Reply To: Questions regarding DPF.

[Brian H]

Breakable wrote: This is what article said:

A “Type I” error in Statistics (Stats Math) means the conclusion is incorrect for the data and the hypothesis must be rejected.

This is what Wikipedia said:

The hypothesis can be inappropriately rejected, this is called type I error…

Just stating the obvious, but it seems to me that “hypothesis can be inappropriately rejected” and “hypothesis must be rejected” are absolutely different things.

Wikipedia’s wording is simply a bit fuzzy. It means that, “When a (null) hypothesis is inappropriately rejected, this is called a Type I error,” or “The inappropriate rejection of a (null) hypothesis is a sort of error called a Type I error.”

It does not mean that it is optional to reject the null hypothesis. It means a mistake was made in doing so. Note that the null hypothesis asserts that the ‘positive’ hypothesis is false.

Not that Wikipedia is any sort of authority, in any case!

Here’s the Statistics Glossary:

Type I Error

In a hypothesis test, a type I error occurs when the null hypothesis is rejected when it is in fact true; that is, H0 is wrongly rejected.

For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average, than the current drug; i.e.
H0: there is no difference between the two drugs on average.

A type I error would occur if we concluded that the two drugs produced different effects when in fact there was no difference between them.

The following table gives a summary of possible results of any hypothesis test:
Decision
Reject H0 Don’t reject H0

H0 Type I Error Right decision
Truth
H1 Right decision Type II Error

A type I error is often considered to be more serious, and therefore more important to avoid, than a type II error. The hypothesis test procedure is therefore adjusted so that there is a guaranteed ‘low’ probability of rejecting the null hypothesis wrongly; this probability is never 0. This probability of a type I error can be precisely computed as
P(type I error) = significance level =alpha

Warning: thinking too much about the null hypothesis may cause brain pain! :coolmad: :-S