Most of the hypothesis testing we have seen so far comes under the category of what is known as the null hypothesis significance testing (NHST). In this framework, we have two competing hypotheses:
- The Null Hypothesis, H0, where there is no impact of an intervention
- Alternate Hypothesis, HA, where there is an impact of the intervention.
Hypothesis testing aims to collect data (evidence) and assess the fit for one of the above models. At the end of NHST, you either ‘reject’ or ‘fail to reject’ your Null hypothesis – at a specified significance value – using the well-known p-value.
p-value ~ P(Data|H0)
On the contrary, we can define a ratio that gives equal weightage for the null and the alternative hypotheses. That is the Bayes Factor. It compares the probability of the data under one hypothesis with the probability under the other.
Bayes Factor01 = P(Data|H0) / P(Data|H1)
If BF01 > 1, the data is likely supporting H0
If BF01 < 1, the data is likely supporting H1
