Content
There's an important property of χ2 tests that we haven't talked about yet: they are unreliable if any of the expected frequencies are 5 or smaller. In fact, as the frequencies get larger χ2 tests increase in reliability. This is because
so if the denominator E is small, then even a small deviation is magnified quite quickly.
If 5 seems like an arbitrary number, welcome to statistics 😂! The thing to understand is that all of the statistical tests we learn are approximations. 5 is the agreed upon cutoff simply because statisticians ran a bunch of computer simulations, and noticed that frequencies greater than 5 make χ2 reliable "enough".
In HL, you will encounter examples where expected frequencies are smaller than 5, in which case you must combine categories such that all frequencies are larger than 5. In exams, it will be fairly obvious which categories to combine, as long as you remember to combine!