Comprehensive evaluation of treatment effects is aided by considerations for moderated effects. In educational research, the combination of natural hierarchical structures and prevalence of group-administered or shared facilitator treatments often produces three-level partially nested data structures. Literature details planning strategies for a…

Simulation of physics phenomena is an indispensable part of experimental studies. Undergraduate and postgraduate physics students are often introduced to the simulation of various phenomena as one of the most important pedagogical tools. In this document, we demonstrate the simulations of the two-body decay of a particle and equilibrium states in…

Traditional visualization in meta-analysis uses forest plots to illustrate the combined treatment effect, along with the respective results from primary trials. While the purpose of visualization is clear in the pairwise setting, additional treatments broaden the focus and extend the results to be illustrated in network meta-analysis. The…

In this digital ITEMS module, Dr. Brian Leventhal and Dr. Allison Ames provide an overview of "Monte Carlo simulation studies" (MCSS) in "item response theory" (IRT). MCSS are utilized for a variety of reasons, one of the most compelling being that they can be used when analytic solutions are impractical or nonexistent because…

This contribution shows a simple implementation of Monte Carlo simulation method when presenting Bayes' rule. The implementation is carried out in the environment of Microsoft Excel spreadsheets by means of a generator of random numbers. The empiric results gained by simulation serve to confirm the correctness of the chosen procedures in…

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…

The recent popularity of models that capture the dynamic coevolution of both network structure and behavior has driven the need for summary indices to assess the adequacy of these models to reproduce dynamic properties of scientific or practical importance. Whereas there are several existing indices for assessing the ability of the model to…

Social networks in education commonly involve some form of grouping, such as friendship cliques or teacher departments, and blockmodels are a type of statistical social network model that accommodate these grouping or blocks by assuming different within-group tie probabilities than between-group tie probabilities. We describe a class of models,…

For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…

Equity Indexed Annuities (EIAs) are controversial financial products because the payoffs to investors are based on formulas that are supposedly too complex for average investors to understand. This brief describes how Monte Carlo simulation can provide insight into the true risk and return of an EIA. This approach can be used as a project…

Two Monte Carlo simulation studies investigated the effectiveness of the mean adjusted X[superscript 2]/df statistic proposed by Drasgow and colleagues and, because of problems with the method, a new approach for assessing the goodness of fit of an item response theory model was developed. It has been previously recommended that mean adjusted…

We present a Monte Carlo simulation of a cylindrical luminescent volume and a typical lens-detector system. The results of this simulation yield a graphically simple picture of the regions within the cylindrical volume from which this system detects light. Because the cylindrical volume permits large angles of incidence, we use a modification of…

Sensitivity analysis is the study of how the different input variations of a mathematical model influence the variability of its output. In this paper, we review the principle of global and local sensitivity analyses of a complex black-box system. A simulated case of application is given at the end of this paper to compare both approaches.…

There are many definitions that are attributable to the meaning of sustainability. Sustainability can be viewed as long-lasting, effective result of a project, venture, action, or investment without consuming additional future resources. Because of the wide nature of its applicability, a universal measure of sustainability is hard to come by. This…

A procedure modelling ideal classical and quantum gases is discussed. The proposed approach is mainly based on the idea that modelling and algorithm analysis can provide a deeper understanding of particularly complex physical systems. Appropriate representations and physical models able to mimic possible pseudo-mechanisms of functioning and having…