Abstract
Simulation studies allow researchers to answer specific questions about data analysis, statistical power, and best-practices for obtaining accurate results in empirical research. Despite the benefits that simulation research can provide, many researchers are unfamiliar with available tools for conducting their own simulation studies. The use of simulation studies need not be restricted to researchers with advanced skills in statistics and computer programming, and such methods can be implemented by researchers with a variety of abilities and interests. The present paper provides an introduction to methods used for running simulation studies using the R statistical programming environment and is written for individuals with minimal experience running simulation studies or using R. The paper describes the rationale and benefits of using simulations and introduces R functions relevant for many simulation studies. Three examples illustrate different applications for simulation studies, including (a) the use of simulations to answer a novel question about statistical analysis, (b) the use of simulations to estimate statistical power, and (c) the use of simulations to obtain confidence intervals of parameter estimates through bootstrapping. Results and fully annotated syntax from these examples are provided.
Highlights
Use of commands for generating, indexing, and combining vectors, including the c command for generating and combining vectors, the length command for obtaining the number of items in a vector, and the rbind and cbind commands for combining vectors by row or column, respectively
An additional function for setting the randomization seed, set.seed, is useful for generating the same sets of random numbers each time a simulation study is run, allowing exact replications of results. Statistical models in these tutorials will be fit using the lm command, which models linear regression, analysis of variance, and analysis of covariance
The lm command returns an object with information about the fitted linear model, which may be accessed through additional commands
Summary
Simulation studies allow researchers to answer specific questions about data analysis, statistical power, and best-practices for obtaining accurate results in empirical research. Three examples illustrate different applications for simulation studies, including (a) the use of simulations to answer a novel question about statistical analysis, (b) the use of simulations to estimate statistical power, and (c) the use of simulations to obtain confidence intervals of parameter estimates through bootstrapping. Three examples will be introduced to show the logic and procedures involved in implementing simulation studies, with fully annotated R syntax and brief discussions of the results provided. Despite the specificity of these example applications, the goal of the present paper is to provide the reader with an entry-level understanding of methods for conducting simulation studies in R that can be applied to a variety of statistical models unrelated to mediation analysis
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