A Bayes factor is the ratio of the likelihood of one particular hypothesis to the likelihood of another. It can be interpreted as a measure of the **strength of evidence in favor of one theory among two competing theories. **

That’s because the Bayes factor gives us a way to evaluate the data in favor of a null hypothesis, and to use external information to do so. It tells us what the weight of the evidence is in favor of a given hypothesis.

## Unpacking the Bayes Factor

When we are comparing two hypotheses, H_{1} (the alternate hypothesis) and H_{0} (the null hypothesis), the Bayes Factor is often written as B_{10}. It can be defined mathematically as

The Schwarz criterion is one of the easiest ways to calculate rough approximation of the Bayes Factor.

## Interpreting Bayes Factors

A Bayes Factor can be any positive number. One of the most common interpretations is this one—first proposed by Harold Jeffereys (1961) and slightly modified by Lee and Wagenmakers in 2013:

If B_{10} is… |
then you have… |
---|---|

> 100 | Extreme evidence for H_{1} |

30 – 100 | Very strong evidence for H_{1} |

10 – 30 | Strong evidence for H_{1} |

3 – 10 | Moderate evidence for H_{1} |

1 – 3 | Anecdotal evidence for H_{1} |

1 | No evidence |

1/3 – 1 | Anecdotal evidence for H_{1} |

1/3 – 1/10 | Moderate evidence for H_{1} |

1/10 – 1/30 | Strong evidence for H_{1} |

1/30 – 1/100 | Very strong evidence for H_{1} |

< 1/100 | Extreme evidence for H_{1} |

## References

Kass & Raftery, Bayes Factors. Journal of the American Statistical Association

Vol. 90, No. 430 (Jun., 1995), pp. 773-795

Retrieved from http://www.jstor.org/stable/2291091 on March 31, 2018

Lavine & Schervish. Bayes Factors: What They Are and What They Are Not. The American Statistician, Vol. 53, No. 2 (May, 1999), pp. 119-122. Retrieved from http://www.jstor.org/stable/2685729 on March 31, 2018.

Beard, Dienes, Muirhead, & West. Using Bayes factors for testing hypotheses about intervention effectiveness in addictions research. Addiction. 2016 Dec; 111(12): 2230–2247. Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5111611/ on March 31, 2018

Morey, Richard. What is a Bayes Factor? Bayes Factor, February 2014. Retrieved from http://bayesfactor.blogspot.com/2014/02/the-bayesfactor-package-this-blog-is.html on March 31, 2018

FelixS, What does a B-factor feel like?. R-Blog, January 29, 2015. Retrieved from https://www.r-bloggers.com/what-does-a-bayes-factor-feel-like/ on March 31, 2018

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