Issues, problems and potential solutions when simulating continuous, non-normal data in the social sciences

Abstract

Computer simulations have become one of the most prominent tools for methodologists in the social sciences to evaluate the properties of their statistical techniques and to offer best practice recommendations. Amongst the many uses of computer simulations, evaluating the robustness of methods to their assumptions, particularly univariate or multivariate normality, is crucial to ensure the appropriateness of data analysis. In order to accomplish this, quantitative researchers need to be able to generate data where they have a degree of control over its non-normal properties. Even though great advances have been achieved in statistical theory and computational power, the task of simulating multivariate, non-normal data is not straightforward. There are inherent conceptual and mathematical complexities implied by the phrase "non-normality" which are not always reflected in the simulations studies conduced by social scientists. The present article attempts to offer a summary of some of the issues concerning the simulation of multivariate, non-normal data in the social sciences. An overview of common algorithms is presented as well as some of the characteristics and idiosyncrasies that implied in them which may exert undue influence in the results of simulation studies. A call is made to encourage the meta-scientific study of computer simulations in the social sciences in order to understand how simulation designs frame the teaching, usage and practice of statistical techniques within the social sciences.