Based on the foundation of hypothesis testing, in a Bayesian setting, the statistician has some basic prior knowledge which is being assumed: for example, that the average height is somewhere between 50cm and 250cm. 

Bayesian hypothesis testing, itself, would then involve measuring the height of specific American citizens, and with each measurement, distribution would become a bit more “bell-shaped” around the average height measured so far. As more data is collected, the “bell” becomes sharper and more concentrated around the measured average height.

Within the Bayesian approach, a statistical analysis of data relies heavily on probabilities directly related to current knowledge about an event. This means, for example, that in a Bayesian view, we can meaningfully talk about the probability that the true conversion rate lies in a given range, and that probability codifies our knowledge of the value based on prior information and/or available data. This varies greatly from a frequentist approach, wherein this number is unknown but fixed.

With a degree of certainty about any given statement on reality, a hypothesis would be chosen based on the highest posterior probability.

If you want to find out if your test results are statistically significant, try this free bayesian A/B testing calculator.

Please select from the menu above