A NEW DISTRIBUTION-FREE TEST FOR THE LATIN SQUARE DESIGN
Francisco
J. P. ZIMMERMANN[1]
Christopher
A. ROBERTSON[2]
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ABSTRACT: In this work we present
a new score, the rank-sum score, introduce a new test based on it and prove
that asymptotically it has an F-distribution. Data we simulated from seven
probability distributions under the null and the alternative hypothesis in a
Monte Carlo study in order to estimate the size and power of the test. The
approximation of the F-distribution with (n-1) and n(n-1) degrees of freedom to
the new test can be improved by the use of a power transform, as demonstrated
in another simulation of 10000 experiments for each number of treatments.
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KEYWORDS: Non-parametric; tests;
experimental design; lain square; distribution-free; analysis of variance.