Ordered Hypotheses for Multiple Treatments: A Significance Test for Linear Ranks

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Abstract
In many experiments the background evidence, theories, or conditions suggest an expected ordering among the treatment effects, yet in the analysis of variance such implicit hypotheses are typically neglected. A ranking statistic L is presented as test of a monotonic relationship among the treatment groups in the two-way analysis of variance. Used with accompanying table of L, it combines considerable power with computational ease, and assumes data of only ordinal strength. L is related to the test of the linear component of the treatment sum of squares in the parametric randomized-block design, to the product-moment correlation and regression, to the normal deviate test of Lyerly's average rho, and to Friedman's chi-square of ranks. Where either L or the Friedman test may be used, L is often more accurate and appropriate, and it has some advantages over other tests of trend and monotonicity.

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