The Use And Misuse Of P Values

John Mount and Nina Zumel explain what p-values are and how people routinely misuse them:

The many things I happen to have issues with in common mis-use of p-values include:

  1. p-hacking. This includes censored data bias, repeated measurement bias, and even outright fraud.

  2. “Statsmanship” (the deliberate use of statistical terminology for obscurity, not for clarity). For example: saying p instead of saying what you are testing such as “significance of a null hypothesis”.

  3. Logical fallacies. This is the (false) claim that p being low implies that the probability that your model is good is high. At best a low-p eliminates a null hypothesis (or even a family of them). But saying such disproof “proves something” is just saying “the butler did it” because you find the cook innocent (a simple case of a fallacy of an excluded middle).

  4. Confusion of population and individual statistics. This is the use of deviation of sample means (which typically decreases as sample size goes up) when deviation of individual differences (which typically does not decrease as sample size goes up) is what is appropriate . This is one of the biggest scams in data science and marketing science: showing that you are good at predicting aggregate (say, the mean number of traffic deaths in the next week in a large city) and claiming this means your model is good at predicting per-individual risk. Some of this comes from the usual statistical word games: saying “standard error” (instead of “standard error of the mean or population”) and “standard deviation” (“instead of standard deviation of individual cases”); with some luck somebody won’t remember which is which and be too afraid to ask.

Even if you know what p-values are, this is definitely worth reading, as it’s so easy to misuse p-values (even when I’m not on my Bayesian post hurling tomatoes at frequentists).

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