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Number of womeninState Awho died fromheartdiseasein 2011
Number of womeninStateeAwhodied from cancer in 2011
Number of womeninState Awho died fromlung cancer in 2010
Estimated revenue (in dollars)in StateAfromcigarette salesin 2010
After the numerator is divided by the denominator, the result is often expressed as the result “to
one” or written as the result “:1.”
Note that, in certain ratios, the numerator and denominator are different categories of the same
variable, such as males and females, or persons 20 to 29 years and 30 to 39 years of age. In other
ratios, the numerator and denominator are completely different variables, such as the number of
environmental laboratories in a city and the number of manufacturing industries operating in that
cit y.
EXAMPLE 8.1
Problem: Between 1971 and 1975, as part of the National Health and Nutrition Examination Survey
(NHANES), 7381 persons ages 40 to 77 years were enrolled in a follow-up study (Kleinman et al.,
1988). At the time of enrollment, each study participant was classified as having or not having dia-
betes. From 1982 to 1984, enrollees were documented as either having died or being still alive. The
results are summarized as follows.
Open Enrollment
(1971-1975)
Dead at Follow-Up
(1982-1984)
Diabetic men
189
100
Non-diabetic men
3151
811
Diabetic women
218
74
Non-diabetic women
3823
511
Of the men enrolled in the NHANES follow-up study, 3151 were non-diabetic and 189 were dia-
betic. Calculate the ratio of non-diabetic to diabetic men.
Solution:
Ratio = (3151/189) × 1 = 16.7:1
8.2.1.1 Properties and Uses of Ratios
Ratios are common descriptive measures used in all fields. In environmental health and epidemiol-
ogy, ratios are used as both descriptive measures and as analytic tools. As a descriptive measure,
ratios can describe the male-to-female ratio of participants in a study, or the ratio of controls to cases
(e.g., two controls per case). As an analytical tool, ratios can be calculated for the occurrence of ill-
ness, injury, or death between two groups. These ratio measures, including risk ratio (relative risk),
rate ratio, and odds ratio, are described later in this chapter.
As noted previously, the numerators and denominators of a ratio can be related or unrelated.
In other words, you are free to use a ratio to compare the number of males in a population with
the number of females, or to compare the number of residents in a population with the number of
hospitals or dollars spent on over-the-counter medicines. Usually, the values of both the numerator
and denominator of a ratio are divided by the value of one or the other so that either the numerator
or the denominator equals 1.0; thus, the ratio of non-diabetics to diabetics cited in Example 8.1 is
more likely to be reported as 16.7:1 than 3151:189. Calculating ratios for different variables is dem-
onstrated by Example 8.2A and Example 8.2B.
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