# RE: st: RE: joint significant

 From "Nick Cox" <[email protected]> To <[email protected]> Subject RE: st: RE: joint significant Date Wed, 17 Jan 2007 17:03:54 -0000

```Thanks for the gracious reply. But I reiterate
my warning against casting significance test reports
in confidence terminology.

Nick
[email protected]

White, Justin

> I am sorry for the misinformation.  After I read Nick's response, it
> jogged my memory from Intro to Econometrics.  It's been a
> while.  Sorry.
>
> What I should have said is this:
> Let's say you have a p-value of 0.0890 from an F-test.  This tells us
> that we can expect coefficients as extreme as observed in 8.9
> out of 100
> random samples given the null hypothesis is true.  We can use this
> information to either reject or fail to reject the null based on
> personal confidence criterion.  In this case we can reject
> the null at a
> 91.1% confidence interval.

Nick Cox

> Note that this is wrong. The P-value is emphatically not
> the probability that the null hypothesis is true.
> The P-value is the probability of getting results as or
> more extreme than those observed _if_ the null hypothesis
> is true and if the associated assumptions are correct.
>
> In any case, the picture here that there is a spike of probability
> corresponding to a zero test statistic does not match basic
> facts about the sampling distribution, which in this kind of
> problem is continuous.

White, Justin

> > Here is how to interpret a p-value.  Let's say you have a p-value of
> > 0.0890 from an F-test.  This tells us that given the data
> > sample, we can
> > expect the estimated coefficients to be jointly equal to zero in 8.9
> > times out of 100.  This is known as Type-1 error.

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