Absolute vs. Relative Values (Don’t be fooled)
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It’s amazing just how misleading some claims being made are. OK, it’s advertising, but seriously?
When an ad claims that their product “improves ‘x’ by 50%”, does that mean it improves ‘x’ (or whatever ‘x’ is) by 50% relatively or absolutely, and what’s the difference?
Example 1 (using fictitious lightening data):
Say, the absolute risk of being struck by lightening is 0.00001% or 1 in 1,000,000 (made up number for illustration).
Then, let’s say the absolute risk of being struck by lightning while holding an umbrella under a tree in a thunderstorm is 0.00003%. So, in absolute risk terms, we’ve only increased our risk by 0.00002% or about 1 chance in 333,333. Not that much in absolute (real) terms, right?
What an advertisement might do to make their product more compelling would be to focus on the relative risk instead of the absolute risk (or benefit). That is, focus on the risk increase itself “relative to” the initial absolute risk of 0.000002.
Mathematically, that “relative” risk just a percent difference, or:
((Risk2-Risk1)/Risk1)*100
(0.0.00003 – 0.00001)/0.00001)*100 = 200%.
WOW. Looking at only the relative risk, it’s now a 200% (relative) increased risk!
(or 200% “benefit”, depending on how they’re pitching the number.)
To summarize, our new (fictitious) absolute risk of being struck by lightening by holding an umbrella under a tree during a thunderstorm is: 0.00003% or about 1 in 333,333.
Our relative risk is 200% higher to not having an umbrella and not standing under a tree in a thunderstorm. That (fictitious) risk was 1 in 1,000,000.
So the next time you hear that something is x% more or x% greater than something, ask yourself x% of “what”? Since this % increase is often a relative and not absolute difference, that part is left out.
Below is a graph split into two sections (separated by the horizontal red line). The top portion has the relative risk pairs and the bottom portion (below the red line) is the absolute risk pairs. Note that the risk pairs below the red line are indistinguishable at even a tiny 2% scale.
The actual data for this graph are:
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x-axis (vert) y-axis (horizontal)
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1 0.000001
2 0.000003
3 1
4 2
Caveat Emptor
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