The reliability of the Shotgun Stochastic Parameter Estimation Algorithm for analysing rank ordered data

Abstract

The introduction of the Shotgun Stochastic Parameter Estimation Algorithm (the Algorithm) in 2006 by A. Stacey offered a simple method of introducing interval level data into rank ordered observations thus allowing the application of more powerful statistical analysis on ordinal level data. As this is a relatively new development in the debate regarding treating ordinal level data as if it were interval the Algorithm’s mechanics (i.e. its internal relationships) remain relatively unknown. This study, by means of a series of simulations, looks at the standard errors of the sample means simulated by the algorithm after two variables, intrinsic to the Algorithm, are systematically changed. The variables changed are the number of items ranked and the size of the internally generated interval level based sample. What was found was that as the number of items ranked increases so too does the inconsistency of the algorithm, conversely as the size of the simulated sample increases the consistency improves, initially at an accelerated rate but then slowing rapidly into very small changes for large increases in the sample size. The results were then compared with the sample error that results from using observed sample sizes of the same magnitude as those of the simulated samples in the study and it was discovered that the Algorithm has comparatively much less error in it. The study concludes that the Algorithm is a reliable method to use and offers guidelines for the safe use of the algorithm that hope to ensure consistent and reliable generation of outputs.