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# Applied statistics, theoretical statistics and mathematical statistics

Hang on, did we do our homework to make sure that we actually collected enough evidence to give ourselves a fair shot at changing our minds? That’s what the concept of power measures. It’s really easy not to find any mind-changing evidence… just don’t go looking for it. The more power you have, the more opportunity you’ve given yourself to change your mind if that’s the right thing to do. Power is the probability of correctly leaving your default action.

When we learn nothing and keep doing what we’re doing, we can feel better about our process if it happened with lots of power. At least we did our homework. If we had barely any power at all, we pretty much knew we weren’t going to change our minds. May as well not bother analyzing data.

Use power analysis to check that you budgeted for enough data before you begin.

Power analysis is a way to check how much power you expect for a given amount of data. You use it to plan your studies before you begin. (It’s pretty easy too; in a future post I’ll show you that all it takes is a few for loops.)

Uncertainty means you can come to the wrong conclusion, even if you have the best math in the world.

What is statistics not? Magical magic that makes certainty out of uncertainty. There’s no magic that can do that; you can still make mistakes. Speaking of mistakes, here’s two mistakes you can make in Frequentist statistics. (Bayesians don’t make mistakes. Kidding! Well, sort of. Stay tuned for my Bayesian post.)

Type I error is foolishly leaving your default action. Hey, you said you were comfortable with that default action and now thanks to all your math you left it. Ouch! Type II error is foolishly not leaving your default action. (We statisticians are so creative at naming stuff. Guess which mistake is worse. Type I? Yup. So creative.)