Solved – How to calculate odds ratio and p-values for Fisher’s test

fishers-exact-testodds-ratior

I'm trying to perform Fisher's exact test in R. I'm calculating odds ratio like this

$$\frac{(\text{no. of successes in my set}) \cdot (\text{no. of failures in background set})}{\text{(no. of successes in background set)} \cdot (\text{no. of failures in my set})}$$

In the denominator, I get 0 for some cases, because there are 0 failures in my set for some cases.

Can anyone tell me how to calculate p-values from odds ratio?

Also what does it mean if we say odds ratio should be greater or less than 1?

If I want to test over-representation in my set against the background set what should be the odds ratio and how can I calculate that?

Best Answer

You can't directly test significance of the odds ratio, instead you have to take log(OR) and then use the standard error $se = (\frac{1}{n_{00}} + \frac{1}{n_{01}} +\frac{1}{n_{10}} + \frac{1}{n_{11}})^.5$

and log(OR) is approximately distributed $\mathcal{N}(log(OR), \sigma^2)$

but that is asymptotic.

For Fisher's, you probably want two-sided option

Related Solutions

Solved – Alternative argument in Fisher’s exact test in R

This is the alternative hypothesis, commonly denoted by $H_1$. For example if you type or=1 and alternative=less, the $H_1$ hypothesis is $\psi<1$ where $\psi$ is the odds ratio (or).

Solved – How to calculate probabilities for a 4 by 2 table

To calculate the probabilities, you first sum up each row and each column. For you that would be:

             present     not present     TOTAL
Category A    4          22               26
Category B    7          13               20
Category C   16          12               28
Category D   30           6               36  

TOTAL        57          53              110

Then you divide each value by the total to get the percentage. Thus, you could get probabilities for the condition being present (or not) by row, for being in a given category by column, or being in a particular combination of condition and category by the whole table; which you should use depends on which makes sense in your situation. For example, the probability of a subject in Category A having the condition present is $4/26=.154$. The odds is the ratio of present to not present, for Category A it is $4/22=.182$. Finally, the odds ratio is the ratio of the odds for some category to some other category, for instance, the odds ratio for Category A vs. Category B is $.182/.538=.338$. Since it's less than 1, the odds of the condition being present, if you're in Category A, is lower than the odds of the condition being present, if you're in Category B ($.182<.538$). The odds ratio gives you the multiplicative factor for converting one odds into the other, it is also a measure of effect size. Mathematically, you can move from probabilities to odds and back again:
$$ \text{odds}=\frac{\text{probability}}{(1-\text{probability})} $$
$$ \text{probability}=\frac{\text{odds}}{(1+\text{odds})} $$
As to the question of whether you should say that the category is correlated with the condition, I guess you could, but I would just say that the probability of the condition being present varies by category.

Best Answer

Related Solutions

Solved – Alternative argument in Fisher’s exact test in R

Solved – How to calculate probabilities for a 4 by 2 table

Related Question