"How to lie with statistics" is the title of a little book by Darrell Huff, first published in 1954. Here's an example of the kind of question Huff writes about in the book:
A new business makes a very respectable one hundred thousand dollars in profits in its first year. In its second year, the business enjoys a 100 percent increase in profits, relative to the previous year. But in its third year, the business suffers a 75 percent decrease in profits, relative to the previous year. Look on the bright side, someone says. Up 100 percent the second year, then down 75 percent the third yearoverall, this person says, profits are still 25 percent above the first year's level.
What's Wrong With This Argument?
What's wrong, of course, is that the argument glosses over the fact that each of those percentages expresses profits in terms of the previous year's profits.
In the first year, remember, the business made one hundred thousand dollars. In the second year profits increased 100 percentthat means second-year profits were two hundred thousand dollars.
In the third year profits decreased 75 percentrelative to the second year.
Do The Math!
So now we have to subtract 75 percent of two hundred thousand dollars from two hundred thousand dollars leaving only fifty thousand dollars as the third year's profits. Third-year profits are really only half of first-year profits!
Darrell Huff calls this bit of confusion the Battle of the Shifting Base. The 100 percent increase was figured on one base, the 75 percent decrease on another. Concealing that fact is one way of lying with statistics.