I have to calculate log2 ratio for odds and don't know how to do it.
Group A Group B
0.031571 0.0170071
There are occurrences of event in GroupA and Group B – I want to calculate how much Group A has this specific event compared to Group B, hence I need log2 for odds ratio.
I was thinking that such ratio should be calculated like this:
log2(GroupA/GroupB) = log2(0.031571/0.0170071) = 0.892463
However in this stackoverflow answer they calculate it like this:
(GroupA/GroupB)/log(2) = (0.031571/0.0170071)/log(2) = 2.67814
My question is – how to calculate log2 ratio; and what is the difference between these two approaches?
Best Answer
The log odds ratio is the log of the odds ratio, not the odds ratio divided by a log. I don't know what problem the link you gave was trying to solve, but it wasn't this one. You take the log of the OR because the OR is bounded by 0 and infinity and is multiplicatively symmetric around 1; while the log(OR) is unbounded and additively symmetric around 0.