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One way to think about it is that the p-value is trying to account for sampling and measurement error. Imagine you are a scientist and want to find out whether
by thinkmoore 11y ago
One way to think about it is that the p-value is trying to account for sampling and measurement error.
Imagine you are a scientist and want to find out whether the hypothesis that men are on average taller than women is true. If you could just exactly measure and take the average of the entire male and female populations you wouldn't need a hypothesis test.
Since you can't, you can do an experiment where you take a random sample of men and women. Now, you can do the average in the same way, but you need something to help figure out whether to trust the results. That's where the p-value comes in. The reason you need to be careful to select hypotheses in advance is because in order for statistics to help you account for error you need the noise in the data to be uncorrelated with the result you are trying to assess---which it won't be if you chose the result because it was the one that looked best after you account for the noise.