Random-Number Generator Validity in Simulation Studies: An Investigation of Normality

Abstract

Random-number generators are frequently used in Monte Carlo simulation studies to examine expected statistical outcomes. The purpose of this study was to investigate the normality of number distributions generated by various random-number generators. The research question focused on when the random-number generator reached a normal distribution (efficiency) and at what sample size. Findings suggest that when using a random-number generator in a Monte Carlo simulation study, the following steps should be observed: (a) normality of number distribution should be checked-means and standard deviations, (b) sample size should be large (n > 10,000), (c) starting seed values should be tested with regard to normality of resulting number distribution, (d) the length of periods before numbers repeat should be considered, (e) serial correlation between number sequences should be examined, and (f) uniformity of number distributions should be checked.