be defined to minimize the expected costs of a decision. Secondly, the same model can be applied to evaluate the evidence of blood doping from a full sequence of individual test results, and not just from a single test result as a function of previous results. We obtained unprecedented sensitivity on a database of 1239 blood samples. Thirdly, if applied to a population of athletes, an extension of the model makes it possible to estimate the prevalence of blood doping for reasonably large populations of athletes. Knowledge of the prevalence allows the decision maker to estimate the prior odds of an athlete being doped. As a consequence, the false-positive fallacy, a form of the prosecutor's fallacy that originates from today multiplication of the number of anti-doping tests, is removed. The joined application of the Bayesian model for (1) the estimation of the prevalence at the population level and (2) the evaluation of the evidence at the individual level will allow anti-doping organizations to prosecute cases for which evidentiary values are derived from indirect blood tests.

]]> 2008-01-11 info:doi/10.1093/lpr/mgm042 Oxford University Press 2008-01-11 Article