An Introduction to Critical Thinking and Creativity - always yours

150 STATISTICS AND PROBABILITY
A misleading use of relative quantity
In April 2010, an oil rig in the Gulf of Mexico owned by British Petroleum
(BP) exploded and a huge amount of oil started leaking from the deep
sea and BP was unable to stop the spill. In a newspaper interview, Tony
Hayward, who was the chief executive of BP, tried to downplay the consequences
of the leak. He said that the amount of leaked oil and dispersant
used to tackle the oil slick is small compared with the very big ocean
(Martel, 2010):
The Gulf of Mexico is a very big ocean. The amount of volume
of oil and dispersant we are putting into it is tiny in relation
to the total water volume.
This is a rather disingenuous use of relative quantity. The amount of spill
might be rather small compared with the total volume of the ocean in the
Gulf of Mexico, and even smaller when compared with all the water in
the world, but it is still a huge amount of pollution that can affect a lot of
people and animals and bring about terrible environmental destruction.
The absolute vs. relative distinction is particularly important in healthcare. The
risks associated with illnesses, drugs and medical treatments can often be specified
in absolute or relative terms. Take these two headlines:
• New miracle drug lowers liver cancer risk by 50%!
• New drug results in 1% drop in liver cancer risk!
The first headline is presumably a lot more impressive, but both can be correct
in describing the result of a clinical trial. Imagine two groups of normal people,
100 in each group. The first group took the drug to see if it reduced the number of
liver cancer. After 10 years, 1 out of 100 developed liver cancer. The other control
group took a placebo pill and 2 out of 100 had liver cancer after 10 years. The
absolute risk of getting liver cancer is 2% for those without the drug, and 1% for
those taking the drug. So the second headline correcüy describes the reduction in
absolute risk. But reducing 2% to 1% amounts to a relative risk reduction of 50%.
So the first headline is correct as well.
Why should we care about whether risk information is presented in absolute
or relative terms? First of all, note that information about relative risk tells you
nothing about absolute risk. If eating farmed salmon increases your chance of
getting a certain disease by 100%, this sounds very scary. But this relative increase
tells you nothing about the absolute likelihood of getting the disease. If the disease
is extremely rare, the chance of getting it can remain negligible even after it has
been doubled.