P-Value of a Statistical Test
The P-Value of a statistical test refers to the probability (under the null hypothesis) of getting a value for the test statistic as extreme or more extreme than that observed.
- The P-Value of a test provides a measure of the strength of evidence against the null hypothesis: the smaller the P-Value, the stronger the evidence against the null hypothesis.
- In practice, we often test statistical hypotheses by comparing the
P-Value with the pre-specified alpha-level
for the test. Printout from software packages usually give the
corresponding P-Values when they report the values of relevant test
statistics. Since a test statistic is in the
critical region when the corresponding
P-Value is less than the alpha-level, an equivalent rule we can apply
when testing statistical hypotheses is:
Reject H0 if the P-Value is less than the alpha-level.
- To detemine the P-Value of a test, you need to know what values of the test statistic constitute "as or more extreme than that observed". This basically depends on the nature of the critical region. For a left-tail test, these values refer to those of the test statistic which are less than or equal to that observed. So, in this case, we compute the P-Value by finding the maximum value of P(T <= t0 ) under H0 where t0 is the (observed) value obtained from sample information for the test statistic T. The problem reduces to one in which you find P(T <= t0 ) using the same distribution for T as that used to determine the critical region of the test (e.g., use the same t distribution as the one for the corresponding t-test etc.).
Examples:
- See Examples 9 and 10 in Johnson and Bhattacharyya (1996), p. 335-338.
