According to a new paper, a full half of neuroscience papers that try to do a (very simple) statistical comparison are getting it wrong: Erroneous analyses of interactions in neuroscience: a problem of significance.
Here's the problem. Suppose you want to know whether a certain 'treatment' has an affect on a certain variable. The treatment could be a drug, an environmental change, a genetic variant, whatever. The target population could be animals, humans, brain cells, or anything else.
So you give the treatment to some targets and give a control treatment to others. You measure the outcome variable. You use a t-test of significance to see whether the effect is large enough that it wouldn't have happened by chance. You find that it was significant.
That's fine. Then you try a different treatment, and it doesn't cause a significant effect against the control. Does that mean the first treatment was more powerful than the second?
No. It just doesn't. The only way to find that out would be to compare the two treatments directly - and that would be very easy to do, because you have all the data to hand. If you just compare the two treatments to control you might end up with this scenario:
Both treatments are very similar but one (B) is slightly better so it's significantly different from control, while A isn't. But they're basically the same. It's probably just fluke that B did slightly better than A. If you compared A and B directly you'd find they were not significantly different.
An analogy: Passing a significance test is like winning a prize. You can only do it if you're much better than the average. But that doesn't mean you're much better than everyone who didn't win the prize, because some of them will have almost been good enough.
Usain Bolt is the fastest man in the world (when he's not false-starting himself out of races). Much faster than me. But he's not much faster than the second fastest man in the world.
Nieuwenhuis S, Forstmann BU, & Wagenmakers EJ (2011). Erroneous analyses of interactions in neuroscience: a problem of significance. Nature neuroscience, 14 (9), 1105-7 PMID: 21878926