Ok, so we were cleaning out the library in the GOPB office, and there were a bunch of old textbooks that were going to be thrown away, so I picked up a couple, who could blame me? As I recently learned, the '70s were remarkably more different from my time than I previously thought. I mean, apparently my dad didn't use gloves in dental school, "unless we were absolutely positive the patient had hepatitis." (0_0) But odd '70s-style writing and cartoons aside, the book is a good pastime while waiting for code to compile; and I can say I've come across my fair share of mega-super-duper statistical fallacies in my work.
I have to say, I think Campbell stole my idea. I mean, I was gonna right a book (someday) on how to win any argument with statistics (though that idea is technically copyrighted by Apple I'm sure), but he sort of beat me to the punch. In any case, this old text has plenty of fascinating examples (some incomprehensibly not politically correct), and they make for excellent warnings about statistics gone crazy.
To begin, do not suppose that I think all statistics are meant to mislead or beguile you. Quite the contrary, I think many statistics are meaningful and highly useful. Some wilt at the absolute power of a figure or phrases like, "studies have shown..." or "statistics prove...", while others immediately dismiss all figures and studies as biased. Both positions are easy to fall back on, and our goal is to help you fit into neither category. Enough of that; let's tell some stories.
What better place to start than with communists? Stalin put forth the first five year plan with fantastic promises. From advances in consumer industries and food production to housing and prices. Gosplan (the planning agency) expected a rise of 20 percent in the purchasing power of their currency while real wages would increase by 66 percent and the cost of living would go down by 14 percent.
At the end of the period, Stalin nearly admitted the plan was a dismal failure in a speech. Only 18 months later, however, he declared that the plan was a fantastic success at 93.7 percent fulfillment. Great success! The subtle sleight of hand in that figure demonstrates the ease with which we can mislead an unwary public.
The calculation was based on ratios of (total output)/(total planned output). This seems reasonable, right? Wrong! For example, in 1928 steel output was 4.2 million tons. The plan expected an increase to 10.3 million tons. Actual production was 5.9 million tons by the end of the five years. Thus the plan predicted an increase of 6.1 million tons and achieved an increase of only 1.7 million tons. However, Stalin's statistic was based on simply taking 5.9/10.3=57%, quite a bit larger than the actual 28% "success" they really achieved. I've even charted this out for you:
Thus with the same logic, suppose steel output hadn't grown one bit. Then at the end of the plan, they would have achieved 40% success!
To put this in perspective, let's look at the Obama stimulus package (this is not to grind a political ax, nor am I saying the stimulus was a failure. Furthermore, I'm not saying the Obama administration used statistics inappropriately. I'm just illustrating what the Stalinist way would have been).
The Obama administration said the stimulus plan would bring us to 137,550,000 jobs as opposed to the 133,846,000 jobs we'd have without stimulus (these are actual figures from the Romer/Bernstein plan proposal). Then when we look at the actual jobs in December 2010, 130,346,000 (BLS seasonally adjusted), the Stalin approach would have been for the Obama administration to say, "Hey look, we've achieved 94.8% success!" Of course, in reality, the projection was to gain 3.9 million jobs but we actually lost 3.2 million so we achieved -80% of our goal (that's a weird statistic). Now the Obama administration didn't say we had 94.8% success; I'm merely helping you see the absurdity of Stalin's statistic. Aren't you glad we aren't communists?
And now, the next time you want to become a dictator and rule over a communist nation, you've got a great new trick!
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