**Fisher’s Exact Test**, and its appropriate application within the R programming language.

Like the F-Test, Fisher’s Exact Test utilizes the F-Distribution as its primary mechanism of functionality. The F-Distribution being initially derived by Sir. Ronald Fisher.

*(The Man)*

*(The Distribution)*

The test itself was created for the purpose of studying small observational samples. For this reason, the test is considered to be “conservative”, as compared to The Chi-Squared Test. Or, in layman terms, you are less likely to reject the null hypothesis when utilizing a Fisher’s Exact Test, as the test errs on the side of caution. As previously mentioned, the test was designed for smaller observational series, therefore, its conservative nature is a feature, not an error.

Let’s give it a try in today’s…

__Example:__A professor instructs two classes on the subject of Remedial Calculus. He believes, based on a book that he recently completed, that students who consume avocados prior to taking an exam, will generally perform better than students who did not consume avocados prior to taking an exam. To test this hypothesis, the professor has one of classes consume avocados prior to a very difficult pass/fail examination. The other class does not consume avocados, and also completes the same examination. He collects the results of his experiment, which are as follows:

Class 1 (Avocado Consumers)

Pass: 15

Fail: 5

Class 2 (Avocado Abstainers)

Pass: 10

Fail: 15

It is also worth mentioning that professor will be assuming an alpha value of .05.

**# The data must first be entered into a matrix #**

Model <- matrix(c(15, 10, 5, 15), nrow = 2, ncol=2)

# Let’s examine the matrix to make sure everything was entered correctly #

Model

Model <- matrix(c(15, 10, 5, 15), nrow = 2, ncol=2)

# Let’s examine the matrix to make sure everything was entered correctly #

Model

__Console Output:__

*[,1] [,2]*

[1,] 15 5

[2,] 10 15

[1,] 15 5

[2,] 10 15

**# Now to apply Fisher’s Exact Test #**

fisher.test(Model)

fisher.test(Model)

__Console Output:__

*Fisher's Exact Test for Count Data*

data: Model

p-value = 0.03373

alternative hypothesis: true odds ratio is not equal to 1

95 percent confidence interval:

1.063497 20.550173

sample estimates:

odds ratio

4.341278

data: Model

p-value = 0.03373

alternative hypothesis: true odds ratio is not equal to 1

95 percent confidence interval:

1.063497 20.550173

sample estimates:

odds ratio

4.341278

**Findings:**Fisher’s Exact Test was applied to our experimental findings for analysis. The results of such indicated a significant relationship as it pertains to avocado consumption and examination success: 75% (15/20), as compared to non-consumption and examination success: 40% (10/25); (p = .03).

If we were to apply the Chi-Squared Test to the same data matrix, we would receive the following output:

**# Application of Chi-Squared Test to prior experimental observations #**

**chisq.test(Model, correct = FALSE)**

__Console Output:__

*Pearson's Chi-squared test*

data: Model

X-squared = 5.5125, df = 1, p-value = 0.01888

data: Model

X-squared = 5.5125, df = 1, p-value = 0.01888

__Findings:__As you might have expected, the application of the Chi-Squared Test yielded an even smaller p-value! If we were to utilize this test in lieu of The Fisher’s Exact Test, our results would also demonstrate significance.

That is all for this entry.

Thank you for your patronage.

I hope to see you again soon.

-RD

That is all for this entry.

Thank you for your patronage.

I hope to see you again soon.

-RD