One-Sided Tests

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   p4
```
The odds ratio is defined as
```           p1*p4
theta = -----.
p2*p3
```
The 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.

Binomial Model: In the binomial model, the observations in each row are from a binomial population. In this model,
`   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.

Multinomial Model: In the multinomial model, each observation is classified according to the row variable and the column variable. In this model,
`   p1 + p2 + p3 + p4 = 1.`
One way to express these hypotheses is in terms of conditional probabilities. Let p(i) be the probability of being in the first column, given that the observation is in the ith row. Then the hypotheses can be expressed as
```   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.