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USING STATISTICS: Spotting and Avoiding Them
different uses of the word "risk"
In everyday usage, "risk" is
essentially synonymous with "danger."
For example, we might say that someone walking alone on a poorly lit
after dark has a risk of being mugged.
However, "risk" is also used to quantify a danger. In the most basic
form, a risk is a probability. For example, we might say that the risk
that a U.S. resident dies from a heart attack is about 25%, meaning
that about 25% of all deaths in the U.S. are from heart attacks.
Just this usage alone brings up the question of reference category,
especially if we
phrase the risk as "Your risk of dying of a
heart attack is about 25%." The risk may be higher or lower depending
on other factors (gender, occupation, age, etc.) in addition to being a
Another common use of the word risk is in the term relative risk
(also called risk ratio).
This is a method
of comparing the risk of one group with the risk of another. One group
might be people with a certain condition (or receiving a certain
treatment) and the other group people without that condition (or not
treatment). Relative risk is the
ratio of the risks for the two groups.
brings in two possible source of confusion:
are the two groups?
group's risk is
in the numerator and which group's risk is in the denominator?
Another source of misunderstanding when relative risks are given is
that sometimes only the relative
risk is given. We also need to know the "absolute risk" (the risk of at
least one of the groups involved) in order to interpret what the
relative risk is telling us.
The report on a clinical trial of a new drug might say that the
relative risk of a heart attack
for people with high cholesterol in a certain age group who take the
drug, compared with people in that same age group with high cholesterol
who take a placebo instead of the drug, is 75%. (This might also be
presented as a 25% reduction
in risk.) This might sound
substantial. But whether or not it is depends on the absolute
1: If the risk of a heart
attack for people in that age group
cholesterol who take the placebo is 40%, then "relative risk is 75%"
tells us that taking the drug reduces the
risk from 40% to 30%. In other words, 10% of people in the category
would benefit from taking the drug. That does not sound as substantial
as "25% reduction in risk" might initially lead someone to believe, but
it is still
2: If the risk for people in
this catgory who take the placebo
2%, then taking the drug reduces the risk to 1.5%. In other words, 0.5%
of people in the group being studied would benefit from taking the
drug. This is not so substantial.
For a consumer-oriented
explanation of health risks at a
basic level of quantitative literacy, see
Steven, Schwartz, Lisa, and Welch, H.
Gilbert (2008). Know
Your Chances, University of