# Questions tagged [fishers-exact-test]

A hypothesis test for contingency tables.

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### Given the power of computers these days, is there ever a reason to do a chi-squared test rather than Fisher's exact test?

Given that software can do the Fisher's exact test calculation so easily nowadays, is there any circumstance where, theoretically or practically, the chi-squared test is actually preferable to Fisher'...
54k views

### A/B tests: z-test vs t-test vs chi square vs fisher exact test

I'm trying to understand the reasoning by choosing a specific test approach when dealing with a simple A/B test - (i.e. two variations/groups with a binary respone (converted or not). As an example I ...
62k views

### Fisher's Exact Test in contingency tables larger than 2x2

I was taught to only apply Fisher's Exact Test in contingency tables that were 2x2. Questions: Did Fisher himself ever envision this test to be used in tables larger than 2x2 (I am aware of the tale ...
2k views

### On Fisher's exact test: What test would have been appropriate if the lady hadn't known the number of milk-first cups?

In the famous lady tasting tea experiment by RA Fisher, the lady is informed of how many milk-first/tea-first cups there are (4 for each out of 8 cups). This respects the fixed marginal total ...
894 views

### Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation)

Recently, Nassim Nicholas Taleb made this post about the recent Danish mask study, a randomized controlled trial which concluded that the proportions of newly diagnosed coronavirus infections was not ...
6k views

### Why do odds ratios from formula and R's fisher.test differ? Which one should one choose?

In the following example ...
11k views

### Fisher's Exact Test and Hypergeometric Distribution

I wanted to understand fisher exact test better, so I devised up the following toy example, where f and m corresponds to male and female, and n and y corresponds to "soda consumption" like this: <...
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### Which test for cross table analysis: Boschloo or Barnard?

I am analyzing a 2x2 table from a small dataset of 30 patients. We are retrospectively trying to find some variables that give a hint about which treatment to choose. The variables (obs normal / ...
1k views

### What does the assumption of the Fisher test that “The row and column totals should be fixed” mean?

As this source states, one of the assumptions to perform Fisher's exact test of independence is that the row and column totals should be fixed. However, I find the explanation coming with it pretty ...
17k views

### Fisher Test in R

Suppose we have the following data set: Men Women Dieting 10 30 Non-dieting 5 60 If I run the Fisher exact test in ...
1k views

### Fisher's exact test gives non-uniform p-values

I am trying to apply Fisher's exact test in a simulated genetics problem, but the p-values appear to be skewed to the right. Being a biologist, I guess I'm just missing something obvious to every ...
3k views

### What distribution does Fisher's exact test assume?

In my work I have seen several uses of Fisher's exact test, and I was wondering how well it fits my data. Looking at several sources I understood how to calculate the statistic, but never saw a clear ...
10k views

### Alternatives for chi-squared test for independence for tables more than 2 x 2

What are some alternatives to the chi-squared test for categorical variables with tables larger than 2 x 2 and cells with a count less than 5, if I don't want to merge classes?
219 views

### Enrichment analysis by gene duplication level

Biological Background Over time, some plant species tend to duplicate their entire genomes, gaining an additional copy of each gene. Due to the instability of this setup, many of these genes are then ...
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### How to interpret Cochran-Mantel-Haenszel test?

I'm testing the independence of two variables, A and B, stratified by C. A and B are binary variables and C is categorical (5 values). Running Fisher's exact test for A and B (all strata combined), I ...
4k views

### What is the difference using a Fisher's Exact Test vs. a Logistic Regression for $2 \times 2$ tables?

For a $2 \times 2$ table, two ways to do inference on the table is through Fisher's Exact Test and also a Logistic Regression. I was told that using a Fisher's Exact Test, we are only interested in ...
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### What is the test statistic in Fisher's exact test?

For a 2 by 2 contingency table, some said Fisher's exact test uses the count $X_{1,1}$ in the (1,1) cell in the table as the test statistic, and under null hypothesis, $X_{1,1}$ will have a ...
5k views

### Fisher exact test on paired data

Given $40$ cases with lung cancer and $40$ matched controls (without lung cancer) (matching based on age, sex, etc.). To try to find evidence between the effect of smoking on lung cancer, I used ...
16k views

### Interpretation of the Fisher-exact test

I'm running some R code, where I would like to check if some data is independent. I could use a Chi-square test, which rejects independence. However I would like to ...
1k views

### Power of lady tasting tea experiment

In the famous Fisher's experiment the observable is the number of corrected guessed cup $k$ having two kind of cup $A$ and $B$. Usually it is interesting to compute the critical region to reject the ...
926 views

### Surprising behavior of the power of Fisher exact test (permutation tests)

I met a paradoxical behavior of so-called "exact tests" or "permutation tests", the prototype of which is Fisher test. Here it is. Imagine you have two groups of 400 individuals (e.g. 400 control vs ...
23k views

### Fisher's exact test in R

First, I am no expert but I am analyzing some marketing data. I have information on two versions of the same site, and I have data on the number of times people filled out a form on each version of ...
555 views

### When and how to avoid inappropriate use of Fisher's exact test

Could someone explain why Richard McElreath says Fisher's exact test is rarely used appropriately in his excellent Bayesian introduction book (Statistical Rethinking)? For reference, the context is ...
1k views

