Tables for Testing the Equality of Two Proportions when Prior Information on their Common Value May be Available

In testing the equality of two proportions, one may define a rejection point T? such that if the test statistic T (in this paper, the ordinary Pearsonian chi-squared) exceeds T? then the hypothesis may safely be rejected, whatever the common value p of the two proportions may be; and similarly define an acceptance point A? such that if T ≦ T? then one may safely accept. These points may be refined if prior information is available, for example that p must lie in the central interval (c, 1 – c) or one of the extremal intervals (v, w) and (1 – w, 1 – v). Smallsample tables are provided both for the unrestricted case and for situations where one has such prior information.