Nitrate is a crucial parameter for assessing water quality, owing to its dual function in ecological systems. These functions can be beneficial or detrimental depending on whether nitrate concentrations are low or high, respectively. The ultraviolet spectrophotometric method (standard as 4500-NO[subscript 3]--B) is a classic method for determining…

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

Schools are scrambling to prepare students for the writing assessments aligned to the Common Core State Standards. In some states, writing has not been assessed for over a decade. Yet, with the use of computerized grading of the student's writing, many teachers are wondering how to best prepare students for the writing assessments that will…

This article was inspired by a set of 12 cylindrical cups, which are volumetrically indexed; that is to say, the volume of cup "n" is equal to "n" times the volume of cup 1. Various sets of volumetrically indexed cylindrical cups are explored. I demonstrate how this children's toy is ripe for mathematical investigation, with connections to…

Research synthesis of evaluation findings is a multistep process. An investigator identifies a research question, acquires the relevant literature, codes findings from that literature, and analyzes the coded data to estimate the average treatment effect and its distribution in a population of interest. The process of estimating the average…

To rule out the need for a two-parameter item response theory (IRT) model during item analysis by Rasch models, it is important to check the Rasch model's assumption that all items have the same item discrimination. Biserial and polyserial correlation coefficients measuring the association between items and restscores are often used in an informal…

The Lithuanian Informatics Olympiad is a problem solving contest for high school students. The work of each contestant is evaluated in terms of several criteria, where each criterion is measured according to its own scale (but the same scale for each contestant). Several jury members are involved in the evaluation. This paper analyses the problem…

The purpose of this article is to discuss specific techniques for the computation of the volume of a tetrahedron. A few of them are taught in the undergraduate multivariable calculus courses. Few of them are found in text books on coordinate geometry and synthetic solid geometry. This article gathers many of these techniques so as to constitute a…

Power computations for one-level experimental designs that assume simple random samples are greatly facilitated by power tables such as those presented in Cohen's book about statistical power analysis. However, in education and the social sciences experimental designs have naturally nested structures and multilevel models are needed to compute the…

Extreme-value statistics is often used to estimate so-called return values (actually related to quantiles) for environmental quantities like wind speed or wave height. A basic method for estimation is the method of block maxima which consists in partitioning observations in blocks, where maxima from each block could be considered independent.…

Presents a visualization tool for information retrieval that can display two different similarity measures, angle and distance, in the same space. Discusses the visual display of information-retrieval evaluation models and develops a new retrieval means based on the visual retrieval tool, the controlling bar. (Author/LRW)

Discussion of the assessment and comparison of scientific journals, bibliometrics, and types of impact factors focuses on a general framework for the relative comparison of journal impact. Highlights include the relative impact of a journal within a set of journals, or meta-journal; and mathematical explorations of relative indicators. (Author/LRW)

Discussion of information retrieval focuses on a general method for the construction of measures of similarity taking into account the rank of presentation of the document, called ordered similarity measures. Presents an experimental evaluation used to quantify the filtering impact of a system and discusses recall and precision. (Author/LRW)

Studies aggressive automated word removal in text categorization in large databases based on corpus statistics to reduce the noise in free texts and to enhance the computational efficiency of categorization. Topics include stop word identification, categorization methods for comparison, tests on four document collections, and evaluation…

Discusses the use of logical imaging in information retrieval. Topics include the use of nonclassical logic in information retrieval; imaging and possible worlds semantics; retrieval by imaging; evaluation processes; worlds mass and worlds distance; and future work. (LRW)