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On exact distributions of rank tests for ordered alternatives in block designs. (English) Zbl 0875.62182

Summary: Small sample critical values of distribution-free rank tests for two types of ordered alternative hypotheses, namely, the simple order and the simple tree alternatives, useful in testing treatments versus a control, are generated. For large designs, the Monte Carlo simulation technique is used to generate nearly exact distributions to complement the exact tables. Simulation provides a better approximation of the exact critical values than the limiting \(\bar \chi ^{2}\)-distribution. A graphical comparison as well as the \(\chi ^{2}\)-goodness of fit test comparing the exact and simulated distributions for a particular design indicate that the simulated distribution is almost identical to the exact distribution while requiring only a fraction of the computation time of the latter.

MSC:

62G10 Nonparametric hypothesis testing
62E15 Exact distribution theory in statistics
62K10 Statistical block designs

Software:

AS 149
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Full Text: DOI

References:

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