Question on Fisher's Exact Test

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SUMMARY

The Fisher's Exact Test is a statistical method used to determine the significance of the association between two categorical variables in a 2x2 contingency table. It calculates the exact p-value based on the observed frequencies of responder and non-responder patients treated with either verum or placebo. The test operates under the null hypothesis (H0) that there is no difference between the treatments. By summing the probabilities of all combinations equal to or more extreme than the observed data, researchers can ascertain the likelihood of their results occurring by chance.

PREREQUISITES
  • Understanding of binary outcomes in clinical trials
  • Familiarity with contingency tables
  • Knowledge of null hypothesis testing
  • Basic statistical concepts, particularly p-values
NEXT STEPS
  • Study the implementation of Fisher's Exact Test in statistical software like R or Python's SciPy library
  • Explore the assumptions and limitations of Fisher's Exact Test
  • Learn about alternative tests for larger sample sizes, such as the Chi-Squared Test
  • Investigate the interpretation of p-values in the context of clinical trials
USEFUL FOR

Statisticians, clinical researchers, and data analysts involved in analyzing binary outcomes in clinical trials will benefit from this discussion.

Mathwizard6254
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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!
 
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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.
 
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