### Testing a 2x2 contingency table: male/female, employed/unemployed

I major in science, and my knowledge of statistics is rather superficial. Problem I had to find a data set and analyze it to the best of my ability as an assignement for my statistics course. This ...
3k views

### Simulation of Fisher's exact test is underestimating power

Summary: My simulations don't match my power calculation. (This question has become rather long, so you might not read to the bottom. I think it's a sample size problem.) I'm running some ...
2k views

### Is the chi-squared test appropriate with many small counts in a 5x2 table?

I have two sample populations, A, and B, which are independent. ...
1k views

### Fisher's tea tasting, binomial exact test

Please see the famous Fisher's experiment on biologist B. Muriel Bristol-Roach's ability to discern taste in red tea here (see Lady Tasting Tea). In this experiment Fisher gave Bristol-Roach 8 cups ...
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### Why do p values for test of likelihood ratio vs Fisher's Exact Test not agree

In a 2x2 analysis of categorical data, what causes the p value for the test of the likelihood ratio to differ from both the Fisher's Exact Test and the test of linear-by-linear Association? ...
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### McNemar or Fisher exact test for propensity score matched data?

I want to analyze some propensity score matched data. In the literature McNemar test is usually used, since the data is "paired". However matching is not pairing in the common sense. Would it be ...
3k views

### Which are differences between the hypergeometric distribution and chi-square distribution

As the title suggest...I have a very basic question. I have a case with the following data: ...
3k views

### Use Fisher's Exact Test or a Hypergeometric Test?

I'm looking to test for set enrichment and I'm wondering whether a fisher's exact test or hypergeometric test is more appropriate (and, if there isn't a straightforward answer, what the relative ...
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### Effect size for Fisher's exact test?

Does anyone know a way to calculate the effect size of a Fisher's exact test? Does that even make sense?
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### Does Fisher's Exact test for a $2\times 2$ table use the Non-central Hypergeometric or the Hypergeometric distribution?

In doing a Fisher's exact test, on wikipedia it states that the p-value is calculated as the sum of the probabilities of tables having probability less than or equal to the probability of the observed ...
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### Different p-values for Chi squared and Fisher's Exact R

I'm trying to find whether there's a correlation between two variables using Chi Square test and Fisher's Exact test. I get two different p values when I run Chi Square test and Fisher's Exact test. ...
2k views

### Logistic regression gives very different result to Fisher's exact test - why?

I have a confusing situation where I have strongly conflicting results from two ways of analyzing my simple data. I measure two binary variables from each participant, AestheticOnly and ChoiceVA. I ...
2k views

### Chi-square/G-test/Fisher exact with replicates

I want to use Fisher exact or G-test/Chi-squared (the choice depends on the numbers of observations in a particular case) to test difference in species frequencies between and within replicated groups ...
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### 2-Sample Proportions z-test vs Fisher's Exact Test

I want to evaluate the difference in proportions in declined applications and exceptions from policy from one quarter of data to the next. My sample sizes are generally not small (several hundred to ...
393 views

### Sample size calculation in COVID-19 study

From A Randomized Trial of Hydroxychloroquine as Postexposure Prophylaxis for Covid-19 by Boulware et al. in the New England Journal of Medicine (https://www.nejm.org/doi/full/10.1056/NEJMoa2016638), ...
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### Fisher exact test on 4 x 3 table, with low count?

I'm thinking about applying Fisher Exact Test for the following contingency table: ...
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### Computing the power of Fisher's exact test in R

Suppose that I have the following 3 x 3 contingency table: ...
2k views

### Fisher overall p-value vs. pairwise comparisons

I am doing comparisons on response rates across three sites. Following are the cell counts ...
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### One-sided Fisher's exact test and its complement

If a one-sided Fisher's exact test testing the null hypothesis that A is not superior to B has a p-value of 0.98, is it true that the Fisher's exact test p-value for the null hypothesis that B is not ...
9k views

### Is the Fisher's exact test “parametric” or “non-parametric”?

It is not clear to me whether we can consider the Fisher's exact test as a "parametric" or "non-parametric" one. My gut feeling is that it should be defined as "parametric" as it involves a fully ...
755 views

### Using $\chi^2$ or Fisher's exact test with low expected counts

Let's say I have 7 urns filled with random numbers of colourful marbles. An example dataset is as below: ...
216 views

### Why is my Fisher's test “significant” but odds ratio overlaps 1?

Given a contingency table of the following rare event, why does my Fisher's exact test produce a "significant value" (i.e., < 0.05) but also show that the confidence interval for OR ...
695 views

### Fisher's Exact test with zeros in data?

I have a question about conducting independence tests for categorical data with Fisher's Exact when I have zeros in my data. Since I observed no data for a category in both groups, is it right to ...
986 views

### Fisher's exact test vs kappa analysis

I was reading a paper where the authors assessed the association between two different diagnostics tests intended to diagnose the same disease and they performed the analysis with Fisher's exact test. ...
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### How to report the results of Fisher's exact test for larger than 2 by 2 tables

What is an acceptable phrase for reporting a Fisher's exact test where the number of rows and the number of columns are both $>2$. An example in R: ...