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 σ 2 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. Keywords: Exact critical points, testing subhypotheses, three-way interaction, tucker3 analysis. doi:10.4038/jnsfsr.v36i4.264 Journal of the National Science Foundation of Sri Lanka 36 (4) 267-273
Highlights
The primary objective of a three-factor factorial experiment, or a three-way experiment, is to examine the interaction between the three factors simultaneously
The null distribution of some convenient approximation of this test statistic has been simulated, and critical points computed by them using Monte Carlo methods, for selected cases
To carry out the above likelihood ratio test[8] one needs to compute critical points based on the exact null distribution of the statistic Λ
Summary
The primary objective of a three-factor factorial experiment, or a three-way experiment, is to examine the interaction between the three factors simultaneously. When the experiment is replicated, an analysis of variance (ANOVA) can be used to test for three-way interaction. The focus of this paper is a follow up of the work by Wickremasinghe and Johnson[8] They developed a likelihood ratio test for testing subhypotheses in nonreplicated three-way experiments. The null distribution of some convenient approximation of this test statistic has been simulated, and critical points computed by them using Monte Carlo methods, for selected cases. The above null distribution is re-examined for exact values of the test statistic. This is based on Monte Carlo simulations that require running the alternating least squares algorithm iteratively[9]. Critical points are computed for selected cases based on exact values. A comparison is made between the approximate and exact results based on pre-analyzed data
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