Eli5: What is a null hypothesis and how do type 1 and type 2 errors work.
In: Mathematics
A null hypothesis is “this thing isn’t the case.” Then you do tests and analyze the results with statistical methodologies (student t-test, z-tsst, etc) and determine whether to reject that null hypothesis in favor of “turns out this thing actually is the case.”
Now one of four things can happen. Either it wasn’t the case and you didn’t reject the null, which means you’re right, or it is the case and you did reject the null, which also means you’re right, or it wasn’t the case but you did reject the null, which is type I error (thought you proved a thing that actually wasn’t true), or it was the case but you failed the reject the null, which us type II error (thought the thing wasn’t true but it turns out it was).
So for an example imagine a roulette table. Someone says “every time there’s three reds, the next number is black.” So the null hypothesis would be “there is no relationship between one roll and the next.” So you watch the wheel for a few hours and keep track of the results. One of four things happens:
1. You observe a number of times that three reds come up and then the next number isn’t black, or you never observe three reds come up, and you say “well, I still believe there is no relationship.” You’re correct.
2. You observe a number of times that three reds come up.and the next number after that is black. You conclude “well I’ll be; it’s true!” You have rejected a null hypothesis, but that null hypothesis was true. Type 1 error.
3. You never observe three reds come up in a row and say “well, I still believe there’s no relationship.” But it turns out this is a crooked wheel and it really does work that way, you just didn’t know it. Type 2 error.
4. You see it happen a number of times and conclude that what the person said is true and you reject the null hypothesis. It turns out it is a crooked wheel specifically rigged to give a black every time there’s three reds. You’re correct.
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