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.