In a two-way analysis of variance, we are confronted with many cases in which it is not enough to test only if there are interaction effects or not. Those are the cases we must consider the alternatives with inequality restrictions to the interaction effects. In this paper, a simple method for constructing a score statistic is proposed, and the usefulness of the proposed statistic is shown by comparing the powers of the proposed score method, other score methods and usual F test against some typical alternatives. Further we indicate that we can construct the score which can be applied for the case of unbalanced replications, which has not been examined yet.
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