Abstract
We review some results obtained in an earlier paper on the relation between some standard multidimensional test statistics and their corresponding one-dimensional versions in a sequential setup. One conclusion is that, in general, no one-dimensional (marginal) null hypothesis can be rejected even though the multidimensional null hypothesis is. An alternative method based on a multiple maximum modulus test is proposed with a somewhat better conclusion. The results are extended to the case of general linear contrasts, in particular to pairwise comparisons.
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