New methodical findings on D-efficient factorial survey designs: Impacts of design resolution on aliasing and sample size

In empirical surveys, finding a sufficient number of respondents can be challenging. For factorial survey experiments, drawing a vignette-sample (“fraction”) from a vignette-universe can reduce the minimum number of respondents required. Vignette-samples can be drawn by applying D-efficient designs. Theoretically, D-efficient resolution V designs are ideal. Due to reasons of practicability, however, resolution IV designs have usually been applied in empirical social research and are considered to be sufficient when it is clear up front, which two-way interactions are likely to have an effect. Against this backdrop, this article focusses on two research questions: (1) In resolution IV designs, are those two-way interactions that are not orthogonalized truly not aliased with any main effects? (2) How does design resolution affect the minimum size of the vignette-sample that is necessary for achieving an adequate level of D-efficiency? These questions are examined by applying SAS-macros for computing D-efficient samples, pre-construction assessment and post-construction evaluation. The resulting aliasing structures indicate a discrepancy between previous definitions of design resolutions and the aliasing structures of designs resulting from the SAS-macros. Additionally, they suggest taking a second look at the assumption that higher resolutions or larger vignette universes will always necessitate designs with larger vignette-samples (and thus larger sets or more respondents).