In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.
Not everything in mathematics works out the way we’d prefer it to. For example, in statistics, a Type I error, whose probability is denoted by , is rejecting the null hypothesis even though the null hypothesis is true. Conversely, a Type II error, whose probability is denoted by , is retaining the null hypothesis even though the null hypothesis is false.
Ideally, we’d like and , so there’s no chance of making a mistake. I’ll tell my students:
There are actually two places in the country where this can happen. One’s in California, and the other is in Florida. And that place is called Fantasyland.