It is very well known that the Cauchy-Schwarz inequality is an important property shared by all inner product spaces and the inner product induces a norm on the space. A proof of the Cauchy-Schwarz inequality for real inner product spaces exists, which does not employ the homogeneous property of the inner product. However, it is shown that a real…

Classical test theory is based on the concept of a true score for each examinee, defined as the expected or average score across an infinite number of repeated parallel tests. In most cases, there is only a score from a single administration of the test in question. The difference between this single observed score and the underlying true score is…

This report examines the relationship between various characteristics of students with disabilities and the probability that they would participate in the NAEP assessments, given the current methods of accommodation adopted by their state. The report describes the methodological approach which calculates for each state an expected inclusion rate…

This report focuses on the performance of fourth-and eighth-grade students in Puerto Rico in various mathematics content areas on the 2005 National Assessment of Educational Progress (NAEP) in mathematics. The NAEP mathematics assessment was administered to public school students in Puerto Rico for the first time in 2003. Although NAEP had…

An inventory replenishment policy is developed for a deteriorating item and price-dependent demand. The rate of deterioration is taken to be time-proportional and the time to deterioration is assumed to follow a two-parameter Weibull distribution. A power law form of the price dependence of demand is considered. The model is solved analytically…

This report presents results of the 2011 National Assessment of Educational Progress (NAEP) in mathematics at grades 4 and 8. Nationally representative samples of 209,000 fourth-graders and 175,200 eighth-graders participated in the 2011 National Assessment of Educational Progress (NAEP) in mathematics. At each grade, students responded to…

The main aim of this study was to gain a better understanding of why students abandon their studies, or perform less well than expected given their high school grades, and to develop predictive models that can help identify those students most at-risk at the time they enter college. This will allow teachers and those responsible for student…

The National Household Education Survey (NHES) is a data collection system of the National Center for Education Statistics. The NHES is a telephone survey of the noninstitutionalized civilian population using households selected using random digit dialing methods. Approximately 60,000 households are screened for each administration, and people who…

Presents an application of the binomial distribution in which the distribution is used to detect differences between the sensory properties of food products. Included is a BASIC computer program listing used to generate triangle and duo-trio test results. (JN)

Three numerical coefficients for analyzing the validity and reliability of ratings are described. Each coefficient is computed as the ratio of an obtained to a maximum sum of differences in ratings. The coefficients are also applicable to the item analysis, agreement analysis, and cluster or factor analysis of rating-scale data. (Author/BW)

This short note introduces an interesting random walk on a circular path with cards of numbers. By using high school probability theory, it is proved that under some assumptions on the number of cards, the probability that a walker will return to a fixed position will tend to one as the length of the circular path tends to infinity.

The volume is the second of two and presents additional statistical analyses of data discussed in the first, which presented 1960 and 1961 census data from 53 countries in an attempt to identify and quantify factors which determined the occupational and educational structure of the labor force. The second volume consists of eight chapters: (1) a…

This study sought to determine: (1) what children understand about "chance" when they begin secondary school?; and (2) how common and how influential the use of informal heuristics, approaches, and biases is in their thinking about probability in the school context. Children's understanding of chance, attributions of events to…

The National Education Longitudinal Studies Program (NELS) is a long-term effort that encompasses the educational experience of youth from three decades. This report is based on the National Education Longitudinal Study of 1988 (NELS:88), a component of the NELS series that began as a national probability sample of eighth grade schools and…

The psychometric research done by G. Rasch between 1951 and 1959, which is explained and illustrated in this book, takes psychometrics from being purely descriptive to being a science of objective measurement. Individual centered statistics require models in which each individual is characterized separately and from which, given adequate data,…