In this article, an overview is given of four methods to perform factor score regression (FSR), namely regression FSR, Bartlett FSR, the bias avoiding method of Skrondal and Laake, and the bias correcting method of Croon. The bias correcting method is extended to include a reliable standard error. The four methods are compared with each other and…

An IRT-based sequential procedure is developed to monitor items for enhancing test security. The procedure uses a series of statistical hypothesis tests to examine whether the statistical characteristics of each item under inspection have changed significantly during CAT administration. This procedure is compared with a previously developed…

We investigated methods of including covariates in two-level models for cluster randomized trials to increase power to detect the treatment effect. We compared multilevel models that included either an observed cluster mean or a latent cluster mean as a covariate, as well as the effect of including Level 1 deviation scores in the model. A Monte…

Research has shown that many educators do not understand the terminology or displays used in test score reports and that measurement error is a particularly challenging concept. We investigated graphical and verbal methods of representing measurement error associated with individual student scores. We created four alternative score reports, each…

Undergraduate students who have just completed an introductory statistics course often lack deep understanding of variability and enthusiasm for the field of statistics. This paper argues that by introducing the commonly underemphasized concept of measurement error, students will have a better chance of attaining both. We further present lecture…

In the discussion of mean square difference (MSD) and standard error of measurement (SEM), Barchard (2012) concluded that the MSD between 2 sets of test scores is greater than 2(SEM)[superscript 2] and SEM underestimates the score difference between 2 tests when the 2 tests are not parallel. This conclusion has limitations for 2 reasons. First,…

In 1988, the National Center for Education Statistics (NCES) introduced a proposal to develop a private school data collection that would improve on the sporadic collection of private school data dating back to 1890 and improve on commercially available private school sampling frames. Since 1989, the U.S. Bureau of the Census has conducted the…

This article considers two methods of estimating standard errors of equipercentile equating: the parametric bootstrap method and the nonparametric bootstrap method. Using a simulation study, these two methods are compared under three sample sizes (300, 1,000, and 3,000), for two test content areas (the Iowa Tests of Basic Skills Maps and Diagrams…

The Bologna Declaration brought reforms into higher education that imply changes in teaching methods, didactic materials and textbooks, infrastructures and laboratories, etc. Statistics and mathematics are disciplines that traditionally have the worst success rates, particularly in non-mathematics core curricula courses. This research project,…

Abuses and misuses of statistics are frequent. This digest attempts to warn against these in three broad classes of pitfalls: sources of bias, errors of methodology, and misinterpretation of results. Sources of bias are conditions or circumstances that affect the external validity of statistical results. In order for a researcher to make…