I seem to have some gaps in understanding t-tests/significance testing. I tried searching but am missing the search terms to fill my knowledge gaps.
My knowledge so far:
- unpaired t-test: take a bunch of people, split them by a characteristic (male/female) and see if they differ
- paired t-test: take a bunch of people and have a before, effect, after. E.g. IQ Test on 50 people, cut their fingers off and repeat IQ Test. Are they now smarter or dumber?
My confusion: Humans are weird, there is a lot of subconscious stuff. This is why we introduce control groups. But neither the unpaired nor the paired test fill this gap. How do I test significance when I want a paired t-test with a control and experimental group?
In more sciency words: I (probably) want to do a paired test (before and after) for the experimental group and subtract the changes also induced on the control group. How do I achieve that?
To add better formulated question: What type of significance tests do drug trials? Where they have pre+post measures and a control+experimental group