Introductory Biostatistics

‘‘the di¤erence is statistically significant (p< 0 :05).’’ In doing so, researchers
generally agree on the conventional terms listed in Table 5.2.
Finally, it should be noted that the di¤erence between means, for example,
although statistically significant, may be so small that it has little health conse-
quence. In other words, the result may bestatistically significantbut may not
bepractically significant.

Example 5.2 Suppose that the national smoking rate among men is 25% and
we want to study the smoking rate among men in the New England states. The
null hypothesis under investigation is

H 0 :p¼ 0 : 25

Ofn¼100 males sampled,x¼15 were found to be smokers. Does the pro-
portionpof smokers in New England statesdi¤erfrom that in the nation?
Sincen¼100 is large enough for the central limit theorem to apply, it
indicates that the sampling distribution of the sample proportionpis approxi-
mately normal with mean and variance underH 0 :

mp¼ 0 : 25

sp^2 ¼

ð 0 : 25 Þð 1 
 0 : 25 Þ

100

¼ð 0 : 043 Þ^2

The value ofpobserved from our sample is

15

100

¼ 0 : 15

representing a di¤erence of 0.10 from the hypothesized value of 0.25. Thep
value is defined as the probability of getting a value of the test statistic as
extreme as, or more extreme than, that observed if the null hypothesis is true.
This is represented graphically as shown in Figure 5.6.

TABLE 5.2

pValue Interpretation

p> 0 : 10 Result is not significant

0 : 05 <p< 0 : 10 Result is marginally significant

0 : 01 <p< 0 : 05 Result is significant

p< 0 : 01 Result is highly significant

200 INTRODUCTION TO STATISTICAL TESTS OF SIGNIFICANCE