And in particular with probability. It's amazing how difficult it is for people to fake random data.
If you ask half a class to actually perform and record 100 coin flips and half to fake the data, it's almost trivial to guess which is which either by looking for a string of 5-6 heads or tails in a row (which humans almost never have), or by calculating the percentage flips following a heads that are tails (which should be ~50%, but for humans tends to be much higher).
What's alarming and interesting isn't that they have a lot of years of school and miss this, but that interpreting diagnostic tests correctly is a core part of their job and they miss it. How many lives are adversely effected and how many billions are wasted by doctors making inappropriate decisions because they don't know how to interpret data correctly?
A few years ago I read that around 50% of all medicine prescribed in the US is providing zero or less net benefit to the patient. Granted by prescribing something doctors get you out of the office and in a few days most things get better on their own. But a lot was simple misunderstanding on the part of doctors about how helpful a given drug actually was.
No, it was specifically talking about prescribed medicine. Granted not the cost of said medicine. Something like this (http://www.nytimes.com/2008/10/24/health/24placebo.html) but rather reviewing what drugs patents where taking and comparing it to their symptoms.
.01 x .8 /(.01 x .8 + (.99 x 9.6 / 100)) ~= 0.0776 or 7.8%