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What a P Value Actually Means, and the Four Things People Think It Means Instead
A p value measures your data against a pretend world, the one where the effect you are hunting does not exist. The number describes data, given a hypothesis. Swap those two around and every misreading in this article follows. We define the thing properly, then take apart four beliefs the club has had to argue with at its own table: that p is the probability the hypothesis is wrong, that a smaller p means a bigger effect, that 0.049 and 0.051 are different animals, and that a non-significant result means nothing happened. Our own simulation of 200,000 experiments under a true null backs the definition, with the p values coming out flat to a Kolmogorov-Smirnov distance of 0.0014 from perfect uniformity. Another 400,000 simulate a whole literature. Now the headline. In a field where 10% of tested hypotheses are true and studies have 50% power, 47.4% of everything published as significant at is false, with no fraud, no p-hacking, no hidden analyses and no arithmetic errors anywhere. Two honest studies of one real effect disagree half the time, and one line of arithmetic gives you both numbers. No results section reads the same way afterwards.
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