Your first line says...
"odds of ED post COVID = 0.4/0.6 = 2/3"
First, I think you meant pre-covid not post.
But pre-covid odds are 40% according to the commercial.
40% does not equal 2/3.
Your calculation of 2/3 is the ratio of men over 50 with ED to the men over 50 without ED. And not a particularly useful number.
The odds of pre-covid ED is 0.4 over the entire population of 1. (.4/1)=40%.
your second line says
"3*”odds of ED post COVID” = (2/3)*3 = 2"
If you convert 2 to a probability, 2 = 200%!!!
40% * 3 =120% is lower than (2/3)*3=200%
So you've not exactly helped us here. lol
But you're right you can't do what I did.
You can't have 120% odds of getting ED.
But the problem wasn't my math, it was the assumptions.
If you assume the commercial is true, and the odds are 40% for men over age 50.
Then the 3x figure can't be for men over age 50. Because you cant exceed 100%.
The most the odds multiplier could be for men over age 50 is 2.5x.
40% * 2.5 = 100%.
But an age range isn't given for the 3x.
It could include much younger men or based entirely on much younger men.
It's more likely a seat of the pants estimate based on a small sample.
But thanks for trying at least you recognized it couldn't be right.
It was funny though. Funny but not funny.
> But pre-covid odds are 40% according to the commercial.
No, this is not the odds. The odds is a value between 0 and infinity and therefore would never be expressed as a percentage. This value (40%) is the estimated proportion of the population over 50 with ED.
If the proportion is p then the odds is p/(1-p). So the probability p is a value between 0 and 1 (or 0% and 100%), while the odds is between 0 and infinity. In the example were discussing the odds is 0.4/(1-0.4) = 0.4/0.6=2/3.
Note that multiplying the odds by a factor (often called the odds ratio) is a sensible thing to do, while multiplying a probability (or proportion) by a factor can lead to nonsense (like the 120% value you obtained.)