Play It Again: Teaching Statistics With Monte Carlo Simulation

Abstract

Monte Carlo simulations (MCSs) provide important information about statistical phenomena that would be impossible to assess otherwise. This article introduces MCS methods and their applications to research and statistical pedagogy using a novel software package for the R Project for Statistical Computing constructed to lessen the often steep learning curve when organizing simulation code. A primary goal of this article is to demonstrate how well-suited MCS designs are to classroom demonstrations, and how they provide a hands-on method for students to become acquainted with complex statistical concepts. In this article, essential programming aspects for writing MCS code in R are overviewed, multiple applied examples with relevant code are provided, and the benefits of using a generate-analyze-summarize coding structure over the typical "for-loop" strategy are discussed.

Numerical approximation of the observed information matrix with Oakes' identity

“…Finally, the absolute difference between the condition numbers of the ACOV estimates and the condition number from Louis’ ACOV were collected (denoted by ), as well as the mean, maximum, and Euclidean norm of the RD matrix in equation (denoted by ) for the three finite‐difference approximations. Each condition was repeated using 500 independent replications using the SimDesign package (Sigal & Chalmers, ).…”

Using R as a Simulation Tool in Teaching Introductory Statistics

“…Hagtvedt, Jones and Jones (2008), Mills (2002), and Raffle and Brooks (2005) have all reported positive outcomes from the use of statistical software. Sigal and Chalmers (2016) elaborated the essential aspects for writing Monte Carlo simulation code in R. Alias (2009) had positive outcomes for even basic forms of statistical visualizations using technology, both in terms of an improvement in student grades and student satisfaction with the class.…”

“…The nature of many statistical concepts is difficult for students to grasp without visual representations or a hands-on exercise (Alias, 2009;Ridgway, Nicholson, & McCusker, 2007). Many basic aspects of introductory statistics involve hypothetical ideas, and thus they can only be properly observed through the use of computer simulations (Sigal & Chalmers, 2016). When proper visualization and data manipulation is available, students as young as 12 could develop at least a functional understanding of multivariate data (Ridgway, Nicholson, & McCusker, 2007).…”

“…Students then can use R's pre-set functions to create their own Monte Carlo simulations in order to grasp statistical concepts. Sigal and Chalmers (2016) overviewed the essential aspects for writing Monte Carlo simulation code in R in detail. It also advertises the use of one of R's many useful packages that make creating Monte Carlo simulations easier.…”

“…Loops and conditional statements in R allows us to create our own simulations. This is how Monte Carlo simulations, which use known parameters to generate random samples of data that can then be used to analyze the behavior of certain statistics, are created (Sigal & Chalmers, 2016). R loops include For loop, While loop and Repeat loop.…”