If 8.8% of group A and 2.2% of group B experience something, how much more likely is someone from group A to experience it than someone from group B?
I was told by a co-worker that her math-strong cousin said it's 300%, which sounds right, that a person from group A is 300% more likely to experiece it than somebody from group B, but what is the mathematical formula you would use to calculate this? (I haven't completed statistics yet, and I suck at it, anyway!)
I have a few more similar questions, so while I could just keep posting them here, I'm the type who wants to know how to do it myself!
Thanks for being that type! That's our goal for you, too -- if you posted multiple questions of the same type, it would mean we failed our mission!
I think one issue here is language: the difference between N times
as likely and N times
more likely.
Starting with the problem itself, you can see (as Mark said) that A is 4 times
as likely, which is 400% as likely if you want to use percentage.
Many people would express this as "400%
more likely", meaning "more likely, by a factor of 400%" - A's probability is 400% of B's.
Others take the word "more" literally, saying that that would mean the
difference in probability is 400%. Then that answer would be wrong; the
difference here is 400% - 100% = 300%. That may be why the cousin gave the answer of 300%. That is, she would be calculating (8.8 - 2.2)/2.2 = 6.6/2.2 = 3 = 300%. This is a percent increase.
There is yet a third possible meaning, since the data are themselves percentages. We could just subtract 8.8% - 2.2% = 6.6%, and say that the difference in probability is 6.6%: A's probability is 6.6 percentage points more than B's. (Note how "percentage points" make it clearer what I mean.) Here we are just talking about the
increase, not a
percent increase. Since the problem doesn't specifically ask for a percentage, this is also reasonable.
Unfortunately, because people interpret the phrase "how much more likely" differently, I can't be sure of the intent of the question. If this came from a textbook, I would look in the book for similar wording to check how they take it.
But personally, since it is more meaningful in this problem to talk about a ratio of probabilities, I would probably answer, A is
4 times as likely as B. I would not use a percentage, and I would not use the tricky word "more".
