Question on Fisher's Exact Test

[Mathwizard6254]

Hey all, hope everyone had a great thanksgiving. I was wondering if anyone could explain to me what the Fisher's Exact Test is about and how to use it. Thanks!

[Dr.ThinkDeep]

At the elementary level consider a two parallel-group double-blind trial with binary outcome just prior to the unblinding.
Let us call
A the number of responder patients treated with verum
B the number of responder patients treated with placebo
C the number of nonresponder patients treated with verum
D the number of nonresponder patients treated with placebo

You know that A+B patients responded to the treatment and B+C did not.
You know that A+C patients were treated with verum and B+D were treated with placebo.

Given these marginal row and column totals, you compute a probability to find certain numbers A B C D und assumption of the hypothesis
H0: placebo and verum did not make a difference.
(Just like taking out (without replacement) A+B balls from an urn known to contain A+C white balls and B+D black balls initially.)

Now unblind yourself and sum up all probabilities that are equal or lower than assigned to the combination A B C D which you have found.
This sum of probabilities is your exact p-value, i.e. the probability that your result or one that is even less probable has occurred by chance given that verum or placebo do not matter.

I did not take the time to make this shorter but I do not know on what level to argue yet.