A Multiple Comparison Sign Test: Treatments Versus Control

Let (Xoj, X1j, …, Xkj) be the result of a single trial, where the subscripts o is associated with a control and the subscripts 1, …, k with treatments. To test the joint hypothesis P(Xij – Xoj > 0)=l/2 = P(Xij – Xoj < 0), all i, compute the test criterion (r1, …, rk) where ri is the number of times Xij, – Xoj is negative in n trials. A method for computing the distribution of (r1, …, rk) is illustrated. Exact probability distributions of min ri are given for k = 2, n = 4(1)10 and k = 3, n = 4(1)7. It is conjectured that 2(min r – n/2)/ is distributed approximately as Dunnett's t. Tables based on this conjecture are computed and values are seen to agree well with comparable values from the exact distribution.