10.3, independent-samples vs one-sample

[michaeladamkatz]

I'm confused about the difference between the one-sample t test example of section 10.2.1 and the independent-samples t test example of section 10.3. You say

A much more common situation arises when you’ve got two different groups of observations. In psychology, this tends to correspond to two different groups of participants, where each group corresponds to a different condition in your study

So the example in 10.3 is dividing the students by who their tutor is, and seeing if it makes a difference in their grades. But 10.2.1 was parallel because it divided the students by whether they are taking a psychology course (vs. students who are not taking a psychology course). So there are two conditions also. Or maybe the distinction is that 10.2.1 is comparing the psychology students to the full set of students in Harpo's class (including the psychology students), whereas in 10.2.1 we are comparing two disjoint groups. Is that's the case, I think it's a subtle point and should be called out. Because when I just think of "two different conditions" it feels to me like 10.3 is also testing two different conditions (being in a psychology class vs (probably) not).

[michaeladamkatz]

Now that I get to the summary of chapter 10 I see the helpful summary statements:

A one sample t-test is used to compare a single sample mean against a hypothesised value for the population mean.

An independent samples t-test is used to compare the means of two groups, and tests the null hypothesis that they have the same mean.

That first statement, in particular, would have been extremely helpful at the introduction section 10.2.1.

But I think it would still be worth pointing out that in a certain sense there are always two "things" being compared, just in one case one of those things is the population as a whole.