Many national science frameworks (e.g., Next Generation Science Standards) argue that developing mathematical modeling competencies is critical for students' deep understanding of science. However, science teachers may be unprepared to assess these competencies. We are addressing this need by developing virtual lab performance assessments that…

A maximum likelihood estimation procedure is developed for the simple and the weighted additive models. The data are assumed to be taken by either one of the following methods: (1) categorical ratings--the subject is asked to rate a set of stimuli with respect to an attribute of the stimuli on rating scales with a relatively few observation…

The normal curve has long been important in statistics. Most interval variables yield normal or quasi-normal distributions when data are collected from large samples, and the normal "Z" distribution is also used as a test statistic (e.g., to test differences between two means when sample size is large, since "t" approaches…

Various methods have been suggested for the analysis of data collected in research settings where random assignment of subjects to groups has not occurred. For the purposes of this paper the set of allowable nonrandomized designs is made up of those research designs where data are collected for one or more groups of subjects at two or more time…

Monte Carlo studies of statistical tests are prominently featured in the methodological research literature. Unfortunately, the information from these studies does not appear to have significantly influenced methodological practice in educational and psychological research. One reason is that Monte Carlo studies lack an overarching theory to guide…

Multiple matrix sampling (MMS) theory indicates how data may be gathered to most efficiently convey information about levels of attainment in a population, but standard analyses of these data require random sampling of items from a fixed pool of items. This assumption proscribes the retirement of flawed or obsolete items from the pool as well as…

This paper provides a progress report on an investigation to validate and extend the autocatalytic model for the adoption of educational innovations. Three topics are dealt with: (1) a brief description is provided of the autocatalytic model and its current application, (2) the design of a survey to collect data for further tests of the model is…

Many studies of educational outcomes collect data on the socioeconomic characteristics of parents from students, and not from the parents themselves. Nevertheless, students are often fallible informants of parental status factors. A series of distinct hierarchical measurement models were used to examine the structure of errors in high school…

This paper argues that no single measurement strategy serves all purposes and that applying methods and techniques which allow a variety of data elements to be retrieved and juxtaposed may be an investment in the future. Item response theory, Rasch model, and latent trait theory are all approaches to a single conceptual topic. An abbreviated look…

Structural equation models incorporating unmeasured variables make possible the rigorous testing of theories previously difficult to test adequately because of fallible measures of the theoretic variables. This paper first discusses a simple causal model; incorporating a single unmeasured variable for the purpose of exposition. A substantive…