Nondichotomous response models have been of greater interest in recent years due to the increasing use of different scoring methods and various performance measures. As an important alternative to dichotomous scoring, the use of continuous response formats has been found in the literature. To assess finer-grained skills or attributes and to…

Various tests to check the homogeneity of variance assumption have been proposed in the literature, yet there is no consensus as to their robustness when the assumption of normality does not hold. This simulation study evaluated the performance of 14 tests for the homogeneity of variance assumption in one-way ANOVA models in terms of Type I error…

Extreme Learning Machine (ELM) is a training algorithm for Single-Layer Feed-forward Neural Network (SLFN). The difference in theory of ELM from other training algorithms is in the existence of explicitly-given solution due to the immutability of initialed weights. In practice, ELMs achieve performance similar to that of other state-of-the-art…

The Monte Carlo method is one of the basic simulation statistical methods which can be used both to demonstrate basic probability and statistical concepts as well as to analyse the behaviour stochastic models. The introduction part of the article provides a brief description of the Monte Carlo method. The main part of the article is concentrated…

Co-written by a student and his teacher, this article illustrates how a carefully structured individual education program supported by appropriate software can provide suitable challenges for a gifted Year 3 student. While the focus is on one student's statistical investigation, the story has relevance to the wider primary school environment.

This study aims to analyse the approaches to probability that were carried out by the participants of the teaching practice of Primary Education teachers and, more specifically, their teaching trajectories. To do this we analysed 23 video-recorded classes of all levels, using a previously validated instrument. Results show trajectories…

Quantitative decision making (management science, business statistics) textbooks rarely address data cleansing issues, rather, these textbooks come with neat, clean, well-formatted data sets for the student to perform analysis on. However, with a majority of the data analyst's time spent on gathering, cleaning, and pre-conditioning data, students…

A longstanding concern about admissions to higher education is the underprediction of female academic performance by admission test scores. One explanation for these findings is selection system bias, that is, not all relevant KSAOs that are related to academic performance and gender are included in the prediction model. One solution to this…

Statistical learning (SL), sensitivity to probabilistic regularities in sensory input, has been widely implicated in cognitive and perceptual development. Little is known, however, about the underlying mechanisms of SL and whether they undergo developmental change. One way to approach these questions is to compare SL across perceptual modalities.…

This paper introduces a web-based, interactive point pattern analysis "game" that allows users to generate quickly and repeatedly a point pattern on screen and immediately learn whether the pattern is statistically different from random. It uses two point pattern analysis methods: quadrat analysis (QA) and nearest neighbor analysis…

Algorithms for approximate Bayesian inference, such as those based on sampling (i.e., Monte Carlo methods), provide a natural source of models of how people may deal with uncertainty with limited cognitive resources. Here, we consider the idea that individual differences in working memory capacity (WMC) may be usefully modeled in terms of the…

Over the past 30 years, the way in which the first course in statistics has been taught has moved away from a mathematics mode to take account of the distinctiveness of statistics. This article considers exercises for the typical introductory course and gives some evidence that many of these look like somewhat expanded versions of mathematics…

Practice problems and worked examples are both well-established teaching techniques. Research in math and physics suggests that having students study worked examples during their first contact with new material, instead of solving practice problems, can be beneficial to their subsequent performance, possibly due to the reduced cognitive load…

This paper describes a lesson centered around a metric for measuring partisan gerrymandering: the efficiency gap. We situate the efficiency gap in the current US political climate, describe the activity itself, and then provide recommendations for readers interested in adapting the lesson for their own classrooms.

When data for multiple outcomes are collected in a multilevel design, researchers can select a univariate or multivariate analysis to examine group-mean differences. When correlated outcomes are incomplete, a multivariate multilevel model (MVMM) may provide greater power than univariate multilevel models (MLMs). For a two-group multilevel design…