Pretty sure most mad scientists are in applied science, which are usually just going to research for health effects and potency.

So you'd have a control group which had dyed water with no goat elixir, a group which had water with 10% of the goat elixir,a group with 20% of the goat elixir etc... And then you see over ten years which group develops cancer or other health problems, and try to extrapolate from there.

And then you find out that the water you used for testing was actually undyed goat elixir and that all your results are shit.

"Mad? Mad?! I'm not mad! Maybe a little angry, but not MAD!"

So they're just mad engineers.

"Gimmie a minute, I need to run this through SPSS to check that these differences are statistically significant."

Not all scientists run experiments or run the kind of experiments that require a control group. Descriptive studies are a thing and there are other methods to establish causality.

Mad scientist uses a control group when testing their death ray. Said control group has a flashlight shine on them instead. However, because it's a double-blind experiment, the entire control group gets so worked up thinking that they're going to die that they all suffer fatal heart attacks. The mad scientist concludes that their death ray does nothing and scraps the project.

Could be a fun twist for a tabletop RPG. The party ends up trapped in a lab while hunting the scientist. Their arrival was not as unexpected as they'd been hoping and they're being watched to ensure compliance. If they don't player-character a way out, they'll have to participate in the experiment.

Start with a hidden roll for which group you're in and then additional rolls with a table for effects. If thematically appropriate, control group members who roll just right (or wrong, depending on perspective) might get a real effect from the water. A door pops open and guards arrive to escort the party to their observation cells.