Environmental Health Criteria 214

HUMAN EXPOSURE ASSESSMENT
values in the data set. Graphical representation of percentiles is
discussed in the next section.
Multivariate summary statistics allow one to evaluate
relationships between or among different variables. Most of these
examine correlation (the strength of the linear relationship) between
variables, where the direction and magnitude of the relationship, or
association, is described by the correlation coefficient (p). The
correlation coefficient ranges from -1 to +1, where negative values
indicate an inverse relationship between two variables, positive
values indicate a direct relationship, and values near zero, whether
negative or positive, indicate a weak relationship. In the example
case, the correlation between blood lead and faeces lead in the
Maltese study population is 0.57, indicating these biomarkers of lead
exposure have a moderate to strong positive association.
4.2.2 Graphical summaries
Graphical summaries of data provide illustrative information
about the distribution of the observed values and associations between
variables. Graphical presentations of data can suggest the shape of
the distribution and aid in exploring hypothesized relationships
between factors included in the study. In many situations and for many
exposure analysts, graphical summaries of data convey information more
readily than numerical summaries. Fundamental graphical presentation
methods are described here. A description of advanced visualization
methods may be found in Cleveland (1993) and Tufte (1983, 1997).
4.2.2.1 Histograms
Histograms are bar charts used to illustrate the relative
frequency of values or ranges of values within an exposure metric.
Observations are assigned to ranges of the data, and the height of the
bar represents the frequency of observations in that range. It is
important to note that the choice of ranges can be arbitrary,
resulting in many possible different pictures of the results. A
histogram of the Maltese blood lead data is shown in Fig. 11. Here,
the data were grouped into bins with interval ranges of 25 µg/litre.
Blood lead concentrations between 200-225 µg/litre and 275-300
µg/litre were observed the most often. Histograms can be used to
illustrate absolute or relative frequency.
4.2.2.2 Cumulative frequency diagrams
Cumulative frequency or probability diagrams can be used to
graphically express percentiles of a distribution. A cumulative
probability chart for the Maltese blood lead data is shown in Fig. 12.
The value associated with a given percentile, or vice versa, can
easily be determined from such a figure.
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