field, we will cover this part in more general terms and include examples in
fields other than cancers.
Recall that in testing a null hypothesis, two types of errors are possible. We
might rejectH 0 when in factH 0 is true, thus committing a type I error. How-
ever, this type of error can be controlled in the decision-making process; con-
ventionally, the probability of making this mistake is set ata¼ 0 :05 or 0.01. A
type II error occurs when we fail to rejectH 0 even though it is false. In the
drug-testing example above, a type II error leads to our inability to recognize
the e¤ectiveness of the new drug being studied. The probability of committing
a type II error is denoted byb, and 1bis called thepowerof a statistical test.
Since the power is the probability that we will be able to support our research
claim (i.e., the alternative hypothesis) when it is right, studies should be
designed to have high power. This is achieved through the planning of sample
size. The method for sample size determination is not unique; it depends on the
endpoint and its measurement scale.
12.9.1 Comparison of Two Means
In many studies, the endpoint is on a continuous scale. For example, a
researcher is studying a drug that is to be used to reduce the cholesterol level in
adult males aged 30 and over. Subjects are to be randomized into two groups,
one receiving the new drug (group 1), and one a look-alike placebo (group 2).
The response variable considered is the change in cholesterol level before and
after the intervention. The null hypothesis to be tested is
H 0 :m 1 ¼m 2vs.
HA:m 2 >m 1 or m 20 m 1Data would be analyzed using, for example, the two-samplettest of Chapter 7.
However, before any data are collected, the crucial question is: How large a
total sample should be used to conduct the study?
In the comparison of two population means,m 1 versusm 2 , the required min-
imum total sample size is calculated from
N¼ 4 ðz 1 aþz 1 bÞ^2
s^2
d^2assuming that we conduct a balanced study with each group consisting of
n¼N=2 subjects. This required total sample size is a¤ected by four factors:
- The sizeaof the test. As mentioned previously, this is set arbitrarily by
the investigator; conventionally,a¼ 0 :05 is often used. The quantityz 1 a
462 STUDY DESIGNS