A nonparametric dispersion test for unreplicated two-level fractional factorial designs

A consistent product/process will have little variability, i.e. dispersion. The widely-used unreplicated two-level fractional factorial designs can play an important role in detecting dispersion effects with a minimum expenditure of resources. In this paper we develop a nonparametric dispersion test for unreplicated two-level fractional factorial designs. The test statistic is defined, critical values are provided, and large sample approximations are given. Through simulations and examples from the literature, the test is compared to general nonparametric dispersion tests and a parametric test based on a normality assumption. These comparisons show the test to be the most robust of those studied and even superior to the normality-based test under normality in some situations. An example is given where this new test is the only one of those studied that does not incorrectly detect a spurious dispersion effect.