After factoring out the effect of other variables known to affect SAT, such as socioeconomic status, researchers found that music students had a higher SAT score than non-music students. This is an example of

Observational study

Explanation:

Observational studies are the studies whereby researchers look at the impact of a certain risk factor, or diagnostic test and in this research, the researcher doesn't control the independent variable.

Since the effect of other variables known to affect SAT, such as socioeconomic status, has been factored out, this is an observational study.