Re: p-value


Reef Fish wrote:
espyrian wrote:
Ethan.Johnsons@xxxxxxxxx wrote:

espyrian wrote:
Ethan.Johnsons@xxxxxxxxx wrote:

The mean was measured in 12 patients 24 hours after they received a
newly proposed antibiotic was 1.2 mg/dL.
If the mean = 1.0 and sd = 0.4 mg/dL in the general population, with CI
0.05, I need to test if the mean level of patients is different from
that of the general population.

So, I came up with:

Ho = the mean level is the same as that of the general population
H1 = the mean level is different from that of the general population

The test statistic is:

(1.2-1.0)/(0.4/sqrt(12)) = 1.732051

The critical value is:
qt(p=0.05, df=11) = -1.795885

Because the t = 1.732051 > -1.795885,

So, we can accept Ho at the 5% level.

My question is how do you calculate the p-value?
I came up with
p = 2* pt(q=1.732051, df=11) = 1.888827
but, I know it is off far.

thx

ej

You're close. Using tables, you'll see that your t-stat of 1.732 lies
between p=0.10 and p=0.05 on the 11 d.f. row. That is not enough to
reject your H0 in any event, but your H1 is two tailed (i.e. < or >),
so you must double the p-value, putting it between p=0.20 and p=0.10.
So you are correct that you retain H0 at the alpha=0.05 level.

Using software, such as Excel, will give you a more precise figure:
TDIST(1.732,11,2)=0.111

HTH

Thank you for reply.
I am still confused.
If the test statistic is negative, (i.e. -1.52) and n =7
then, it would be TDIST(-1.52,6,2)?
Excel gives no value with TDIST(-1.52,6,2).....

It seems that p-value is:

pt(q=-1.52, df=6)
[1] 0.089661

thx

ej

P(T<-1.52) is equivalent to P(T>1.52). So ignore the minus sign.

This comment is fine with respect to a TWO-tailed Alternative.


The p-value of a one-sided test=TDIST(1.52,6,1)=0.0897.

This point has a LENGTH history of discussion in sci.stat.math.
What you said is incorrect, relative to the DEFINITION of a p-value:

p-value = Pr( Test Statistic T is "more extreme" than the observed T*)

where "more extreme" is defined by the Alternative Hypothesis!

Thus, if the Alternative Hypothesis is Ha: mu < given value,

and the observed T = -1.52, then the p-value is P(T < -1.52) =.089661

and if the Alternative is Ha: mu > given value, then
the p-value is P( T > -1.52) = .91034

Similarly for an observed T of 1.52.

The fact that one seldom sees a p-value greater than 0.5 is one of
the evils of statistical computing software. Most of them give
p-values
correponding to a TWO-tailed test, in which case the removal of the
sign of the observed T makes no difference.

But for ONE-tailed tests, the INEQUALITY in Ho is of paramount
importance.

These points can be found in Google by doing a search on
Definition of "p-value"

returned 14 threads, totally over 300 posts. :-) Not all 300 posts
are strictly on p-value definition, but merely contained the
keywords. In particular, one of the 14 threads was

"Now a RoadMap (was Re: m00es on NOISE; and m00es's
NOISE; and a DATA QUIZ!!!) "

which contained 75 posts, nearly all NOISE by m00es. :-)

Below is a pure post of statistical substance of relevance:

http://groups.google.com/group/sci.stat.math/msg/0677873d9b959a86?hl=en&;

which gave many numerical examples as well as the summary:

RF> the key element of a P value is that you CANNOT determine
RF> a P value unless you know the Alternative Hypothesis,
RF> whether it is one-tailed or two-tailed, and if one-tailed, WHICH
tail.

-- Reef Fish Bob.

I am a little confused as usual :-)

To dobule-check,

If we assume that the sample sd is 0.6 and the sd of the general
population is unknown:

then, the test statistic is:

(1.2-1.0)/(0.6/sqrt(12))
[1] 1.154701

We need to use t-test because "If the population sd is not known but is
estimated by the sample standard deviation then a t-test should be
used."

then, the p-value is pt(q=1.155, df=11) = 0.863718 ????

thx

ej

.

Relevant Pages

  • Re: Two nit-picks re definition of p-value (Was: goodness of fit ?)
    ... The Alternative Hypothesis is Ha: ... the definition of p-value for that problem would be ... -- Reef Fish Bob. ...
    (sci.stat.math)
  • Re: p-value
    ... I think you had already seen three posts by Kevin that should ... KT> What is your alternative hypothesis? ... KT> This is what Reef Fish means by needing to know the alternative ... KT> hypothesis to compute a p-value. ...
    (sci.stat.math)
  • Re: p-value
    ... Ho = the mean level is the same as that of the general population ... My question is how do you calculate the p-value? ... where "more extreme" is defined by the Alternative Hypothesis! ... Below is a pure post of statistical substance of relevance: ...
    (sci.stat.math)
  • Re: p-value
    ... I think you had already seen three posts by Kevin that should ... KT> What is your alternative hypothesis? ... KT> This is what Reef Fish means by needing to know the alternative ... KT> hypothesis to compute a p-value. ...
    (sci.stat.math)
  • Re: Two nit-picks re definition of p-value (Was: goodness of fit ?)
    ... RFB> is the last place anyone wants to learn Statistics! ... We are talking about p-value definition. ... alternative hypothesis: true probability of success is not equal to ...
    (sci.stat.math)
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