A MONTE CARLO STUDY ON THE LATIN SQUARE DESIGNS
Francisco
J. P. ZIMMERMANN[1]
Christopher
A. ROBERTSON[2]
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ABSTRACT: In this work we compare
a test developed by Bennett in 1966; another one by Zimmermann in 1983, and the
F-test, based on the real data and based on some transforms, like the
rank-transform and the normal scores transformation. Data we simulated seven
probability distributions under the null and the alternative hypothesis in a
Monte Carlo study. The test were then compared based on the empirical size and
power thus obtained with the following main conclutions: - the parametric
analysis of variance due to its robustness is competitive with the
distribution-free tests studied, except when data come from density without
finite moments, where then it is conservative and has practically no power; -
the new test more powerfull for small latin square designs and equivalent to
the others for the larger ones.
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KEYWORDS: Non-parametric tests;
experimental design; distribution-free; analysis of variance.