Environmental Health Criteria 214

HUMAN EXPOSURE ASSESSMENT
between two unequally weighted hypotheses; the first is the null
hypothesis, H 0 , which is the safe hypothesis, and the second is H 1 ,
the alternative or sceptical hypothesis, which requires sufficiently
large evidence to believe in. The specifications of the test, based
upon sceptical scientific belief or common usage, are the type I error
and the type II error (defined in section 4.4.3). Introductory
information on sample size determination is presented here; the reader
is referred to Lemeshow et al. (1990) for details.
To determine the minimum sample size required to observe the
desired outcome, one needs to determine the smallest effect that is
scientifically worth detecting (i.e., based on measurement limit or
scientific principles), and use that to collect a sample with enough
information to detect such a difference. The effect is the minimum
significant difference in exposure between two groups. The smaller the
effect, the more information is required to distinguish it. This
effect is related to the type I error of a hypothesis test. There are
two components, the type II error and the sample size, which are
unspecified. When the type II error is specified, the resulting sample
size can be determined. Once the sample size is determined, the power
(1-type II error) of a study can be computed. The smaller the
difference to be detected, the larger the sample size needed for fixed
type I and type II error probabilities.
The following describes the formula for a two-group comparison.
To compare the means of two groups with equal sample size, let Delta
represent a scientifically significant difference that we would like
to detect, if it exists. Suppose that the first group can be modelled
by Y 1 = µ 1 +epsilon 1 , where µ 1 is the mean and epsilon 1 ~
N(0,rho 2 ) is the error term, and the second group can be modelled
by Y 2 =µ 2 + epsilon 2 with the error term epsilon 2 ~ N(0,
rho 2 ). The only difference between the two groups is the mean
response. The groups will be considered statistically different only
if |µ 2 -µ 1 | > Delta. The minimum number of observations in each
group is given by Eq. 4.14 in Table 14 where z gamma is defined as
the value satisfying P(Z > z) = gamma, where Z follows the
distribution of a standard normal random variable, alpha is the type I
error, and ß is the type II error. This formula can also be used to
approximate the sample size needed for a difference of proportions
(e.g., for dose-response models comparing two groups), by letting
Delta represent the difference in proportions (instead of a difference
in means).
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