Computation and Measurement of Risk - Mathematics and Statistics for the Environment - page 180

Many of these pollution prevention and risk control strategies depend on mathematical computa-
tions and measures. Chapter 7 described measures of central location and spread, among other sta-
tistical functions, which are useful for summarizing continuous variables. However, many variables
used by field environmental practitioners (e.g., epidemiologists) are categorical variables, some of
which have only two categories—exposed/not exposed, test positive/test negative, case/control, and
so on. Because many of the variables encountered in field environmental health are nominal-scale
variables, frequency measures are used quite commonly in environmental health. These variables
have to be summarized with frequency measures such as ratios, proportions, and rates. Incidence,
prevalence, and mortality rates are three frequency measures that are used in public health to char-
acterize the occurrence of health events in a population.
In this chapter, we calculate and interpret environmental health measures using ratio, propor-
tion, incidence proportion (attack rate), incidence rate, prevalence, and mortality rate. Specifically,
we will discuss frequency measures, morbidity frequency measures, mortality frequency measures,
natality (birth) measures, measures of association, and measures of public health impact. Note that
many of the examples presented in the following are commonly used in epidemiological practices;
they are presented here to demonstrate the computation and measurement of risk used in all fields.

8.2 FREQUENCY MEASURES
A measure of central location provides a single value that summarizes an entire distribution of data.
In contrast, a frequency measure characterizes only part of the distribution. Frequency measures
compare one part of the distribution to another part of the distribution, or to the entire distribution.
Common frequency measures are ratios , proportions , and rates . All three frequency measures have
the same basic form:

Numerator
Denominator

×10 n

Recall that

10 0 = 1 (anything raised to the 0 power equals 1).
10 1 = 10 (anything raised to the 1st power is the value itself).
10 2 = 10 × 10 = 100.
10 3 = 10 × 10 × 10 = 1000.

So, the fraction of numerator/denominator can be multiplied by 1, 10, 100, 1000, and so on. This
multiplier varies by measure and will be addressed in each section.

8.2.1 r atio
Recall that we presented an introduction to ratios in Section 2.8 of this text. Here, we review the
basics and then demonstrate the actual use of ratios in measuring risk in environmental health and
public health practice. A ratio is the relative magnitude of two quantities or a comparison of any two
values. It is calculated by dividing one interval- or ratio-scale variable by the other. The numerator
and denominator need not be related; therefore, one could compare apples with oranges or apples
with number of chemical spills. The method for calculating a ratio is

Number or rate of events,items,persons,etc.in one group
Number or rate of events, items, persons,etc.inanothergroup

Two examples of ratios are