odds.ratio

or

The generalized odds ratio is a measure of the handedness of a cyclic competition graph.

Usage

odds.ratio(x)

Details

The generalized odds ratio is the product of the odds ratios of the edges in a cyclic competition graph.

In the two-by-two case, the maximum likelihood estimatore of the odds ratio is just $\frac{a_{11}a_{22}}{a_{12}a_{21}}$. The generalization to larger boards with exactly one degree of freedom is immediate: it is just the product of the entries on the diagonal, divided by the product of the off-diagonal elements.

Ranking permissable tables in order of increasing odds ratio thus orders the sample space and allows one to perform one-sided tests.

See Also

pval.1dof

Aliases

• odds.ratio

Examples

data(gear)
odds.ratio(gear)

aylmer.test(gear)
aylmer.test(gear,alternative="less")
aylmer.test(gear,alternative="greater")