Search

This black box study assessed the performance of forensic firearms examiners in the United States. It involved three different types of firearms and 173 volunteers who performed a total of 8640 comparisons of both bullets and cartridge cases. The overall false‐positive error rate was estimated as 0.656% and 0.933% for bullets and cartridge cases, respectively, while the rate of false negatives was estimated as 2.87% and 1.87% for bullets and cartridge cases, respectively. The majority of errors were made by a limited number of examiners. Because chi‐square tests of independence strongly suggest that error probabilities are not the same for each examiner, these are maximum‐likelihood estimates based on the beta‐binomial probability model and do not depend on an assumption of equal examiner‐specific error rates. Corresponding 95% confidence intervals are (0.305%, 1.42%) and (0.548%, 1.57%) for false positives for bullets and cartridge cases, respectively, and (1.89%, 4.26%) and (1.16%, 2.99%) for false negatives for bullets and cartridge cases, respectively. The results of this study are consistent with prior studies, despite its comprehensive design and challenging specimens. [ABSTRACT FROM AUTHOR]

The Hardy-Weinberg principle (HWP) is an application of the binomial expansion theorem that is foundational to the field of population genetics. Because of the important history of the HWP in answering how variation is preserved during evolution, and the ability of Hardy-Weinberg equilibrium (HWE) to detect natural and sexual selection acting on a trait, the HWP is a staple of the introductory biology undergraduate curriculum in the United States. Introductory courses often cover a wide range of topics in ecology and evolution, and it is important that students have enough time during the semester to grasp the foundations of population genetics. At the same time, information needs to be presented clearly to ensure that the student gains a correct understanding of the HWP. This article discusses the importance of the HWP to undergraduate education in biology and describes misconceptions from the instructor's perspective. These misconceptions are pervasive and risk undermining a proper understanding of the HWP. We provide examples adapted from university- and AP-level standardized tests. [ABSTRACT FROM AUTHOR]

While teaching college-level mathematics (from College Algebra to Calculus to Abstract Algebra), I have observed that students are often uncomfortable using negative exponents in calculations. I believe the fault partially lies in the manner in which negative exponents are taught in Algebra 1 or Algebra 2 courses, especially in rigid instructions always to write answers using only positive exponents. After reviewing a sample of algebra texts used in the United States over the last two centuries, it appears that while attitudes toward negative exponents have varied from author to author over time, the current trend is to declare explicitly that an expression is not simplified if it contains negative exponents. I believe that this negative attitude toward negative exponents is at least somewhat to blame for students of Calculus and higher mathematics being less able to solve problems that require conversion between positive and negative exponents, as their algebraic instruction has only taught them to convert negative exponents to positive. [ABSTRACT FROM AUTHOR]

Abstract: Purpose: Wildland fires present many injury hazards to firefighters. We estimate injury rates and identify fire-related factors associated with injury. Methods: Data from the National Interagency Fire Center from 2003 to 2007 provided the number of injuries in which the firefighter could not return to his or her job assignment, person-days worked, and fire characteristics (year, region, season, cause, fuel type, resistance to control, and structures destroyed). We assessed fire-level risk factors of having at least one reported injury using logistic regression. Negative binomial regression was used to examine incidence rate ratios associated with fire-level risk factors. Results: Of 867 fires, 9.5% required the most complex management and 24.7% required the next-highest level of management. Fires most often occurred in the western United States (82.8%), during the summer (69.6%), caused by lightening (54.9%). Timber was the most frequent fuel source (40.2%). Peak incident management level, person-days of exposure, and the fire''s resistance to control were significantly related to the odds of a fire having at least one reported injury. However, the most complex fires had a lower injury incidence rate than less complex fires. Conclusions: Although fire complexity and the number of firefighters were associated with the risk for at least one reported injury, the more experienced and specialized firefighting teams had lower injury incidence. [Copyright &y& Elsevier]

Confidence intervals, in general, have become an important aspect of reporting statistical results. In particular, interval estimators for binomial proportions have been studied extensively in recent literature. The large-sample Wald intervals are known to perform poorly, but the Wilson intervals have been shown to perform well in a variety of situations. One criticism is the relative difficulty of computing the Wilson or quadratic intervals in comparison to the Wald intervals. We offer a computational formula for the Wilson intervals that is a weighted estimator of the observed proportion, p, and that based on an uninformative prior, 1/2. This contribution enhances our understanding of the coverage behavior of the Wilson intervals. In addition, we contrast the Wilson intervals with other well-known intervals for the case of zero successes. [ABSTRACT FROM AUTHOR]