Some of the methods originally used to find relationships between reliability and power associated with a single measurement are extended to difference scores. Results, based on explicit power calculations, show that augmenting the reliability of measurement by reducing error score variance can make significance tests of difference more powerful.…

The effectiveness of two statistical tests of the area between item response functions (exact signed area and exact unsigned area) estimated in different samples, a measure of differential item functioning (DIF), was compared with Lord's chi square. Lord's chi square was found the most effective in determining DIF. (SLD)

A marginal maximum likelihood estimation algorithm is presented for the ordered partition model of M. Wilson that does not require the set of available responses to be fully ordered. The model and its estimation algorithm are illustrated in a comparison of alternative scoring schemes for open-ended science items. (SLD)

A Bayesian approach to sensitivity of inferences to possible outliers involves recalculating marginal posterior distributions of parameters of interest under assumptions of heavy tails. This strategy is implemented in the hierarchical model setting through Gibbs sampling, a Monte Carlo technique, and illustrated through a reanalysis of data on…

Some approximate formulas are presented for standard errors of estimated regression coefficients in two-level designs. If the researcher can make a reasonable guess as to parameters occurring in the model, this approximation can be a guide to the choice of sample sizes at either level. (SLD)

Illustrates the addition, subtraction, and representation of fractions using an area model and a measurement model. Also demonstrates multiplication and division of fractions by employing the area model. (ASK)

Presents a merit pay allocation model based on the principle of awarding comparable percentage salary increases to college/university faculty members with similar merit ratings. The model enables users to calculate merit pay amounts for individual faculty members in a systematic and efficient manner and can incorporate various policy directives…

Presents simple experiments using the flow of water from bell jars that can provide an easily visualized introduction to exponential decay. (Author)

Presents an algebra project in which students build a dance club. Reveals how this project motivates students and makes algebra more accessible, dynamic, and relevant to their society. (ASK)

Statistical methods related to Rasch modeling, social network analysis, and latent variable structural equation modeling for experimental designs are critiqued with regard to three important issues: (1) measuring constructs; (2) modeling processes of change; (3) operationalizing social relations. An argument is made for adequate conceptualization…

Describes the use of manipulatives for solving simple combinatorial problems which can lead to the discovery of recurrence relations for permutations and combinations. Numerical evidence and visual imagery generated by a computer spreadsheet through modeling these relations can enable students to experience the ease and power of combinatorial…

Develops a valuation model of educational output based on individual earnings from cross-sectional data; describes the problems associated with defining certain elements of the model and proposes adjustments related thereto; uses model to estimate the value of university education in Spain. (Contains 68 references.) (PKP)

Suggests an elementary school activity and questions to promote five types of mathematical thinking including modeling, logical analysis, inference, optimization, and abstraction. Discusses evaluating activities for mathematical reasoning opportunities. (ASK)

Investigated the robustness of the group-level polytomous Item Response Theory model to violations of assumptions of school-level normality and within-school normality and constant variance with eight large simulated case samples. Discusses the precision obtained in estimating school ability. (SLD)

Describes an investigation that leads to one of the significant contributions that sabermetrics--new approaches to gaining information about baseball from its numerical records--has made to our understanding of baseball. (ASK)