## 31.2 Hypotheses and notation: Comparing odds

For two-way tables of counts,
the *parameter* is the population odds ratio.
As usual,
the null hypothesis is the
‘no difference, no change, no relationship’
position.
So in this context:

- \(H_0\): The
*population*OR is one; or (equivalently):

The*population*odds are the same in each group.

This hypothesis proposes that
the *sample* odds are not the same
due to sampling variation.
This is the initial **assumption**.

The alternative hypothesis is

- \(H_1\): The
*population*OR is not one; or (equivalently):

The*population*odds are*not*the same in each group.

The alternative hypothesis is *always*
two-tailed for analysing two-way tables of counts.

**are always two-tailed**.

The hypotheses can also be written in terms of differences in percentages (or proportions), though the software output is usually expressed in terms of odds. The hypotheses can also be written in terms of associations:

- \(H_0\): In the
*population*, there is*no association*between the two variables - \(H_1\): In the
*population*, there is*an association*between the two variables

As usual,
following the decision-making process,
start by **assuming** that the null hypothesis is true:
that the *population* odds ratio is one.