I am interested to know if the explanation below is any better than Wikipedia, it is the one I use with students and trainees.
The odds of
something happening is the ratio of the probability of it happening to the
probability of it not happening.
Let
probability of an event = p (NB
p is a proportion between 0 and 1)
Then the
probability of an event not happening = 1–p
So odds =
p/(1–p)
(In racing,
odds are usually given as the odds against something happening but we are
dealing here with more lofty matters than the 2.15 at Epsom).
The odds ratio for two groups is simply the ratio of their odds.
Disorder
present |
Disorder
absent |
|
Exposed
group |
a |
b |
Comparison
group |
c |
d |
p in exposed group = a/(a+b)
Probability
of event not happening in exposed group
= 1–p
=
1– a/(a+b) =
b/(a+b)
Odds in
exposed group
=
{ a/(a+b)}/{ b/(a+b)}= a/b
Similarly,
odds in control group
= c/d
So OR =
{a/b}/{c/d} =
ad/bc
If draw a line between the cells that multiply each other in the 2X2 table (a to d and b to c), you may see why some people call the OR the cross test.
Three important
things you need to know about ORs to get by in life without learning the calculation:
|
Can anyone suggest an easy guide to odds ratios and other basic stats functions?
A clinical friend has asked for some help with a dissertation and understanding source papers, this is not her area of expertise and she has been frightened off by the scholarly texts she has been directed too - I suspect her supervisors are not in their area of comfort with this either.
I have moved professionally away from supporting EBH and so am not up to date with user friendly articles. Dare I admit that I looked at the wikipedia which seemed comprehensive but impenetrable to the novice.
suggestions very welcome
Jane Hartley