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Nonparametric tests for lattice-ordered alternatives in unreplicated two-factor experiments. (English) Zbl 0939.62039

Summary: When conducting comparative experiments, researchers often can anticipate the relative direction that responses will take for some or all pairs of treatments. Tests that account for the anticipated direction can enjoy substantial power advantages over those that do not. Two tests are proposed for lattice-ordered alternatives. Asymptotic normality is established and small sample properties of the tests are investigated. Power comparisons are made between the proposed tests, and a comparison is made to a test that does not account for lattice ordering. Standardized versions of the statistics are suggested as useful descriptive measures of the degree of monotonicity of two-dimensional surfaces.

MSC:

62G10 Nonparametric hypothesis testing
62K15 Factorial statistical designs
62G20 Asymptotic properties of nonparametric inference
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