Then lets switch to a practical example.
In a universe of 100 people of men aged over 50.
If pre-covid 40% have ED, then that is 40 people.
You’re answer for post covid was 66%, which would be 66 people.
How is 66 people vs 40 people equal to 3 times the likelihood?
To take that practical example a little further...
Let’s assume pre-covid was only 10%.
That would be 10 people in our universe of 100 people.
Post Covid at 3x the likelihood would be 3x 10% = 30%, OR 30 People.
Clearly 30 out of 100 is 3x the likelihood of 10 out of 100.
At 20% it’s 20 people vs 60.
At 30% it’s 30 people vs 90.
40% won’t work, you can’t have 3x the liklihood when you start with 40%. One of the 2 assumptions has to be wrong. Either you’re not starting with 40%, or it can’t be 3X the liklihood.
Not 3 times the “likelihood”, but 3 times the odds (likelihood, by the way, is a different concept very important in statistics.)
Let p0=0.4 denote the prevalence of ED in population 0.
Let p1=2/3 denote the prevalence of ED in population 1.
odds0 = p0/(1-p0) = 0.4/(1 - 0.4) = 0.4/0.6 = 2/3
odds1 = p1/(1-p1) = (2/3)/(1 - 2/3) = (2/3)/(1/3) = 2
So odds1 = 3*odds0, i.e. the odds of ED in population 1 is 3 times the odds of ED in population 0.