British Journal of Mathematical and Statistical Psychology

On the solution multiplicity of the Fleishman method and its impact in simulation studies

Journal Article

The Fleishman third‐order polynomial algorithm is one of the most‐often used non‐normal data‐generating methods in Monte Carlo simulations. At the crux of the Fleishman method is the solution of a non‐linear system of equations needed to obtain the constants to transform data from normality to non‐normality. A rarely acknowledged fact in the literature is that the solution to this system is not unique, and it is currently unknown what influence the different types of solutions have on the computer‐generated data. To address this issue, analytical and empirical investigations were conducted, aimed at documenting the impact that each solution type has on the design of computer simulations. In the first study, it was found that certain types of solutions generate data with different multivariate properties and wider coverage of the theoretical range spanned by population correlations. In the second study, it was found that previously published recommendations from Monte Carlo simulations could change if different types of solutions were used to generate the data. A mathematical description of the multiple solutions to the Fleishman polynomials is provided, as well as recommendations for users of this method.

Related Topics

Related Publications

Related Content

Site Footer


This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.