A great resource from skeptics toolbox on medicine. Go here. Thanks to the committee for Skeptical Inquiry. Based on a powerpoint by Harriet Hall MD.
It is particularly good on absolute vs relative risk, about halfway through. Long, but worth the effort to read.
A recent study showed that using a cell phone doubled the risk of acoustic neuroma (a tumor in the ear). The relative risk was reported as 200% and alarmed parents took their children’s phones away. But the baseline risk of acoustic neuroma is 1:100,000. 200% of 1 is 2. The absolute risk was 1 more tumor per 100,000 people. Acoustic neuroma is a treatable, non-malignant tumor. The lead researcher said she would rather accept the risk and know where her kids were. She let them keep their cell phones. She warned that the results were provisional, the study small, and that different results might be found with a larger study. She was vindicated when a later, larger study found no increased risk.
Comments
This issue was raised recently, both in New Scientist and in Scientific American Mind. Even people with high IQ scores make this error. We jump to false conclusions by taking mental shortcuts, that normally work, but in some cases mislead. The examples you give mislead enormously.
It's not that people, who get it wrong, are stupid - it's just that they are not dealing with figures and statistics like this in normal everyday life - so they're unaware of the traps.
Regards, Paul.
http://forum.amateurscientist.org/forum/index.php?topic=1413.0