From Marginal Revolution:
OK. Maybe some people need some explanation.
In statistics, when you test hypotheses, you can make two kinds of mistakes.
But those mistakes are based on your null hypothesis. What’s that? Students and practitioners are often very confused about this. They think the null hypothesis has to have some deep significance to the data they’re looking at. Not so (although it might be useful if it did). What is most important about the null hypothesis is that you can describe how the data is going to behave if it is true. You don’t need to know if the null is true or not to be able to do that, and in fact you may never know if it really is true.
In the images, the null hypothesis is that you’re not pregnant. We never know (before the test, and sometimes even after) whether that’s true or not. But if it were true, the data would behave in a certain way: mustaches might be observed, or maybe presenting a swollen abdomen would not be observed, and a host of other more important details that might show up in urine or blood.
A Type I error is what you get when a true null hypothesis is rejected in favor of the alternative. Again, you never know for sure, but it’s plausible that if you’re null is that someone isn’t pregnant, and they have mustaches, and you conclude that they’re pregnant, you’ve probably made a mistake.
A Type II error is what you get when a false null hypothesis is not rejected. Again, you never know for sure, but it’s plausible that if you’re null is that someone isn’t pregnant, and they present with a swollen abdomen, and you conclude that they’re not pregnant, you’ve probably made a mistake.