Identification of Dispersion Effects in Replicated Two-Level Fractional Factorial Experiments

Abstract

Tests for dispersion effects in replicated two-level factorial experiments assuming a location-dispersion model are presented. The tests use individual measures of dispersion that remove the location effects and also provide an estimate of pure error. Empirical critical values for two such tests are given for two-level full or regular fractional factorial designs with 8, 16, 32, and 64 runs. The powers of the tests are examined under normal, exponential, and Cauchy distributed errors. Our recommended test uses dispersion measures calculated as deviations of the data values from their cell medians, and this test is illustrated via an example.

Keywords:

• Dispersion measures
• Location-dispersion model
• Fractional factorial experiment

Acknowledgments

The authors thank a referee for helpful and thoughtful comments. The work of Dean was supported by grants SES-0437251 and DMS-0806134 from the National Science Foundation, and the work of Ankenman by EPSRC grant GR/S91673 while visiting Southampton Statistical Sciences Research Institute, United Kingdom.