This program performs a specific one-sided test. The data must be entered into the 2X2 table in the correct way so that the test performed is the one of interest to the user.

Denote the cell probabilities for the four cells in the 2X2 table by

p1 p2 p3 p4The odds ratio is defined as

p1*p4 theta = -----. p2*p3The one-sided hypotheses tested by this program are

Ho: theta >= 1 vs Ha: theta < 1.These hypotheses can be expressed in different ways for the binomial and multinomial models.

p1 + p2 = 1 and p3 + p4 = 1.So the hypotheses can be expressed as

Ho: p1 >= p3 vs Ha: p1 < p3.The data must be entered in the first and second rows so these are the appropriate hypotheses.

p1 + p2 + p3 + p4 = 1.One way to express these hypotheses is in terms of conditional probabilities. Let p(

Ho: p(1) >= p(2) vs Ha: p(1) < p(2).Notice the similarity with the binomial hypotheses. Again, the data must be entered in the first and second rows so these are the appropriate hypotheses.

Created 05/02/05. Questions or comments to Roger L. Berger.