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Media Math

If you follow shenanigans related to government waste, fraud, and abuse, Stephen Barr’s Federal Diary is almost always good reading. But today’s installment seems a bit off. He writes:

At the Internal Revenue Service, one employee over a two-year period took sick leave on 13 of the 14 Tuesdays after a Monday holiday.
That’s an extreme case of sick-leave abuse, but the IRS employee had plenty of co-workers who also liked to take Tuesdays off, a report by the Inspector General for Tax Administration found.
For weeks that had a holiday falling on a Monday, 27 percent of all sick leave at the IRS was taken on a Tuesday in 2005 and 2006, the report said. And 24 percent of all sick leave taken by IRS employees during non-holiday weeks was on a Monday.

That last paragraph inspires a bit of head-scratching. During weeks with a Monday holiday, 27 percent of all sick leave is taken on a Tuesday. How exactly is that damning? If there’s a Monday holiday, that leaves four days in the week, and a random distribution of sick-leave days would lead us to assume that 25 percent would be used on that Tuesday. A 2-percent variation isn’t very striking. A random distribution of sick-leave days on non-holiday weeks would mean 20 percent of sick days would be taken on a Monday, which again isn’t all that far out of line with the actual proportion, 24 percent.
I’m not exactly an Olympic-caliber mathelete, but it seems to me that you’d need stronger evidence than a 2-to-4 percent variation to call this “abuse” of sick leave. (And beyond that, there are good reasons that one might expect to see more sick days taken on Mondays; during weekends people play sports, travel, go out to eat, spend time with their children, drink alcohol, and do other things that are more likely to result in sickness or injury than whatever they do on Tuesday nights.)
Maybe IRS workers aren’t the most representative sample. There is plenty of evidence that the average IRS agent is far, far more diligent in his duties than is good for the Republic.

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