As I was teaching class the other day, I told the students I was going to reveal to them the one secret they needed to learn to understand every statistical test they would ever use. The secret was the one thing that would make statistics more of a reasonable science than a bunch of equations to memorize, the one thing they needed to pass my class. (OK, there is a lot more needed to pass the class, but without this one thing doing so is a lot harder.)

When I was an undergrad taking my probability and statistics course, I was definitely in “memorize equations” mode. I didn’t really understand why sometimes we divided by the square root of n and sometimes we didn’t for the z- or t-score. I got an A in that class, but I really didn’t “get” it.

It wasn’t until years later, as I took a series of classes in experimental design, that I finally understood that the answer to life, the universe, and everything statistical was the random sampling distribution. (What did you think it was going to be?)

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