Title: Generalized resolution for factorial designs
Authors: Ulrike Groemping - Beuth University of Applied Sciences Berlin (Germany) [presenting]
Abstract: The confounding structure of factorial designs can be investigated using the generalized word length pattern, which implies the resolution as the length of the shortest word. For factorial designs with only two-level factors, resolution was previously refined to generalized resolution (GR): GR increases the resolution by the distance to worst case confounding and has an interesting geometrical interpretation. We have recently developed squared canonical correlations and average $R^2$ values as means for supplying two types of generalized resolution for general factorial designs, including designs for factors at more than two levels and mixed level designs. The proposed generalized resolutions are coding invariant, i.e., they are particularly suitable for designs with qualitative factors. The squared canonical correlations and average $R^2$ values are also of interest in themselves, and can also be used for factor-specific generalized resolutions, i.e., factor specific worst-case considerations.