Lying with Numbers Part 1: Absolute and Relative Changes

This is the first part of an on going series in which I discuss how numbers (usually statistics) can be used to mislead people.

First an example stat: (hypothetical)

You have a 2% chance of getting cancer.

The issue of absolute vs relative refers to the type of statistic used to represent the change in another statistic.

Your chances of getting cancer have increased 50%.

Here we have a statistic that represents a change in the original 2% stat (an increase of 50%)

The problem that arises is that this change is not labeled, it could either be a relative change or an absolute change. The actual result can change dramatically depending on which one is used.

If the change is absolute:

You have a 52% chance of getting cancer. (a +50% absolute change)

If the change is relative:

You have a 3% chance of getting cancer. (a +50% relative change)

As you can see the absolute percentage change is added to the original percentage, done from the perspective of "revising" (or directly adding to) the original percentage.

While the relative percentage change is done from the perspective of the original 2% increasing by 50% of it's self.

50% of 2% is 1%

2% + 1% = 3%

So the relative increase is the original 2% plus half(50%) of it's self: 3%.

It's important to note that this isn't limited to percentages. There are many ways to represent changes in numbers. For example, ratios and fractions being interchangeable with percentages can fall prey to this as well. Remember that the number that represents a change in another is what is important. The original number cannot be relative or absolute, only the change in it can be.

A final example: (hypothetical) 

Bird Flu cases up 300%

A relative increase from 1 case to 3 cases. Not so scary now is it?

So next time you hear of a change in a statistic be sure to find out if the change is relative or absolute. It can make a world of difference.