In statistics classes, the central limit theorem has been demonstrated using simulation-based illustrations. Known population distributions such as a uniform or exponential distribution are often used to consider the behavior of the sample mean in simulated samples. Unlike such simulations, a number of real-data-based simulations are here…

We examined the performance of coefficient alpha and its potential competitors (ordinal alpha, omega total, Revelle's omega total [omega RT], omega hierarchical [omega h], greatest lower bound [GLB], and coefficient "H") with continuous and discrete data having different types of non-normality. Results showed the estimation bias was…

Informally testing the fit of a probability distribution model is educationally a desirable precursor to formal methods for senior secondary school students. Limited research on how to teach such an informal approach, lack of statistically sound criteria to enable drawing of conclusions, as well as New Zealand assessment requirements led to this…

Mixture Rasch (MixRasch) models conventionally assume normal distributions for latent ability. Previous research has shown that the assumption of normality is often unmet in educational and psychological measurement. When normality is assumed, asymmetry in the actual latent ability distribution has been shown to result in extraction of spurious…

Past research have pointed out that excellent strategies have been written but extremely small have been accomplished in their implementation. It has additionally been proposed that only 10% of formulated strategies are successfully implemented. However, crafting the best strategy is not the end in itself but the ultimate result will only be…

The purpose of this study was to explore the degree of grain size of the attributes and the sample sizes that can support accurate parameter recovery with the General Diagnostic Model (GDM) for a large-scale international assessment. In this resampling study, bootstrap samples were obtained from the 2003 Grade 8 TIMSS in Mathematics at varying…

A workforce that can adapt to the fast changing global dynamics is critical for sustainable growth and development. Secondary level segment in the education cycle of a Kenyan plays a key role in the development of this workforce and is important since it de-links one from elementary (primary) learning, provides a chance for one to complete the…

This study was designed to compare the accuracy of three commonly used ability estimation procedures under the graded response model. The three methods, maximum likelihood (ML), expected a posteriori (EAP), and maximum a posteriori (MAP), were compared using a recovery study design for two sample sizes, two underlying ability distributions, and…

The empirical performance of the technique proposed by P. O. Johnson and J. Neyman (1936) (the JN technique) and the modification of R. F. Potthoff (1964) was studied in simulated data settings. The robustness of the two JN techniques was investigated with respect to their ability to control Type I and Type III errors. Factors manipulated in the…