Monte Carlo Simulation Studies

Methods and Basic Procedures

The most commonly employed application of the Monte Carlo simulation is the examination of sampling distributions, although its application extends to a variety of scenarios for which a complete mathematical analysis is otherwise not feasible or is extremely difficult. Discussion of the enumerable number of applications is beyond the scope of the current entry.

Fundamentally, the methodology allows one to examine a very large number of observations that are created from a set of parameters. In part, the utility of the Monte Carlo methodology includes flexibility and the ability to generate a large number of observations based on existing parameters (e.g., summary data for a population of interest). The basic procedure of the Monte Carlo simulation is to first specify the pseudo-population through the development of a computer algorithm to generate data for the desired statistic. This computer algorithm generates artificial data to simulate a population. These data can then be used by the researcher to study and to better understand the behavior of the statistical estimates from the data. A commonly used algorithm is known as “middle-square digits.” For this algorithm, an arbitrary n-unit integer is squared, creating a 2n-digit product. A new integer is then created by removing the middle n-digits from the product, and then the process is repeated over and over, creating a long chain of integers that will eventually repeat itself. Observations are usually random or pseudorandom and are intended to generalize the population of interest. The extent to which the initial parameters are representative of the population of interest, the generated pseudo-population resembles a real-world population in all relevant aspects. The pseudo-population generally encompasses a very large number of observations, allowing for it to be analyzed with ancillary statistical techniques, which can be useful in better characterizing the actual population and generalizing appropriate inferences.

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