I have some large amount of people take test A. Based on the scores on test A, I assign them either to group A1 or to group A2. A1 are the people with scores at least 50% on test A, and A2 has people with scores less than 50% on test A.
It turns out that half the people are put into group A1 and half the people are put into group A2.
Then, I have people take test B, and do the same thing, grouping into B1 for the high scorers, and B2 for the low-scorers.
Now, the data is analyzed, and what is reported is that "people in group A1 were more likely to be in group B1."
Does this imply that if you're a person who was not in the original study (but you come from the same population as people in the original study), and you take test A and find out you're in group A1, that you're more likely to be in B1 (after taking test B)?
(I'm making the assumption that the findings for the people in the test generalize to the population.)
The curiosity is whether a probability about a group can always be extrapolated to individuals within that group.
EDIT: For context, I'm looking at studies regarding implicit bias. The studies have the aggregate data as to how people who exhibit a strong implicit bias perform on particular tests (such as the first-person-shooter task). I'm curious if this means that if someone takes the first test and has a high bias, if this means that they're more likely to perform on the second task in the way that people similar to them in the first task did.
In short, if someone has an implicit bias, are they more likely to act in particular ways? Or is the effect only at a group level, and I can't tell anything about an individual based on the result from the implicit bias test.