Dispersion Effects from Unreplicated Designs in the 2 k-p Series

Joint Identification of Location and Dispersion Effects in Unreplicated Two-Level Factorials

“…Last, we consider the Dyestuff data first given in Davies (1963) and analyzed for dispersion effects in Bergman and Hynén (1997). The latter authors found a location effect for factor D and a dispersion effect for E, conclusions that were supported by McGrath and Lin (2001a).…”

“…They show that all are biased, with the severity of bias depending on whether an additive or a log-linear model is assumed for the variances. They also show that the bias in the Harvey method is reduced or eliminated when the residuals are computed from the augmented location model used by Bergman and Hynén (1997). They refer to this as the "modified Harvey" method and recommend it for general use because its bias is limited to certain specific cases.…”

“…Thus, the sampling distribution of F d is not clear. Bergman and Hynén (1997) has an F distribution with degrees of freedom depending on the the number of effects not in the augmented location model. Note that this may be different for each d. Pan (1999) and McGrath and Lin (2001a) show that this test can have inflated type I error rate or diminished power when the original location model fails to identify location effects of moderate size.…”

“…These examples have been analyzed multiple times in the literature. Box and Meyer (1986) B, C C Wang (1989) B, C C, H, J Ferrer and Romero (1993) B, C C, J Bergman and Hynén (1997) refers to our re-analysis using the Lenth test for location followed by the modified Harvey test for dispersion. The factor labels used here are those given in first-listed citation for each example.…”

“…Box and Meyer (1986) developed a seminal procedure to test for "dispersion effects" in data from a 2 k experiment using residuals from a given location model. Several authors have followed this approach by developing improvements or extensions to the Box-Meyer test (e.g., Bergman and Hynén 1997, Wang 1989, Brenneman and Nair 2001, McGrath and Lin 2001a. For a nice review of these procedures see Bursztyn and Steinberg (2006).…”