marble at random, do you think I would have a red one?’’, the answer would
be ‘‘90% chance.’’ The first 90% represents a proportion; the second 90%
indicates the probability. In addition, if we keep taking random selections
(calledrepeated sampling), theaccumulated long-term relative frequencywith
which an event occurs (i.e., characteristic to be observed) isequalto the pro-
portion of the subpopulation with that characteristic. Because of this obser-
vation,proportionandprobabilityare sometimes used interchangingly. In the
following sections we deal with the concept ofprobabilityand some simple
applications in making health decisions.
3.1.1 Certainty of Uncertainty
Even science is uncertain. Scientists are sometimes wrong. They arrive at dif-
ferent conclusions in many di¤erent areas: the e¤ects of a certain food ingredi-
ent or of low-level radioactivity, the role of fats in diets, and so on. Many
studies are inconclusive. For example, for decades surgeons believed that a
radical mastectomy was the only treatment for breast cancer. More recently,
carefully designed clinical trials showed that less drastic treatments seem
equally e¤ective.
Why is it that science is not always certain? Nature is complex and full of
unexplained biological variability. In addition, almost all methods of observa-
tion and experiment are imperfect. Observers are subject to human bias and
error. Science is a continuing story; subjects vary; measurements fluctuate.
Biomedical science, in particular, contains controversy and disagreement; with
the best of intentions, biomedical data—medical histories, physical examina-
tions, interpretations of clinical tests, descriptions of symptoms and diseases—
are somewhat inexact. But most important of all, we always have to deal with
incomplete information: It is either impossible, or too costly, or too time con-
suming, to study the entire population; we often have to rely on information
gained from asample—that is, a subgroup of the population under investiga-
tion. So some uncertainty almost always prevails. Science and scientists cope
with uncertainty by using the concept ofprobability. By calculating proba-
bilities, they are able to describe what has happened and predict what should
happen in the future under similar conditions.
3.1.2 Probability
The target population of a specific research e¤ort is the entire set of subjects at
which the research is aimed. For example, in a screening for cancer in a com-
munity, the target population will consist of all persons in that community who
are at risk for the disease. For one cancer site, the target population might be
all women over the age of 35; for another site, all men over the age of 50.
Theprobabilityof an event, such as a screening test being positive, in a tar-
get population is defined as therelative frequency(i.e.,proportion) with which
the event occurs in that target population. For example, the probability of
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