Why does a test return the p value?
I am looking at the Diebold-Mariano-Test (DM Test): https://github.com/johntwk/Diebold-Mariano-Test
Basically, this test gives me a DM statistics, and also the p value. So, do I just the p-value to judge a null hypthoesis?
For instance, if p-val > alpha = 0.05, then I reject the null hypothesis, is this correct?
Actually, it's not correct.
In general, the null hypothesis is rejected if the p-value comes out small.
That's because the p-value is small when an observed data point $P$ (a result of a test, for example) is (far) in the tail of the null-hypothesis-based distribution.
In other words, the probability of observing such or more extreme a data point according to the null-hypothesis is very small. Hence, having NO reasons to believe that we've observed more or less a null-typical point, we reject the null.
