The p-value is the probability of the occurrence of a value for the test statistic as extreme as or more extreme than the actual observed value, under the assumption that the null hypothesis is true.

*p***-VALUES**

The *p*-value
is the probability of the occurrence of a value for the test statistic as
extreme as or more extreme than the actual observed value, under the
assumption that the null hypothesis is true. By more extreme we mean a value in
a direction farther from the center of the sampling distribution (under the
null hypothesis) than what was observed.

For a one-tailed (right-tailed) *t* test, this statement means the
probability that a statistic *T* with a
Student’s *t* distribution satisfies *T* > |*t*|, where *t* is the
observed val-ue of the test statistic. For a one-tailed (left-hand tail) *t* test, this statement means the
probability that a statistic *T* with a
Student’s *t* distribution satisfies *T* < –|*t*|, where *t* is the
observed value of the test statistic. For a two-tailed *t* test, it means the probability that a statistic *T* with a Student’s *t* distribution satisfies |*T*|
> |*t*| (i.e., *T* > |*t*| or *T* < –|*t*|) where *t* is the
observed value of the test statistic.

Now let us now compute the two-sided *p*-value for the test statistic in the
pig blood loss example from Section 9.4. Recall that the standard deviation s =
717.12, the sample mean =
1085.9, the hypothesized value μ_{0} = 2200, and the sample size *n *=
10. From this information, we see that the*
t *statistic is* t *= (1085.9 –* *2200)/(717.12/√10) = –1114.1/226.773 = –4.913.

To find the two-sided *p*-value we must compute the probability that *T* > 4.913 and add the probability that *T* < –4.913. This combination is equal to 2*P*(*T* > 4.913). The
probability *P*(*T* > 4.913) is the one-sided right-tail *p*-value; it is also equal to the one-sided left-tail *p*-value, *P*(*T* < –4.913). The
table of Student’s *t* distribution
shows us that with 9 degrees of freedom, *P*(*T* < 4.781) = 0.9995. So *P*(*T*
> 4.781) = 0.0005.

Since *P*(*T* > 4.913) < *P*(*T* > 4.781), we see
that the one-sided *p*-value *P*(*T*
> 4.913) < 0.0005; hence, the two-sided *p*-value is less than 0.001. This observation is more informative
than just saying that the test is significant at the 5% level. The re-sult is
so significant that even for a two-sided test, we would reject the null
hypoth-esis at the 0.1% level.

Most standard statistical packages (e.g., SAS)
present *p*-values when providing
information on hypothesis test results, and major journal articles usually report
*p*-values for their statistical tests.
SAS provides *p*-values as small as
0.0001, and any-thing smaller is reported simply as 0.0001. So when you see a *p*-value of 0.0001 in SAS output, you
should interpret it to mean that the *p*-value
for the test is actually less than or equal to 0.0001 (sometimes it can be
considerably smaller).

Related Topics

Contact Us,
Privacy Policy,
Terms and Compliant,
DMCA Policy and Compliant

TH 2019 - 2023 pharmacy180.com; Developed by Therithal info.