ENBIS: European Network for Business and Industrial Statistics

A Permutation Test for Effects in Unreplicated Factorial Designs

Abstract

Submitted by

Anna Skountzou

Authors

Anna Skountzou, Christos Koukouvinos and Kalliopi Mylona

Affiliation

Department of Mathematics, National Technical University of Athens, Zografou 15773, Athens, Greece

Abstract

The analysis of unreplicated factorial designs concentrates much of interest, since these designs enable us to estimate the factorial effects using contrasts, while no degrees of freedom are left to estimate the error variance. In order to examine the significance of the effects in unreplicated two-level factorial designs we present a permutation testing procedure. According to our method the permutation estimates of the factorial effects are obtained by applying the Ordinary Least Squares estimation to a set of inequivalent Hadamard matrices. A major reason that led us to use a permutation test is that it requires no a priori assumptions regarding the underlying distribution of the data nor does it impose any practical restriction on the number of potentially significant effects present. Moreover a comparison study, made with previous works and performed by simulated experiments, is given revealing the effectiveness of the proposed method. Finally, we present the application of our method to an example with real data.

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