Jeff Bezos famously said "When the data and the anecdotes disagree, the anecdotes are usually right."
This is dead on, based on my experiences. Data can be manipulated in so many ways - from what is actually measured, to how the measurement is interpreted, to whether the measurement is shared - it's all subject to manipulation.
The example that Jeff Bezos gave was customer support call wait times at Amazon.
One notable example Bezos shared involved Amazon's customer service wait times. While internal metrics suggested customers waited less than 60 seconds, anecdotal feedback indicated otherwise. To prove his point, Bezos called Amazon's customer service during a meeting and demonstrated that the wait time was significantly longer than the data suggested.
My experiences with customer support wait times are that often, the metric used (to assess whether the customer support agent is efficient) is call time. A long call time is bad, a short call time is good.
So what do the agents do? Hang up on people. That reduces their average call time.
Another item - measuring how many school days there are in a year, on the assumption that more school days are better. I don't actually believe that more school days are better, but even that metric is flawed, in the sense that - what are counted as school days are frequently NOT actually school days. For instance, in some public schools in the US, if one grade is taking a test such as the SAT, the other grades stay home. However - this still counts as a school day, for all students!
Another one - when "serving" the homeless, lots of organizations promote metrics such as the number of "comfort packages" given out (it'll be something like a package with blanket, socks, soap, toothbrush, etc). That's a completely useless metric, if it's supposed to be measuring whether people are actually helped. All you end up with is a bunch of blankets and other donated goods, littering the ground wherever the homeless congregate.
How about you folks - what "anecdote vs data" examples do you have?