4WL2 Type 1 and Type 2 errors

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Hi
I’m always appreciated for you guys to make so helpful courses

I have a question

in the “Defining Hypotheses” video,


rejecting H0 means accepting H1
but not rejecting H0 doesn’t mean accepting H1
becuase it’s just like having not enough evidence to reject H0

but in the “Type 1 and Type 2 errors” video
image
in this table, it says “Don’t reject H0 (decide not spam)”

and I think if “deciding not spam”, then it must be a ham
in this case (don’t reject H0) → (accept H0)

because one email being a spam or ham is mutually exclusive and collectively exhaustive

so I’m confused with that “don’t reject H0” doesn’t mean accepting H0

Hello @GIYEON_LEE,

I believe we need to distinguish between whether it is a formal discussion or not.

In a formal, statistical discussion, like in text books, they often only say “reject” or “not reject” the null hypothesis. They don’t use “accept”. Not rejecting H_0 only means, as you said, we are yet to reject it, not accepting it.

However, in an informal discussion, I think we may use whatever terms we like, be it “accept” (your first slide) or “decide” (your second slide) or “reject” (as the opposite to accept). I think all below are just informal wordings:

image
image
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Below, to me, is how one may interpret (informally) a hypothesis testing result to a non-technical person.
image

Whereas “Don’t reject H_0” is the formal, statistical result, “Decide not spam” is the informal interpretation that is used for decision-making purpose. Interpretation can be, in some sense, less rigorous, therefore, we cannot go from it back to the formal, statistical language of “accepting H_0”, not to mention that there may not be any “accept” in the formal discussion at all.

Cheers,
Raymond

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Btw, @lucas.coutinho, I think the “spam” there should have been “ham”? The sentence will make more sense that way, and also because H_0 is “Email is Ham” / “Email is not Spam”.

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Thanks for the explanation :slight_smile:

In hypothesis testing, there are only “reject” or “not reject”

But we can informally interprete spam or ham for decision making

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