H 0 :m¼ 10if the test is a one-sided test, we would have thepvalue shown in Figure 5.5a,
and if the test is a two-sided test, we have thepvalue shown in Figure 5.5b.
The curve in these graphs represents the sampling distribution ofxifH 0 is true.
Compared to the approach of choosing a level of significance and formulat-
ing a decision rule, the use of thep-value criterion would be as follows:
- Ifp<a,H 0 is rejected.
- ifpba,H 0 is not rejected.
However, the reporting ofpvalues as part of the results of an investigation
is more informative to readers than statements such as ‘‘the null hypothesis is
rejected at the 0.05 level of significance’’ or ‘‘the results were not significant at
the 0.05 level.’’ Reporting thepvalue associated with a test lets the reader
know how common or how rare is the computed value of the test statistic given
thatH 0 is true. In other words, thepvalue can be used as ameasureof the
compatibility between the data (reality) and a null hypothesis (theory); the
smaller thepvalue, the less compatible the theory and the reality. A compro-
mise between the two approaches would be to report both in statements such as
Figure 5.5 Graphical display of (a) a one-sided test and (b) a two-sided test.SUMMARIES AND CONCLUSIONS 199