Environmental Health Criteria 214

HUMAN EXPOSURE ASSESSMENT
* Observed variables are on a continuous scale.
* Measurement scale is at least ordinal.
* Population 1 ( X 1 ) has approximately the same distribution as
X 2 .
If we assume that the data follows a normal distribution and that
the data are independent, with the first group distributed N(µ,
rho2 1 ) and the second group distributed N(µ, rho2 2 ) so that the
variances are possibly different, a test can be constructed to see if
the difference (Delta) between the means for the groups is equal to a
hypothesized value (Delta0 ), typically set to zero. This scenario
would result in a two-sample t-test, and the test statistic is
presented in Eq. 4.13 in Table 13, where t is compared with a
t-distribution with df = min( n 1 -1, n 2 -1) degrees of freedom,
and s i 2 is computed as described in section 4.2.1. The possible
alternatives are that Delta > Delta 0 , Delta < Delta 0 , or the
general alternative that Delta not equal Delta 0 . If we are looking
for differences, we reject the null hypothesis that the groups are the
same for the respective alternative if t > T df,alpha, t < -
T df,alpha, or | t| > T df, alpha/2 , where alpha is the prespecified type I
error for the decision to be made.
Referring once again to the blood lead example presented earlier,
the following null hypothesis may be tested: mean blood lead
concentrations in the Maltese sample population are equal to those in
the Mexican sample population. The corresponding alternative
hypothesis is: mean blood lead concentrations are not equal in the two
sample populations. As indicated in Fig. 13, the point estimates of
the respective sample means are different. Completion of the
two-sample t-test will allow for determination of whether the
difference is statistically significant with 1-alpha% confidence.
Using Eq. 4.13, the t-statistic is computed to be 3.30. Setting
alpha = 0.05, the critical t-value is 1.96. Thus, the Maltese and
Mexican sample mean blood concentrations are significantly different
at the 0.05 level.
4.4.4 Statistical models
Statistical models make explicit the potential sources of
variability to be measured. The response, exposure, is dependent upon
a combination of measured factors and background variation from
unmeasured influences. For example, in examining pesticide exposures,
one might consider methods and amounts of applications, climate
conditions and duration of potential exposure. Unmeasured factors
might include exact knowledge of individual behaviours and locations,
which may cause different levels of exposure between two individuals
who are equal with respect to other exposure characteristics. One must
consider as many of the potential relationships between the responses
as possible, as well as how the possible factors will affect each
other, before finalizing a study design.
Since no simple model will perfectly describe all relationships,
the goal is to construct a parsimonious model that describes the major
factors of the process resulting in exposure. For example, in studying
the exposure of children to lead, the presence of lead in paint, in
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