Environmental Health Criteria 214

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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 http://www.inchem.org/documents/ehc/ehc/ehc<strong>214</strong>.htm Page 68 of 284 6/1/2007
HUMAN EXPOSURE ASSESSMENT -1.751 0.04 1.341 0.91 -1.645 0.05 1.405 0.92 1.476 0.93 -1.555 0.06 1.555 0.94 -1.476 0.07 -1.405 0.08 1.645 0.95 -1.341 0.09 1.751 0.96 -1.282 0.10 1.881 0.97 1.960 0.975 -1.036 0.15 2.054 0.98 -0.842 0.20 -0.674 0.25 2.326 0.99 -0.524 0.30 2.576 0.995 -0.385 0.35 3.090 0.999 3.291 0.9995 -0.253 0.40 3.719 0.9999 -0.126 0.45 3.891 0.99995 0 0.50 4.265 0.99999 is indicative of the precision of the collection and analysis methodology. Descriptive statistics generated from a set of differences between duplicate samples can be used to characterize the average degree of precision as well as variability in precision. Consider a hypothetical study of respirable particulate matter (RSP) in outdoor air where 20 duplicate pairs of 24-h average measurements were made. Assume the average 24-h average concentration among the 40 measurements was 50 µg/m 3 . Further assume that the distribution of differences between the 20 pairs of duplicate samples was normally distributed with a mean and standard deviation of 5 and 1 µg/m 3 , respectively. On average, then, a single measurement can be expected to be within 5 µg/m 3 of the actual concentration. Utilizing Page 69 of 284 Table 12. Probability distribution for the number of exceedances, using the with expected number of exceedances of 1.0 1-Year period 3-Year peri Number of Probability Cumulative Probability Cu exceedances probability pr k Pk {k} Fk{k} PM{k} FM 0 0.36737 0.36737 0.04958 0. 1 0.36838 0.73576 0.14916 0. 2 0.18419 0.91995 0.22414 0. 3 0.06123 0.98118 0.22435 0. 4 0.01522 0.99640 0.16826 0. 5 0.00302 0.99942 0.10086 0. 6 0.000498 0.999920 0.05034 0. http://www.inchem.org/documents/ehc/ehc/ehc<strong>214</strong>.htm 6/1/2007
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