What is a p-value Anyway?

What Is A P-value Anyway?

The definition of a p-value is the probability of observing your statistic (or one more extreme in favor of the alternative) if the null hypothesis is true .

In this video, you learned exactly how to calculate this value. The more extreme in favor of the alternative portion of this statement determines the shading associated with your p-value.

Therefore, you have the following cases:

If your parameter is greater than some value in the alternative hypothesis, your shading would look like this to obtain your p-value:

If your parameter is less than some value in the alternative hypothesis, your shading would look like this to obtain your p-value:

If your parameter is not equal to some value in the alternative hypothesis, your shading would look like this to obtain your p-value:

You could integrate the sampling distribution to obtain the area for each of these p-values. Alternatively, you will be simulating to obtain these proportions in the next concepts.