Typical difficulties in learning probabilistic subjects are concerned with big data, complicated formulas and inconvenient figures in statistical analyses. The present research considers the usage of innovative teaching methods (e.g. electronic summary of lectures, presentations of lecture courses, task solution templates, electronic training…

In recent years, there has been increasing focus on the issue of multiple hypotheses testing in education evaluation studies. In these studies, researchers are typically interested in testing the effectiveness of an intervention on multiple outcomes, for multiple subgroups, at multiple points in time or across multiple treatment groups. When…

The content validity ratio originally proposed by Lawshe is widely used to quantify content validity and yet methods used to calculate the original critical values were never reported. Methods for original calculation of critical values are suggested along with tables of exact binomial probabilities.

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the…

The Portland Timbers won their first Major League Soccer (MLS) Cup Championship in December 2015. However, if it had not been for a kind double goalpost miss during a penalty shootout a few weeks earlier, the Timbers would never have been in the finals. On Oct. 30th, after what has been called "the greatest penalty kick shootout in MLS…

Calculating Laplace transforms from the definition often requires tedious integrations. This paper provides an integration-free technique for calculating Laplace transforms of many familiar functions. It also shows how the technique can be applied to probability theory.

This paper presents a comparison of three approaches to the teaching of probability to demonstrate how the truth table of elementary mathematical logic can be used to teach the calculations of conditional probabilities. Students are typically introduced to the topic of conditional probabilities--especially the ones that involve Bayes' rule--with…

Nonnormality of univariate data has been extensively examined previously (Blanca et al., 2013; Micceri, 1989). However, less is known of the potential nonnormality of multivariate data although multivariate analysis is commonly used in psychological and educational research. Using univariate and multivariate skewness and kurtosis as measures of…

Estimating the prerequisite structure of skills is a crucial issue in domain modeling. Students usually learn skills in sequence since the preliminary skills need to be learned prior to the complex skills. The prerequisite relations between skills underlie the design of learning sequence and adaptation strategies for tutoring systems. The…

Despite the popularity of propensity score (PS) techniques they are not yet well studied for matching multilevel data where selection into treatment takes place among level-one units within clusters. This paper suggests a PS matching strategy that tries to avoid the disadvantages of within- and across-cluster matching. The idea is to first…

Complex surveys are often used to estimate causal effects regarding the effects of interventions or exposures of interest. Propensity scores (Rosenbaum & Rubin, 1983) have emerged as one popular and effective tool for causal inference in non-experimental studies, as they can help ensure that groups being compared are similar with respect to a…

The motivating example for this paper comes from a distributed health data network, the International Consortium of Orthopaedic Registries (ICOR), which aims to examine risk factors for orthopedic device failure for registries around the world. Unfortunately, regulatory, privacy, and propriety concerns made sharing of raw data impossible, even if…

Since the seminal introduction of the propensity score (PS) by Rosenbaum and Rubin, PS-based methods have been widely used for drawing causal inferences in the behavioral and social sciences. However, the PS approach depends on the ignorability assumption: there are no unobserved confounders once observed covariates are taken into account. For…

Although social scientists devote considerable effort to mitigating measurement error during data collection, they often ignore the issue during data analysis. And although many statistical methods have been proposed for reducing measurement error-induced biases, few have been widely used because of implausible assumptions, high levels of model…

This article is written to share teaching ideas about using commonly available computer applications--a spreadsheet, "The Geometer's Sketchpad", and "Wolfram Alpha"--to explore three classic and historically significant problems from the probability theory. These ideas stem from the authors' work with prospective economists,…