# odds ratio

Suppose the probability of an event $A$ is not 1. The *odds* of the event $A$ is the ratio

$$\mathrm{odds}(A):=\frac{P(A)}{P({A}^{c})}=\frac{P(A)}{1-P(A)}.$$ |

For example, if the odds of landing a head in a coin flip is 2, then the probability of landing a head is twice as likely as that of landing a tail.

In a $2\times 2$ contingency table^{}, with a dichotomous explanatory variable $X$ having levels 1 and 2, and a binary response variable $Y$ with success and failure as two possible levels of outcomes:

Title | odds ratio |
---|---|

Canonical name | OddsRatio |

Date of creation | 2013-03-22 14:41:07 |

Last modified on | 2013-03-22 14:41:07 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 10 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 62H20 |

Classification | msc 62H17 |

Defines | odds |

Defines | log-odds ratio |

\@unrecurse |