You wish to test the hypothesis that blue stars are rich in helium. You take a sample of 10000 stars chosen at random and throw out all the non-blue ones, giving you 1000 blue stars. You take another sample of 10000 stars chosen at random in the same way as the first - they are the control group. You measure the helium abundances by observing the spectra of both groups of stars using identical procedures.

Congratulations, you have carried out a controlled experiment in astronomy.

Is there anything experimental in this? Randomization alone doesn't make an experiment, and
the study you describe seems exactly analogous to observational studies in the social sciences.

You wish to test the hypothesis that white Americans have received more formal education than
Americans in general. You take a random sample of Americans and calculate the mean level of
education of the whites. You take a second random sample and calculate overall mean
education of that second sample. You test for significant differences between your two means,
e.g., with a t-test.

Congratulations: you have an observational study. It's hardly an experiment: you've
manipulated nothing and controlled nothing. It may have descriptive validity -- it may let you
know that whites are better-educated -- but there's no manipulation here, and the study isn't
much use if you want to make causal claims about education levels.

You take another sample of 10000 stars chosen at random in the same way as the first -- they are the control group.

In what sense is this a control group? Nothing is manipulated in this study -- there is no
difference between your "control" and "treatment" samples, certainly none that you impose.
This doesn't even qualify as a "natural experiment."

--John