Synchronized Permutation Tests in 2^k Factorial Designs

Abstract

In this article, based on the notion of synchronized permutations (Salmaso, L. (2000). Orthogonal Two-Level Factorial Designs and Permutation Tests for Effects. Ph.D. thesis, Department of Statistics, University of Padova.), we provide a new full exact solution for testing effects in replicated 2 ^k factorial designs within a nonparametric framework. Synchronized permutations allow for testing separately all effects by shuffling the appropriate set of sufficient statistics. Such tests are exact, unbiased, and consistent. Furthermore, they are uncorrelated to each other and asymptotically at least as powerful as the parametric solution when the latter is appropriate. A simulation study shows that also for small sample sizes their power is close to that of parametric counterparts based on normality of errors. This approach preserves the exchangeability of error components for testing all 2 ^k -1effects.

Keywords:

• Conditional inference
• Exchangeability
• Hadamard matrices
• Interaction
• Resolution