Inadequacy of p-value as a measure of support for a statistical hypothesis provided by dadta has been pointed out by many authors. Likelihood ratio asa such a measure, proposed by Richard Royall (2000), has an intuitive appeal and the advantage of being very simple. In this paper, however, we first state some properties that we want such a measure to have and propose an optimality criterion. Then it is shown that although a continuous optimal measure dose not exist, thete exists a continuous measure that has many desirable properties and is nearly optimal.

Inadequacy of p-value as a measure of support for a statistical hypothesis provided by dadta has been pointed out by many authors. Likelihood ratio asa such a measure, proposed by Richard Royall (2000), has an intuitive appeal and the advantage of being very simple. In this paper, however, we first state some properties that we want such a measure to have and propose an optimality criterion. Then it is shown that although a continuous optimal measure dose not exist, thete exists a continuous measure that has many desirable properties and is nearly optimal.

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