The H0 is the null hypothesis and H1 is the alternative hypothesis.
Sometimes the notation can be different. It can be H0 is the null and
Ha is the alternative. I always thought the H0 and Ha notation was more
intuitive than the H0 and H1.
In this case, the null hypothesis (H0) is B2=B3=B4=0.
The alternative hypothesis (H1) is the estimated coefficients (Bi) are
not jointly equal to zero.
Therefore, if you reject the null, you automatically accept the
alternative which means the estimated coefficients are jointly
significantly different from zero.
If the fail to reject the null, then you are effectively accepting the
null to be true and the estimated coefficients are jointly
insignificantly different from zero.
The joint test is different from the variable-specific test (T-test).
Just because the F-test tells us that the variables are jointly
different from zero does not imply that all of the estimated
coefficients are different from zero independently. You use a T-test to
determine the significance of an individual variable and use the F-test
for joint tests.
I hope this helps.
Justin White
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Joanne
Marshall
Sent: Tuesday, January 16, 2007 1:14 PM
To: [email protected]
Subject: RE: st: RE: joint significant
Dear Justin,
Thank you for making such a clear statment on the test and my result. I
now
understand much more than I did, and that was a much better explanation
than
my textbook gives!
Regarding the null hypothesis, is that equivalent to H1? I always
confused
my H0 and H1.
h0=null= estimated coefficients are jointly insignificantly different
from
zero. (b2=b3=b4=0)
ho= estimated coefficients are not jointly insignificantly different
from
zero. (b2 not equal to b3... not equal to b4/0
or is it the other way round?
Thank you for your time and patience. I am finally getting this!
Cheers Jo
>From: "White, Justin" <[email protected]>
>Reply-To: [email protected]
>To: <[email protected]>
>Subject: RE: st: RE: joint significant
>Date: Tue, 16 Jan 2007 12:51:40 -0500
>
>The 91% confidence level comes from the p-value given in the Wald test.
>
>
>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. If you are using a
>confidence criterion of 95%, you are only willing to make a Type-1
error
>in 5 out of 100 times. Therefore, a confidence level of 91.1% falls
>outside of your confidence criteria and you would fail to reject the
>null. This means the estimated coefficients are jointly
insignificantly
>different from zero.
>
>If you are using a 95% confidence level, then you want a p-value that
is
>less than or equal to 0.05. The smaller the p-value, the less likely
>you are to make a Type-1 error. You get the confidence level by
>subtracting the p-value from one (1-0.0890 = 0.0911 = 91.1%)
>
>This would be the statement(s) you would make.....
>Based on a confidence level of 95%, I would fail to reject the null
>hypothesis that the estimated coefficients are jointly equal to zero.
>
>Or
>
>Based on a confidence level of 90%, I would reject the null hypothesis
>that the estimated coefficients are jointly equal to zero.
>
>Or
>
>I reject the null hypothesis that the estimated coefficients are
jointly
>equal to zero at a confidence level of 91.1%.
>
>Hope this helps.
>
>
>Justin White
>
>
>-----Original Message-----
>From: [email protected]
>[mailto:[email protected]] On Behalf Of Joanne
>Marshall
>Sent: Tuesday, January 16, 2007 12:31 PM
>To: [email protected]
>Subject: RE: st: RE: joint significant
>
>Thank you, Justin.
>
>"Assuming you have a 95% confidence level criterion, you will fail to
>reject the null hypothesis that the estimated coefficients are jointly
>equal to zero with a confidence level of 91%."
>
>How can you tell we reject the null though hypothesis and where is the
>91%
>from?
> > F( 1, 538) = 2.1
> > Prob > F = 0.0890
>
>the p value is 0.0890, which is bigger than 0.05 therefore we reject
the
>
>null.
>i am using 0.05 as the p value because it is 95% confidnece level
>criterion.
>is this correct?
>thank you.
>
>Cheers Jo
>
> >From: "White, Justin" <[email protected]>
> >Reply-To: [email protected]
> >To: <[email protected]>
> >Subject: st: RE: joint significant
> >Date: Tue, 16 Jan 2007 12:23:19 -0500
> >
> >The Wald Test is a joint significance test. It depends on how you
set
> >up the test if you want to determine if a specific coefficient has
the
> >appropriate sign. The results you included tell us:
> >
> >Assuming you have a 95% confidence level criterion, you will fail to
> >reject the null hypothesis that the estimated coefficients are
jointly
> >equal to zero with a confidence level of 91%.
> >
> >There is no need to use an F-table. The p-value given in the test
>tells
> >you the level of confidence. As one of my professors told me
> >"statistical tables are for luddites".
> >
> >
> >Hope this helps.
> >
> >
> >Justin White
> >
> >-----Original Message-----
> >From: [email protected]
> >[mailto:[email protected]] On Behalf Of Joanne
> >Marshall
> >Sent: Tuesday, January 16, 2007 12:15 PM
> >To: [email protected]
> >Subject: st: joint significant
> >
> >Dear Stata fellow,
> >
> >If the result which I have worked out is for a joint sign test (Wald
> >test)
> >
> > F( 1, 538) = 2.1
> > Prob > F = 0.0890
> >
> >how can I tell if this is jointly significant or not? do I look at
> >0.0790 or
> >3.10 as F observ to compare with my F crit. Also from the stat.
table,
> >do I
> >look for F crit under (1,538) at my desirable level on significance
or
> >others?
> >
> >Cheers
> >Jo
> >
> >_________________________________________________________________
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