Parallel analysis has been considered one of the most accurate methods for determining the number of factors in factor analysis. One major advantage of parallel analysis over traditional factor retention methods (e.g., Kaiser's rule) is that it addresses the sampling variability of eigenvalues obtained from the identity matrix, representing the…

Computer simulation can be used to demonstrate why the unbiased sample variance uses degrees of freedom (n-1). This is first demonstrated for sampling from a normal random variable, and in additional simulations for some selected non-normal random variables, namely, chi-square and binomial.

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to…

Single subject (SS) designs are popular in educational and psychological research. There exist several statistical techniques designed to analyze such data and to address the question of whether an intervention has the desired impact. Recently, researchers have suggested that generalized additive models (GAMs) might be useful for modeling…

This article discusses the sample size requirements for the interaction, row, and column effects, respectively, by forming a linear contrast for a 2×2 factorial design for fixed-effects heterogeneous analysis of variance. The proposed method uses the Welch t test and its corresponding degrees of freedom to calculate the final sample size in a…

Purpose: Computer simulation was used to estimate the statistical properties of searches for maximum word recognition ability (PB max). These involve presenting multiple lists and discarding all scores but that of the 1 list that produced the highest score. The simulations, which model limitations inherent in the precision of word recognition…

The main aim of this research is to display research trends in studies on augmented reality (AR) in teaching English as a foreign language by using bibliometric mapping and content analysis. For this purpose, 64 studies in total published up to 2019 were accessed for bibliometric analysis. In addition, 49 articles published between 2007 and 2019…

A simulation study is presented to evaluate and compare three methods to estimate the variance of the estimates of the parameters d and "C" of the signal detection theory (SDT). Several methods have been proposed to calculate the variance of their estimators, "d'" and "c." Those methods have been mostly assessed by…

Randomized experiments are considered the gold standard for causal inference because they can provide unbiased estimates of treatment effects for the experimental participants. However, researchers and policymakers are often interested in using a specific experiment to inform decisions about other target populations. In education research,…

The gold standard for identifying more effective pedagogical approaches is to perform an experiment. Unfortunately, frequently a hypothesized alternate way of teaching does not yield an improved effect. Given the expense and logistics of each experiment, and the enormous space of potential ways to improve teaching, it would be highly preferable if…

Recommended learning goals for students in introductory statistics courses include the ability to recognize and explain the key role of randomness in designing studies and in drawing conclusions from those studies involving generalizations to a population or causal claims (GAISE College Report ASA Revision Committee, 2016). The purpose of this…

While looking for an inexpensive technology package to help students in statistics classes, the author found StatKey, a free Web-based app. Not only is StatKey useful for students' year-end projects, but it is also valuable for helping students learn fundamental content such as the central limit theorem. Using StatKey, students can engage in…

Ragin's Qualitative Comparative Analysis (QCA) is often used with small to medium samples where the researcher has good case knowledge. Employing it to analyse large survey datasets, without in-depth case knowledge, raises new challenges. We present ways of addressing these challenges. We first report a single QCA result from a configurational…

In education research, small samples are common because of financial limitations, logistical challenges, or exploratory studies. With small samples, statistical principles on which researchers rely do not hold, leading to trust issues with model estimates and possible replication issues when scaling up. Researchers are generally aware of such…

In observational studies, selection bias will be completely removed only if the selection mechanism is ignorable, namely, all confounders of treatment selection and potential outcomes are reliably measured. Ideally, well-grounded substantive theories about the selection process and outcome-generating model are used to generate the sample of…