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.