Contrast analysis is a relatively simple but effective statistical method for testing theoretical predictions about differences between group means against the empirical data. Despite its advantages, contrast analysis is hardly used to date, perhaps because it is not implemented in a convenient manner in many statistical software packages. This…

In Ramsay curve item response theory (RC-IRT) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's EM algorithm, which yields maximum marginal likelihood estimates. This method, however, does not produce the…

A fundamental goal of educational research is identifying students' current stage of skill mastery (complete/partial/none). In recent years a number of cognitive diagnosis models have become a popular means of estimating student skill knowledge. However, these models become difficult to estimate as the number of students, items, and skills grows.…

Introduction: The cognitive processes that underpin successful mathematical processing in children have been well researched by experimental psychologists, but are not widely understood among teachers of primary mathematics. This is a shame, as an understanding of these cognitive processes could be highly useful to practitioners. This paper…

Benford's law of the "first digits" states that in spite of intuitively expected equal frequency of 1/9 of the decimal digits r = 1, ... , 9 appearance on the first place of any number, various empirical studies show another pattern of these frequencies distribution, which is log[subscript 10](1 + 1/r). The article considers this law and other…

The interpretation of a Thurstonian model for paired comparisons where the utilities' covariance matrix is unrestricted proved to be difficult due to the comparative nature of the data. We show that under a suitable constraint the utilities' correlation matrix can be estimated, yielding a readily interpretable solution. This set of identification…

This article compares two methods for analyzing small sets of repeated measures data under normal and non-normal heteroscedastic conditions: a mixed model approach with the Kenward-Roger correction and a multivariate extension of the modified Brown-Forsythe (BF) test. These procedures differ in their assumptions about the covariance structure of…

Researchers studying monitoring accuracy currently use two different indexes to estimate accuracy: relative accuracy and absolute accuracy. The authors compared the distributional properties of two measures of monitoring accuracy using Monte Carlo procedures that fit within these categories. They manipulated the accuracy of judgments (i.e., chance…

The Second International Conference on Educational Data Mining (EDM2009) was held at the University of Cordoba, Spain, on July 1-3, 2009. EDM brings together researchers from computer science, education, psychology, psychometrics, and statistics to analyze large data sets to answer educational research questions. The increase in instrumented…