A one-sided test is indicated for research questions like these: Is a new drug
superiorto a standard drug? Does the air pollutionexceedsafe limits? Has
the death rate beenreducedfor those who quit smoking? A two-sided test is
indicated for research questions like these: Is there adi¤erencebetween the
cholesterol levels of men and women? Does the mean age of a target popula-
tiondi¤erfrom that of the general population?
Level of Significance The decision as to which values of the test statistic go
into the rejection region, or as to the location of the cut point, is made on the
basis of the desired level of type I errora(also called thesizeof the test). A
computed value of the test statistic that falls in the rejection region is said to be
statistical significant. Common choices fora, the level of significance, are 0.01,
0.05, and 0.10; the 0.05 or 5% level is especially popular.
Reproducibility Here we aim to clarify another misconception about hypoth-
esis tests. A very simple and common situation for hypothesis tests is that the
test statistic, for example the sample meanx, is normally distributed with dif-
ferent means under the null hypothesisH 0 and alternative hypothesisHA.A
one-sided test could be represented graphically as shown in Figure 5.4. It
should now be clear that a statistical conclusion is not guaranteed to be repro-
ducible. For example, if the alternative hypothesis is true and the mean of the
distribution of the test statistic (see Figure 5.4) is right at the cut point, the
probability would be 50% to obtain a test statistic inside the rejection region.
5.3.2 pValues
Instead of saying that an observed value of the test statistic is significant (i.e.,
falling into the rejection region for a given choice ofa) or is not significant,
many writers in the research literature prefer to report findings in terms ofp
values. Thepvalue is the probability of getting values of the test statistic as
extreme as, or more extreme than, that observed if the null hypothesis is true.
For the example above of
Figure 5.4 Graphical display of a one-sided test.198 INTRODUCTION TO STATISTICAL TESTS OF SIGNIFICANCE