Fundamentally, hypothesis testing is based on conditional probability.

We base our thinking on these premises:

1. Null Hypothesis H_{0} --> no effect

2. Alternative Hypothesis H_{1 }--> There is an effect

If we assume H_{0 }is true and the P-Value of 5% is. There is a chance of 5% that we would have gotten the test results given the Null Hypothesis is true. Since this is a very low probability, we are rejecting the Null Hypothesis. So usually, a high p-Value indicates that my test results are significant.

HOWEVER,

What does a p-value of p=.2 indicate? It means given the Null Hypothesis is true there is a 20% that we would have gotten these effects.

However, this is the problem: We fail to reject the Null Hypothesis --> 20%, but we can also not accept it. We have absence for evidence for an effect but we don't have evidence for the absence of an effect.

In other words, the p-value does not tell us anything about how likely it is that a hypothesis is true.

SOLUTION:

Bayesian Hypothesis Testing

deals with: Which of the hypotheses is better supported by the data?

Answer: The model that predicted the data best !

The ratio of predictive performance is known as the Bayes Factor (over 10 is usually good)