When we read, errors in oculomotor programming can cause the eyes to land and fixate on different words from what the mind intended. Previous work suggests that these "mislocated fixations" form 10-30% of first-pass fixations in reading eye movement data, which presents theoretical and analytic issues for eyetracking-while-reading…

This paper investigates two specific probabilistic biases which middle graders usually exhibit when reasoning about probability and randomness on assessment items. We discuss how students' reasoning about key probability concepts undergirds statistics literacy related to randomness, independence, and the likelihood of future events based on past…

The internet has had a vast and pervasive effect on many industries. It has resulted in the creation of new industries and has overhauled the dynamics that governed existing industries. One of the most traditional industries that is now struggling to cope with the changes brought on by the internet is the industry of higher education. Students can…

This note extends the results in the 2016 article by Raykov, Marcoulides, and Li to the case of correlated errors in a set of observed measures subjected to principal component analysis. It is shown that when at least two measures are fallible, the probability is zero for any principal component--and in particular for the first principal…

Probability and chance are essential concepts, not just in statistics but in real life. We present an adaptable activity which investigates what we mean by bias, how we can identify bias, and how we can use it to our advantage!

The well-known recency effect in immediate free recall reverses when subjects attempt to recall items studied and tested on a series of prior lists, as in the final-free-recall procedure (Craik, 1970). In this case, the last few items on each list are actually remembered less well than are the midlist items. Because dual-store theories of recall…

Several statistical models have been developed in educational measurement to determine and track the performance of students in longitudinal studies. An example of a model designed for such purpose is the latent transition analysis (LTA) model. The LTA model (Graham, Collins, Wugalter, Chung, & Hansen 1991) is a type of autoregressive model…

This study focuses on the relationship between various leadership goal setting and students' decisions about further education in the context of the Danish educational system. Furthermore, the potential of school leadership to reduce social disparities in such decisions is explored. The data set is based on repeated measurements of school leaders'…

Multiple choice results are inherently probabilistic outcomes, as correct responses reflect a combination of knowledge and guessing, while incorrect responses additionally reflect blunder, a confidently committed mistake. To objectively resolve knowledge from responses in an MC test structure, we evaluated probabilistic models that explicitly…

Psychiatric disorders are common in youth with intellectual and developmental disabilities. This is a vulnerable group of children whose behavioural problems often have more complicated care needs than other children, which can place a great deal of stress on their families. However, the association of family mental health issues, level of…

Engineering design plays an important role in education. However, due to its open nature and complexity, providing timely support to students has been challenging using the traditional assessment methods. This study takes an initial step to employ learning analytics to build performance prediction models to help struggling students. It allows…

Previous studies provided evidence for a connection between language processing and language change. We add to these studies with an exploration of the influence of lexical-distributional properties of words in orthographic space, semantic space, and the mapping between orthographic and semantic space on the probability of lexical extinction.…

When equating two test forms, the equated scores will be biased if the test groups differ in ability. To adjust for the ability imbalance between nonequivalent groups, a set of common items is often used. When no common items are available, it has been suggested to use covariates correlated with the test scores instead. In this article, we reduce…

Propensity score analysis is a statistical method that balances pre-existing differences across treatment conditions achieving a similar condition as randomization and thus, allowing the estimation of causal effects in non-randomized experimental designs. The four stages in propensity score analysis are (1) propensity score estimation, (2)…

The Birthday Paradox problem can be investigated either with a carefully constructed spreadsheet (for greatest precision) or a calculator process (for reasonable precision). A number of ways of approaching this problem as a class activity are provided.