Common Errors in Statistics (and How to Avoid Them), 4th Edition

INDUCTION

Behold! human beings living in an underground den, which has a mouth open towards the light and reaching all along the den; here they have been from their childhood, and have their legs and necks chained so that they cannot move, and can only see before them, being prevented by the chains from turning round their heads. Above and behind them a fire is blazing at a distance, and between the fire and the prisoners there is a raised way; and you will see, if you look, a low wall built along the way, like the screen which marionette players have in front of them, over which they show the puppets.

And they see only their own shadows, or the shadows of one another, which the fire throws on the opposite wall of the cave.

To them, I said, the truth would be literally nothing but the shadows of the images.

—The Allegory of the Cave (Plato, The Republic, Book VII)

Never assign probabilities to the true state of nature, but only to the validity of your own predictions.

A p-value does not tell us the probability that a hypothesis is true, nor does a significance level apply to any specific sample; the latter is a characteristic of our testing in the long run. Likewise, if all assumptions are satisfied, a confidence interval will in the long run contain the true value of the parameter a certain percentage of the time. But we cannot say with certainty in any specific case that the parameter does or does not belong to that interval, Neyman [1961, 1977].

In our research efforts, the ...