Marginalium

How To Rig A Clinical Trial. This one’s a great example of the problems with p-values:

Here’s a dirty little science secret: If you measure a large number of things about a small number of people, you are almost guaranteed to get a “statistically significant” result. Our study included 18 different measurements—weight, cholesterol, sodium, blood protein levels, sleep quality, well-being, etc.—from 15 people. (One subject was dropped.) That study design is a recipe for false positives.

Think of the measurements as lottery tickets. Each one has a small chance of paying off in the form of a “significant” result that we can spin a story around and sell to the media. The more tickets you buy, the more likely you are to win. We didn’t know exactly what would pan out—the headline could have been that chocolate improves sleep or lowers blood pressure—but we knew our chances of getting at least one “statistically significant” result were pretty good.

Whenever you hear that phrase, it means that some result has a small p value. The letter p seems to have totemic power, but it’s just a way to gauge the signal-to-noise ratio in the data. The conventional cutoff for being “significant” is 0.05, which means that there is just a 5 percent chance that your result is a random fluctuation. The more lottery tickets, the better your chances of getting a false positive. So how many tickets do you need to buy?

With our 18 measurements, we had a 60% chance of getting some“significant“ result with p < 0.05. (The measurements weren’t independent, so it could be even higher.) The game was stacked in our favor. It’s called p-hacking—fiddling with your experimental design and data to push p under 0.05—and it’s a big problem. Most scientists are honest and do it unconsciously. They get negative results, convince themselves they goofed, and repeat the experiment until it “works.” Or they drop “outlier” data points.