"Erroneous analyses of interactions in neuroscience: a problem of significance," a paper in Nature Neuroscience by Sander Nieuwenhuis and co, points out an important and fatal statistical error common to many peer-reviewed neurology papers (as well as papers in related disciplines). Of the papers surveyed, the error occurred in more than half the papers where it could occur. Ben Goldacre explains the error:
Let’s say you’re working on some nerve cells, measuring the frequency with which they fire. When you drop a chemical on them, they seem to fire more slowly. You’ve got some normal mice, and some mutant mice. You want to see if their cells are differently affected by the chemical. So you measure the firing rate before and after applying the chemical, first in the mutant mice, then in the normal mice.
When you drop the chemical on the mutant mice nerve cells, their firing rate drops, by 30%, say. With the number of mice you have (in your imaginary experiment) this difference is statistically significant, which means it is unlikely to be due to chance. That’s a useful finding which you can maybe publish. When you drop the chemical on the normal mice nerve cells, there is a bit of a drop in firing rate, but not as much – let’s say the drop is 15% – and this smaller drop doesn’t reach statistical significance.
But here is the catch. You can say that there is a statistically significant effect for your chemical reducing the firing rate in the mutant cells. And you can say there is no such statistically significant effect in the normal cells. But you cannot say that mutant cells and mormal cells respond to the chemical differently. To say that, you would have to do a third statistical test, specifically comparing the “difference in differences”, the difference between the chemical-induced change in firing rate for the normal cells against the chemical-induced change in the mutant cells.