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in order to remember stuff i need to understand their reason. Right now i cannot remember what is type 1 error and what is type 2 error why is the reason type 1 is false positive? i don't just want to remember without understanding thanks.

Jas
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  • I agree that descriptive names like "false positive" and "false negative" would be preferable. There is no inherent order between the types of errors and it is hardly helpful if a) the author better lookup to make sure he doesn't mix things up, then b) the reader looks thing up to ensure he understands right and c) mst be afraid that the author might have nixed things up by forgetting to look up the definitions. – Hagen von Eitzen Jun 29 '14 at 11:31
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    It's the way it is because if it were the other way someone would be asking why it's that way. – Gerry Myerson Jun 29 '14 at 11:41

2 Answers2

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Keeping in mind that we're discussing Neyman-Pearson type hypothesis testing, if we're going to number them (and I am not saying there's necessarily a strong reason to do that), there's a logical reason to give one of the two error types primacy:

The Type I error rate is the one you choose (when you set your significance level).

The Type II error rate is then a consequence of that choice (along with some other things like effect size and sample size).

This distinction (that the first kind of error is the one whose rate you choose while the second rate follows) seems to have been pretty much there right from the start. They (Neyman and Pearson) certainly defined the first and second types, and the NP testing framework has always had that 'choose the first rate the second follows' structure. There's perhaps at least a hint of that idea of primacy for type I in the quotes here.

Glen_b
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In an experiment we want to be 95% sure that our conclusion (the alternative hypothesis) is true. That leaves 5% chance that we are plain wrong. This type of error is pretty straight forward and therefore considered the first type of error that can occur (false positive). The probability is also straight forward. It is simply the 5% that we defined ourself anyway ($\alpha$).

The second type of error is more convoluted. It is the chance we are not sure enough to draw our conclusion (the alternative hypothesis), even though it is true anyway.

The second type of error is not really a false negative, since we can never draw the conclusion that the alternative hypothesis is false (i.e. negative). We can only say we do not have sufficient proof that the alternative hypothesis is true. Usually it cannot be determined either, or at least not without making precarious assumptions. As I said, it is a bit more convoluted.

Klaas van Aarsen
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