If I have 10 kids in my class and two failed last year and one failed this year, I can say two equivalent things:
- 50% less students failed my course this year
- 10% more of my students passed.
The odd thing is most students refuse when looking at such figures to believe they are equivalent statements. In fact, they are prone to believe that if
- 10% more of my students passed, then
- There were 10% less failures
The key is what I chose for a base to calculate the percentage from. I can choose
- total students: 10% more of my students passed,
- failing students: 50% less students failed
- or passing students: 12.5% more students passed
as the base, and each will give me a different percentage. It’s a stunningly easy sort of manipulation that is used all the time to great effect.
Apparently students aren’t the only ones confused. Here’s a paper making a similar error on infant mortality.