Randomization

If you’re not a stats maven, this may sound esoteric, but let’s see if I can express it well.

One of the things that’s hard to learn in orthodox statistics is the whole machinery of statistical tests. You can train yourself (or a monkey) to do it right, but it seems to be a morass of weird rules and formulas. Remember to divide by (n–1) when you compute the standard deviation. You have to have an expected count of at least five in every cell to use chi-squared. You can use z instead of t if df > 30. And then there’s remembering what tests to use in which situation. You wind up with a big flowchart in your head about whether the data are paired, whether the variables are categorical, etc., etc., etc. And as a learner, you lose sight of the big picture: what a test is really saying.

George Cobb wrote a terrific article explaining why this is all unnecessary. The short version goes like this: you can unify a lot of inferential statistics if, instead of the tests we now use (z, t, chi-squared, ANOVA…) we used randomization tests.

Here’s the basic idea, to which we will often refer as the “Aunt Belinda” problem. Your Aunt Belinda claims to have supernatural powers. She says she can make tossed nickels come up heads. You don’t believe her, so you get a dollar’s worth of nickels (20 of them); she speaks an incantation over them; you toss them all at once; and sixteen come up heads.

Does she have supernatural powers?

Continue reading Randomization

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Motivation

I’m inspired to write this by a small group of what seem to be like-minded but more experienced math teachers around the blogosphere (whom I will reference as soon as I learn how). They are scary smart, young, and energetic, and can probably actually type. They sure as hell can write. And you seriously want your kid in their math class.

If they’re so great, why should I blog? Although I can dream that my unique contributions may help others, the real reason is to help me record what I’m thinking, what I try, and what happens in the classroom.  I’m in such a good situation, it seems to demand some sort of record.

Put another way: What happens when you have no excuses? I’ll try to live up to the trust implied by all the resources I get from the school community, and I’ll try to make something good out of a situation most teachers would give various limbs for.

I’m also hoping that by putting some of my plans out there—such as using standards-based grading, OMG, I can’t believe I actually put that in print—I’ll feel some obligation to follow through.