Rationality by Steven Pinker

Author:Steven Pinker [Pinker, Steven]
Language: eng
Format: epub, mobi
Publisher: Penguin Publishing Group
Published: 2021-09-28T00:00:00+00:00

But where should the critical value be placed? The scientist must trade off two kinds of error. She could reject the null hypothesis when it is true, namely a false alarm, or in the argot of statistical decision theory, a Type I error. Or she could fail to reject the null hypothesis when it is false—a miss, or in the patois, a Type II error. Both are bad: a Type I error introduces falsehood into the scientific record; a Type II error represents a waste of effort and money. It happens when the methodology was not designed with sufficient “power” (the hit rate, or 1 minus the Type II error rate) to detect the effect.

Now, deep in the mists of time it was decided—it’s not completely clear by whom—that a Type I error (proclaiming an effect when there is none) is especially damaging to the scientific enterprise, which can tolerate only a certain number of them: 5 percent of the studies in which the null hypothesis is true, to be exact. And so the convention arose that scientists should adopt a critical level that ensures that the probability of rejecting the null hypothesis when it is true is less than 5 percent: the coveted “p < .05.” (Though one might have thought that the costs of a Type II error should also be factored in, as it is in Signal Detection Theory, for some equally obscure historical reason it never was.)

That’s what “statistical significance” means: it’s a way to keep the proportion of false claims of discoveries beneath an arbitrary cap. So if you have obtained a statistically significant result at p < .05, that means you can conclude the following, right?

The probability that the null hypothesis is true is less than .05.

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