On exact Type I and Type II errors of Cochran's test

In this article, we obtain exact Type I and Type II error probabilities for Cochran's test comparing K different treatments using independent blocks with dichotomous responses. A finite Markov chain imbedding technique is used to construct a non-homogeneous Markov chain, and then the exact Type I and Type II error probabilities are cast in terms of the transition probabilities of the imbedded Markov chain. An example from Lehmann [1974. Nonparametrics: Statistical Methods Based on Ranks. Holden-Day Inc., San Francisco, p. 268] is given to illustrate our theorem.