A Non-Parametric Equivalent of Williams' Test for Contrasting Increasing Dose Levels of a Treatment

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Abstract
A Wilcoxon type non-parametric version of Williams'' test for comparing increasing doses of a substance with 0 dose control is proposed. A brief description of Williams'' test is given and the validity of extending this method to Kruskal rank sums in large sample data is proved. A numerical example is given. The toxicity of substances such as drugs, food additives, artificial foods and pesticides are usually assessed at some stage by animal experiments. Increasing doses of the substance are given to groups of animals; a group of control animals receiving a zero dose are also included in the experiment. The experimenter wishes to know if there is evidence of toxicity, and if so, at what dose levels. Williams (1971, 1972) designed a test for answering both these questions.

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