The choice of optimum scores in a Markov chain of order one

Summary The states of a Markov chain may be on an ordinal or a nominal scale. In this situation we need to assign appropriate scores to the states in order to study a given problem in detail. Using Fisher's criterion for assigning optimum scores to the marginals of anm×n contingency table, we shall obtain a system of optimum scores to assign to the states of a stationary Markov chain of order one.