A cautionary note on the use of the third-order polynomial method in simulation studies

The third-order polynomial method to simulate multivariate, non-normal data is ubiquitously present in computer simulation studies within the educational and psychological sciences. At the crux of this method is a system of polynomial equations whose solution is not unique. The idiosyncratic properties of the data generated by each solution can be sufficiently extreme as to impact the conclusions from published simulation research. I will present both a mathematical framework to describe these solutions and examples from well-cited articles (with over 1000 citations such as Curran, West & Finch, 1996) where using different solutions to generate non-normal data changes and even reverses the conclusions from these publications. Recommendations will be presented as well as a call to become acquainted with the theoretical properties of the algorithms used in simulation research.