Percent and Percentage Points

In a previous post today, I mentioned that breast cancer screenings had dropped 4 percentage points from 70-66%. To my eternal annoyance, most headlines I see refer to this as a 4% decline. This is wrong. The actual decline is can be mentioned as a percent decline only if you report that number directly.

\% decline=\frac{(old-new)*100}{old}

This is such basic math that I feel foolish just to point it out, but this nomenclature confusion dominates our reporting. If you assume that the number of women remained constant (In this particular case, the assumption is true because the results are from a survey of 10,000 women), then the actual percent decline would be (70-66)/70 = 5.7%, that would be, well, a lot more than 4%!

See here for wikipedia discussion.

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