Canards, Part I: You can’t prove a negative!

I love being a scientist; I’m very evangelical about it. I want to answer questions, explain things! I want to spread the gospel and love of science all around! (This is my only proselytizing; I’m Jewish.) I love when my artist friends ask me how cell division really works, or whether cell phones make your brain wonky.

The only question I really, really loathe* is “But you can’t prove a negative, can you?”

Yes; yes, you can.

I’ve seen this lead to many misunderstandings: that evolution is a'theory', that you can’t show mercury doesn't cause autism, that leukemia could too be from power lines. (A side note: Scientists never, never say we have ‘proven’ anything; we demonstrate, support, hypothesize, conclude, deduce. Only God has absolute proofs of anything, as far as I’m concerned, because you have to be omniscient to know there exist no counterexamples.)

So say you want to know if Phenomenon X is not caused by Thing Y. You need a large sample size, in case the incidence is low; a long enough observation time, in case the frequency is low; a sample as randomized as possible; a population with regular exposure to the variable; a reasonable assumption that things you know cause Phenomenon X have been minimized; and good controls. If you have all of these things, you can demonstrate to a low probability, say less than 0.1%, that there is no correlation. In plain English: with all these things, you can reasonably conclude that 0.1% of cases, at most, are caused by Thing Y. In the scientific world, that’s the same as It’s Not Happening: if you can’t observe it, it’s not happening.**

Controls are perhaps the most important thing in any experiment. If you don’t choose a good control, you can’t show what you think you’re showing. Controls have to tell you that the experiment worked, that you can observe a negative, that you can observe a positive, that Weird Stuff isn’t happening, that the numbers you get in Condition Y are different from in Conditions A-F. Here’s a great example: On this FDA sheet (pdf) for example, 5% of patients report fatigue, but so do 9% of placebo-receiving patients. Why? Because fatigue is a common effect of depression. So you have no idea if the drug 1) prevents fatigue 2) causes fatigue or 3) alleviates the disease, which removes some fatigue from some people. The right control is healthy volunteers, or people who didn’t experience fatigue from the disease and people who did. In this case, nobody really cares, so they didn’t do it. But the bottom line, is you can’t tell.

Finally, there was this famous study, in Sweden or Denmark or Finland, on cellphones and brain cancer.*** It had a graph: the rate of brain cancer and cellphone ownership went up at about the same rate. QED! But so did fast food consumption, and, say, mp3 player ownership. Do french fries cause brain cancer? Almost certainly not.

They didn’t do their controls. It’s a cardinal sin: that of sloth, indifference, and bad science.

*Okay, I don’t like “But why would anybody do basic science? Shouldn’t you just look for new drugs?” much either, but that’s a topic for another day.
**This is entirely separate from, say, faith. I happen to firmly believe in God, myself. But miracles and blessings are not subject to scientific proof.
***Which now I can’t find. If anyone sees it, please send it along; I loved it. Much better evidence summarized here.