Environmental Health Criteria 214

HUMAN EXPOSURE ASSESSMENT
The second form of interval estimate, the statistical (1-alpha)%
confidence interval, gives a range of estimates, for a parameter,
which is generated in a manner such that it contains the true
parameter value (1-alpha)% of the time. For a normally distributed
random variable, a one-sided confidence interval for the estimate of
the mean is derived from the standard error and Z 1-alpha , while
Z 1-alpha/2 is used for a two-sided confidence interval. The standard
error (rho×) is an expression of uncertainty about the mean and is
calculated as the standard deviation divided by the square root of the
number of observations (n) (Table 9). Continuing with the example
from the Maltese study, the standard error of the blood lead sample
data is 11.8 µg/litre (Table 8). For alpha = 0.05, the two-sided 95%
confidence interval about the estimated mean is computed as 243
µg/litre ± 23.1 µg/litre, where the latter is equal to Z 1-(alpha/2) ×
rho× or 1.96 × 11.8 (Table 11). Details of this procedure and
related considerations may be found in most introductory statistics
textbooks, for example Kleinbaum et al. (1988).
4.4.2 Measurement error and reliability
The term measurement error refers to the accuracy and precision
of a given sample collection and analysis methodology. Accuracy
describes the degree to which a measurement is free of bias. Bias is
systematic deviation in a measurement from the true value of the
process being measured. Precision refers to the reproducibility of a
particular measurement system. Measurement reliability is a closely
related concept in that a measurement with a high degree of accuracy
and precision can be considered to be more reliable than one with a
low degree of accuracy and precision. Additional information on
measurement error and reliability is contained in Chapter 11, where
the topic is discussed in the context of QA in exposure studies.
Methods for assessing the accuracy of an exposure measure are also
discussed in Chapter 11. Here, an approach for quantitatively
estimating the precision of an exposure measurement system is
presented.
Statistical analysis of environmental samples collected
simultaneously in space and time can be used to estimate the precision
of a measurement method. Such samples are often referred to as
duplicates and are often collected in pairs. The difference in the
measurement parameter (e.g., concentration) between a duplicate pair
Table 11. Standard normal cumulative probabilities
z p(Z < z) z p(Z < z)
-4.265 0.00001 0 0.50
-3.891 0.00005 0.126 0.55
-3.719 0.0001 0.253 0.60
-3.291 0.0005
-3.090 0.001 0.385 0.65
-2.576 0.005 0.524 0.70
-2.326 0.01 0.674 0.75
0.842 0.80
-2.054 0.02 1.036 0.85
-1.960 0.025
-1.881 0.03 1.282 0.90
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