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statisticsp-valuehypothesis-test
Sanket Kedia
Sanket Kedia

Reputation: 1

Type-II error in Hypothesis Testing

I am new to Statistics and was reading about Decision errors in Hypothesis Testing. My question is that why is Type-II error an error at all? From what I understand, it arises when we fail to reject a false null hypothesis. When we fail to reject null hypothesis, it simply means that we do not have strong evidence to reject it. We are not making any comment about which of the two hypothesis is true (or false) . Either can be true. We are not saying that the null hypothesis is true. Then, why is such a conclusion called an error?

Upvotes: -1

Views: 434

Answers (2)

sparkstars
sparkstars

Reputation: 87

Type-II error error occurs when we fail to reject the null hypothesis (which should have been rejected).

It is P(Accept H0 | H0 is False)

Upvotes: 0

Sam
Sam

Reputation: 101

Statistics jargon is often times overly complicated. What the type 2 error tells you, really boils down to how "strong" the method is, that you are using. Ultimately, the reason why you perform hypothesis testing (especially outside of the statistical syllogism world that you are citing) is because you are trying to get results.

So let's say you have a test that assesses the null-hypothesis that an animal is a fish. If your test just simply fails to reject on every try, no matter what you are giving it, you are never making a type 1 error, since you never falsely reject the null - brilliant, right? No, obviously not, your test is completely useless, because your type 2 error is 1 (since 100% of the time, you don't reject the null, when it's false).

So to specifically answer your question why it is called an error:

While the statement, that you are making, after not rejecting a null that is false, might be careful enough that you aren't saying something that's wrong, the test DID fail to pick up that the null is false, which you could call an error

Upvotes: 0

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