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Avi Adler points to this post by Felix Schönbrodt on “What’s the probability that a significant p-value indicates a true effect?” I’m sympathetic to the goal of better understanding what’s in a p-value (see for example my paper with John Carlin on type M and type S errors) but I really don’t like the framing in terms of true and false effects, false positives and false negatives, etc. I work in social and environmental science. And in these fields it almost never makes sense to me to think about zero effects. Real-world effects vary, they can be difficult to measure, and statistical theory can be useful in quantifying available information—that I agree with. But I don’t get anything out of statements such as “Prob(effect is real | p-value is significant).”
This is not a particular dispute with Schönbrodt’s work; rather, it’s a more general problem I have with setting up the statistical inference problem in that way. I have a similar problem with “false discovery rate,” in that I don’t see inferences (“discoveries”) as being true or false. Just for example, does the notorious “power pose” paper represent a false discovery? In a way, sure, in that the researchers were way overstating their statistical evidence. But I think the true effect on power pose has to be highly variable, and I don’t see the benefit of trying to categorize it as true or false.
Another way to put it is that I prefer to thing of statistics via a “measurement” paradigm rather than a “discovery” paradigm. Discoveries and anomalies do happen—that’s what model checking and exploratory data analysis are all about—but I don’t really get anything out of the whole true/false thing. Hence my preference for looking at type M and type S errors, which avoid having to worry about whether some effect is zero.
That all said, I know that many people like the true/false framework so you can feel free to follow the above link and see what Schönbrodt is doing.
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