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See also: level of significance, hypothesis testing |
For statistical tests there is one value which specifies the strength
of its evidence:
p-value | The p-value defines the probability that a test statistic equal to or greater than the one obtained in the test, will be observed for the given population if the null hypothesis is true. |
A low p-value for a statistical test should lead to the rejection of
the null hypothesis. Thus, it is important to know the null and the alternative
hypotheses. P-values provide a sense of the strength of the evidence against
the null hypothesis.
An example should clarify the point:
Suppose you have to decide whether there are any differences in the
wear and tear of truck tires between two different brands. The null hypothesis
will be that the wear does not differ, the alternative hypothesis is that
they do differ. Assuming that the data (18 samples each) is normally distributed
and the means (2.03 and 2.69 mm) and standard deviations (1.30, and 1.11,
respectively) are known, we can calculate the test statistic t=1.762. Using
the t-distribution, we can find the corresponding p-value of 0.086. This
means that in 86 out of 1000 cases, the test statistic will exceed the
value of 1.762, although the null hypothesis is true.
Last Update: 2004-Jul-03