The use of computer simulations in the teaching of introductory statistics can help undergraduate students understand difficult or abstract statistics concepts. The free software environment R is a good candidate for computer simulations since it allows users to add additional functionality by defining new functions. In this paper, we illustrate…

This article focuses on a family of restricted latent structure models with wide applications in psychological and educational assessment, where the model parameters are restricted via a latent structure matrix to reflect prespecified assumptions on the latent attributes. Such a latent matrix is often provided by experts and assumed to be correct…

The Monte Carlo method and related multiple imputation methods are traditionally used in math, physics and science to estimate and analyze data and are now becoming standard tools in analyzing business and financial problems. However, few sources explain the application of the Monte Carlo method for individuals and business professionals who are…

Confidence and its accuracy have been most commonly examined in domains such as general knowledge and learning, with less study of other domains, such as applied knowledge and problem solving. Monitoring accuracy in real-world competencies may depend on characteristics of the domain. In this study, we examined whether monitoring accuracy, both…

Policymakers have grown increasingly interested in how experimental results may generalize to a larger population. However, recently developed propensity score-based methods are limited by small sample sizes, where the experimental study is generalized to a population that is at least 20 times larger. This is particularly problematic for methods…

Manipulatives have been found to be effective in increasing mathematics achievement when they are put to good use (Canny, 1984; Clements & Battista, 1990; Clements, 1999; Sowell, 1989; Suydam, 1984), but their use in mathematics instruction is not clear and it is often debated to be effective (Ball, 1992; McNeil & Jarvin, 2007). The…

Quartiles are usually introduced early, often in primary school together with box-and-whisker plots. Various methods are used, and in lack of explanation in many textbooks at elementary level, this leads to unnecessary confusion. We discuss some elementary methods that are consistent with the most common definition and are also easy to understand.

The probability is exceptional in the teaching of mathematics because students often have difficulties to understand the basic terms and the problem solving strategies. Understanding lacks of the probability concept and various types of misconceptions arise from the misleading intuition and misinterpretations of experience with the stochastic…

When a multisite randomized trial reveals between-site variation in program impact, methods are needed for further investigating heterogeneous mediation mechanisms across the sites. We conceptualize and identify a joint distribution of site-specific direct and indirect effects under the potential outcomes framework. A method-of-moments procedure…

The variance formula derived for a two-stage sampling design without replacement employs the joint inclusion probabilities in the first-stage selection of clusters. One of the difficulties encountered in data analysis is the lack of information about such joint inclusion probabilities. One way to solve this issue is by applying Hájek's…

Researchers addressing posttreatment complications in randomized trials often turn to principal stratification to define relevant assumptions and quantities of interest. One approach for the subsequent estimation of causal effects in this framework is to use methods based on the "principal score," the conditional probability of belonging…

The manuscript presents a Visual Basic[superscript R] for Applications function that operates within Microsoft Office Excel[superscript R] to return the area below the curve for a given F within a specified non-central F distribution. The function will be of use to Excel users without programming experience wherever a non-central F distribution is…

Model uncertainty is pervasive in social science. A key question is how robust empirical results are to sensible changes in model specification. We present a new approach and applied statistical software for computational multimodel analysis. Our approach proceeds in two steps: First, we estimate the modeling distribution of estimates across all…

The purpose of this paper is to provide guidance in choice of analytic bias reduction methods for educational studies in which the goal is to estimate a treatment effect in the presence of selection bias into treatment. In addition, issues of dimensionality, collinearity, omitted confounders, missing outcomes, and non-independence may be factors…

Policymakers are increasingly interested in the extent to which experimental results generalize from a sample to a population of inference. When the sample is not randomly selected, propensity score methods are used to reweight the sample. Subclassification by propensity score is commonly used in which the population is partitioned into strata…