## What is the Bayes Factor?

The Bayes factor is an alternative hypothesis testing technique that evaluates the conditional probability between two competing hypotheses. The goal is to quantify support levels for each hypothesis, which can be updated as new information becomes available, instead of generating definitive accept or reject hypothesis decisions.

### How does the Bayes Factor Work?

This approach uses the Bayes theorem equation to compare two models and generate a K value.

The K-value is just the likelihood ratio between both models, with a higher factor supporting the alternative hypothesis H1 (second hypothesis in denominator) and negative values supporting the null hypothesis H0 (first hypothesis in the numerator).

While deciding exactly what factor is needed to accept a hypothesis varies from problem to problem, in general the following chart is used as a guideline to interpret these degrees of beliefs.

Bayes factor K | Label |

> 100 | Extreme evidence for H1 |

30 – 100 | Very strong evidence for H1 |

10 – 30 | Strong evidence for H1 |

3 – 10 | Moderate evidence for H1 |

1 – 3 | Anecdotal evidence for H1 |

1 | No evidence |

1/3 – 1 | Anecdotal evidence for H0 |

1/3 – 1/10 | Moderate evidence for H0 |

1/10 – 1/30 | Strong evidence for H0 |

1/30 – 1/100 | Very strong evidence for H0 |

< 1/100 | Extreme evidence for H0 |