The effects of nonnormality on the analysis of supersaturated designs: A comparison of stepwise, SCAD and permutation test methods

Woon Yuen Koh, Kent M. Eskridge, Dong Wang

Research output: Contribution to journalArticle


Supersaturated designs (SSDs) are useful in examining many factors with a restricted number of experimental units. Many analysis methods have been proposed to analyse data from SSDs, with some methods performing better than others when data are normally distributed. It is possible that data sets violate assumptions of standard analysis methods used to analyse data from SSDs, and to date the performance of these analysis methods have not been evaluated using nonnormally distributed data sets. We conducted a simulation study with normally and nonnormally distributed data sets to compare the identification rates, power and coverage of the true models using a permutation test, the stepwise procedure and the smoothly clipped absolute deviation (SCAD) method. Results showed that at the level of significance α = 0.01, the identification rates of the true models of the three methods were comparable; however at α = 0.05, both the permutation test and stepwise procedures had considerably lower identification rates than SCAD. For most cases, the three methods produced high power and coverage. The experimentwise error rates (EER) were close to the nominal level (11.36%) for the stepwise method, while they were somewhat higher for the permutation test. The EER for the SCAD method were extremely high (84–87%) for the normal and t-distributions, as well as for data with outlier.

Original languageEnglish (US)
Article numberA011
Pages (from-to)158-166
Number of pages9
JournalJournal of Statistical Computation and Simulation
Issue number1
Publication statusPublished - Jan 1 2013



  • Factor screening
  • Least squares
  • Nonparametric method
  • Screening design

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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