Percent or percentage points

Question

Hi everyone, I was hoping to get your thoughts on this phrasing ambiguity which i cam across the other day. First of all, and hypothetically, let's say that smoking increases your risk of getting lung cancer by 20%. And your original chance of getting lung cancer (as a non smoker) is 10 percent.

So, which of the following sentences is representative of those statements:

A) "By taking up smoking your chance of getting lung cancer increases to 30%" (10% + 20%)

OR

B) "By taking up smoking your chance of getting lung cancer increases to 12%" (10% + 2%--(which is 20% of the original 10%)

It's my impression that by saying that "smoking increases your risk of getting lung cancer by 20%." you're in fact expressing B) -- because, if i were to say "smoking increases your chances of getting lung cancer by 100%, that would mean that your then chances of getting lung cancer would be "40%"--it would double, not be 120%--which is un-mathematical.
Would you guys agree with that logic?

And secondly, how then to express A) without saying "increases by 200%" --would the sentence "smoking increases your risk of getting lung cancer by 20 percentage points" then be more accurate?

Anyway, what do you guys think?

P.s sorry that this isn't really a simple, straightforward question, it's just suddenly i realized that i may have been misinterpreting statistics for years!--though i'm not sure whether this kind of phrasing is in fact considered ambiguous by everyone or just me ><

Thanks a lot if you read to the end!
All best
TT

Anonymous · Accepted Answer

It doesn't work that way. You can't simply add two different possibilities, expressed as a percentage of a chance, and say that probability of getting the lung cancer is 30%. If you want use strictly mathematical way to calculate such a probability you would have to multiply 10/100 x 20/100 to get an occurrence-of-lung-cancer chance equal 2/100, i.e. the occurrence two chances at the same time is two percent, which is a nonsense, though mathematically correct.

Twistedthistle · Answer

Thanks for your reply, anonymous. In fact, i just found this on Wikipedia, which pretty much answers my own question!

In the case of http://en.wikipedia.org/wiki/Interest_rate, it is a common practice to state the percent change differently. If an interest rate rises from 10% to 15%, for example, it is typical to say, "The interest rate increased by 5%" — rather than by 50%, which would be correct when measured as a percentage of the initial rate (i.e., from 0.10 to 0.15 is an increase of 50%). Such ambiguity can be avoided by using the term "http://en.wikipedia.org/wiki/Percentage_point". In the previous example, the interest rate "increased by 5 percentage points" from 10% to 15%. If the rate then drops by 5 percentage points, it will return to the initial rate of 10%, as expected.

http://en.wikipedia.org/wiki/Percentage

GPY · Answer

AnonymousIt doesn't work that way. You can't simply add two different possibilities, expressed as a percentage of a chance, and say that probability of getting the lung cancer is 30%. If you want use strictly mathematical way to calculate such a probability you would have to multiply 10/100 x 20/100 to get an occurrence-of-lung-cancer chance equal 2/100, i.e. the occurrence two chances at the same time is two percent, which is a nonsense, though mathematically correct.

To the extent that I understand this answer, I don't agree with it. I think it is common enough to say that a risk increases by some percentage amount. If smoking increases one's chance of getting lung cancer by 20%, then a prior chance of 10% would become 12%, according to the way I understand it.

Percent or percentage points

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