Naked Statistics: Stripping the Dread from the Data

by Charles Wheelan

Percentage change must not be confused with a change in percentage points. Rates are often expressed in percentages. The sales tax rate in Illinois is 6.75 percent. I pay my agent 15 percent of my book royalties. These rates are levied against some quantity, such as income in the case of the income tax rate. Obviously the rates can go up or down; less intuitively, the changes in the rates can be described in vastly dissimilar ways. The best example of this was a recent change in the Illinois personal income tax, which was raised from 3 percent to 5 percent. There are two ways to express this tax change, both of which are technically accurate. The Democrats, who engineered this tax increase, pointed out (correctly) that the state income tax rate was increased by 2 percentage points (from 3 percent to 5 percent). The Republicans pointed out (also correctly) that the state income tax had been raised by 67 percent. [This is a handy test of the formula from a few paragraphs back: (5 – 3)/3 = 2/3, which rounds up to 67 percent.] The Democrats focused on the absolute change in the tax rate; Republicans focused on the percentage change in the tax burden. As noted, both descriptions are technically correct, though I would argue that the Republican description more accurately conveys the impact of the tax change, since what I’m going to have to pay to the government—the amount that I care about, as opposed to the way it is calculated—really has gone up by 67 percent.