# odds.ratio

From aylmer v1.0-1

##### or

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

- Keywords
- array

##### Usage

`odds.ratio(x)`

##### Arguments

- x
- matrix with one degree of freedom, coerced to a board

##### 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

##### Examples

```
data(gear)
odds.ratio(gear)
aylmer.test(gear)
aylmer.test(gear,alternative="less")
aylmer.test(gear,alternative="greater")
```

*Documentation reproduced from package aylmer, version 1.0-1, License: GPL-2*

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