Exact critical points for testing subhypotheses in nonreplicated three-way experiments

Abstract

In the absence of replication, conventional analyses do not provide ways to examine three-way interaction in threeway experiments. Tucker3 analysis based on alternating least squares algorithm is a general approach that can be used in such cases. However, Tucker3 options are not available with standard statistical packages. A few methods for estimating σ2 and testing for three-way interaction using a “single component” Tucker3 model are available in literature. A method based on a convenient approximation to a likelihood ratio test is also available in limited cases for testing three-way interaction in sub-areas once interaction is present. In this paper the null distribution of the above likelihood ratio statistic is simulated using Monte Carlo methods based on exact values obtained from Tucker3 analysis. Critical points are also obtained for the test for selected cases. Though the package 3-WAY PACK® handles Tucker3 analysis it does not conveniently support WINDOWS® based simulations and therefore MATLAB® is used for the simulation. The method is illustrated using two examples involving real data.