Hey guys, In the endless misery that is the prep for this thing, I was reading about type 1 and type 2 errors on wikipedia - it was easier for me to find it there than dig it out of the book - at any rate, they had a Mnemonic for Type 1 and 2 that I thought may be useful to some: “For those experiencing difficulty correctly identifying the two error types, the following mnemonic is based on the fact that (a) an “error” is false, and (b) the Initial letters of “Positive” and “Negative” are written with a different number of vertical lines: * A Type I error is a false POSITIVE; and P has a single vertical line. * A Type II error is a false NEGATIVE; and N has two vertical lines.” Again - Source Was Wikipedia - Not about to violate the ol ethics plagiarism stuff 
Just remember that Type I error is the serious type…you reject something that is true…nothing worse than doing that! If you reject something false, good for you. If you don’t reject something true, good for you as well. If you don’t reject something that is false, that’s bad, but it isn’t really serious…it was false, but you just didn’t care. So, type I is the worst error you can make, like when you reject the claim that it is sunny outside, when it is actually sunny outside. Or you reject someone’s innocence when they are really innocent…that’s just horrible. Having said that, I don’t think you will need to know type I and II in this exam!
Yeah I saw it for one sentence in the CFA quant section, and Passmaster did one sentence on it but I think they might just be refreshers. It’s not in the LOS and I have yet to see a question on it. They made sure to drill us in level I on that so I’m hoping it’s not an extra thing I need to put into my brain here.
This is Level 1 material.
I don’t agree, I think the above examples are actually the wrong way around - particularly the sun example. I do agree that it’s super confusing though! The reason I think it’s so confusing is that there are double and triple negatives involved. This is because the null hypothesis is a negative finding, and the types of error refer to the null hypothesis.
So going with the example of whether or not it is sunny weather, compared to the usual dreary grey skies, our null hypothesis is “the weather is not sunny”.
There’s two possibilities, only one of which is really true:
- The weather is not sunny (and the null hypothesis is true), or
- The weather IS sunny (and the null hypothesis is false)
If your test gets it right (i.e. no error)
- If the truth is that the weather IS sunny, then you’ve correctly rejected the null hypothesis: you say that it is not true that “the weather is not sunny” (there’s that confusing double negative) and you were right about it.
- If the truth is that the weather is not sunny, then you’ve correctly accepted the null hypothesis: you say that it is true that “the weather is not sunny” and you were right about it.
In both of those situations, your test got it right so you didn’t have an error. If you get it wrong, there are two ways you can have gotten it wrong, i.e. two types of error:
- Type I error is where you incorrectly reject a null hypothesis that was actually true. So the null hypothesis was actually right: it’s not sunny. But you’ve rejected it - you’re saying it is not true that “the weather is not sunny”. (Triple negative! bam!)
- Type II error is where you incorrectly accept a false null hypothesis. So the null hypothesis was actually wrong: it IS sunny. But you’ve accepted it - you’re saying it’s true that “the weather is not sunny”.
So to link it back:
Type I error is when you accept something is different when it’s truly not - you fail to reject something that is false, and this can be just as serious as a type II error if it is, for example, a study that finds (incorrectly) that a treatment works (incorrectly rejects the null hypothesis), and so justifies the use of this treatment even if its got toxicities/side effects. The risk here is that people use it, it does not help them, but it harms them.
Type 2 error is when you reject something is different when it truly is - you fail to reject the null hypothesis. So if the null hypothesis is that “Person A is not innocent” and truly they are, and you fail to reject (i.e. accept) the incorrect null hypothesis - you call them guilty.
But here’s the crazy thing: the error of calling someone guilty when they are really innocent could be either a type I or a type II error, depending on what you define your null hypothesis as:
- If your null hypothesis is “Person A is not guilty” and this null hypothesis is true, but you fail to accept it, then it’s a type I error.
- If your null hypothesis is “Person A is not innocent” and this null hypothesis is false, but you fail to reject it, then it’s a type II error.
(either way it is horrible, yes!)
So whether it’s a type I or type II error in that instance depends on whether you are defining your null hypothesis to be the absence of guilt or the absence of innocence. I guess in our system it should be the former so yeh - a type I error.
Similarly, you could define the other example with regard to null hypothesis being “there is no cloud” or “there is no sun”.
I hope this hasn’t made things more confusing!
I use a way to remember this correctly and is a little bit funny too. You wanna know what it is?
Always use the intuition -
Type 1 error - You are too bold.
Type 2 error - You are too timid.
Masticate on it.
That is an interesting way to remember it
I always remembered it as ; You really want to reject the null hypothesis, that is the goal essentially. A Type I being that you ‘rejected’ something (as you wanted), but unfortunately for you, you actually rejected something that was true. A Type II being further away from the goal, that you didn’t even reject anything (when you definitely should have, as the null hypothesis was indeed false).