University of Padova, Italy - Department of Statistics
In this paper we present a new solution to test for effects in unreplicated two-levels factorials designs. The test statistic has the form of a F random variable, and its null distribution in case of normal errors distribution is provided. The nonparametric version of the test is also considered: the proposed procedure is exact and distribution-free. Moreover, the testing procedure can be applied to test for all the effects of a 2k unreplicated factorial and, more generally, of any design when there are no degrees of freedom left to estimate the error variance. As regards this last point, the testing procedure is applied also to a class of inequivalent Hadamard matrices of order n = 24 together with the Inequivalent Permutation Matrices procedure, which consists in exchanging inequivalent Hadamard matrices, rather than permuting rows of the design matrix, in order to obtain the permutation distribution of the test statistic. A comparison in power with Lenth's test and Loughin and Noble's test is provided in case of a 24 unreplicated factorial design.
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