I have always found the justice system example the best way to explain Type I and Type II errors in hypothesis testing.
- If the defendant is innocent but yet the court states he is guilty, this is a Type I error. And the REAL guilty person is still on the streets.
- If the defendant is guilty but yet the court states not guilty this is a Type II error.And the guilty person is still walking the streets.
Certainly, we want to put less innocent people in jail, but sadly this means more guilty people go free to ensure we do not make these errors.
Another thing to think about when I say be careful and never ACCEPT the null hypothesis. Do you ever hear them say in court the person is innocent? No! They say NOT GUILTY, basically this means they do not have enough evidence to convict. That is the same in hypothesis testing. Maybe you just got a bad batch for your test and if you retried the next batch you might reject the null.