FAQ: Hypothesis Testing with R - P-Values

This community-built FAQ covers the “P-Values” exercise from the lesson “Hypothesis Testing with R”.

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In the section used to describe Type I and II errors, I would recommend modifying the language to discuss whether there is a statistically significant difference rather than a meaningful correlation, since correlations are a separate statistical topic (which R can also be used to ascertain, but it is not related to hypothesis testing within this lesson). I think this will aid in understanding for those who have had less exposure to statistical concepts. There are also a few typos within the lesson (volleball in section 7, for instance).

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All four options for this exercise’s multiple-choice question are false.

The correct interpretation is NOT “There is a 20% chance that the difference in average weight of green and red apples is due to random sampling.”

The correct interpretation is “There would be a 20% chance of observing a difference at least as big as the observed difference anyway, even if all differences are only due to random sampling.”

It is impossible in traditional hypothesis testing to say anything about the posterior probability, given an observed difference, that the null is true. That’s only possible in Bayesian statistics (where it depends also on the prior probability; “extraordinary claims require extraordinary evidence” and all that). But we aren’t doing Bayesian statistics here.

In conditional probability terms, p-values tell you p(observation|null), not p(null|observation). These are completely different.