In continuing to explore this subject matter, today's entry will present an additional test of similar nature, the Fisher's Exact Test.

If you are un-familiar with the premise of non-parametric data types, please search the term: "non -parametric", in the search box located on the right.

__Fisher's Exact Test__Fisher's Exact Test provides a non-parametric alternative to the chi-square test, as normality is a requirement for the chi-square test's utilization. This test is sometimes confused with the "F-Test", which was named in honor of biologist and statistician Ronald Fisher. However, Ronald Fisher himself derived this particular test, and as such, it bears his name.

__Example:__While working as a statistician at a local university, you are tasked to evaluate, based on survey data, the level of job satisfaction that each member of the staff currently has for their occupational role. The data that you gather from the surveys is as follows:

__General Faculty__

130 Satisfied 20 Unsatisfied (Total 150 Members of General Faculty)

__Professors__

30 Satisfied 20 Unsatisfied (Total 50 Professors)

First, we will need to input this survey data into R as a matrix. This can be achieved by utilizing the code below:

**# Fisher's Exact Test #**

model <- matrix(c(130, 30, 20, 20), ncol=2)

model <- matrix(c(130, 30, 20, 20), ncol=2)

The result should resemble:

**fisher.test(model, conf.level = .95)**

This produces the output:

Fisher's Exact Test for Count Data

data: model

p-value = 0.0001467

alternative hypothesis: true odds ratio is not equal to 1

95 percent confidence interval:

1.933511 9.623258

sample estimates:

odds ratio

data: model

p-value = 0.0001467

alternative hypothesis: true odds ratio is not equal to 1

95 percent confidence interval:

1.933511 9.623258

sample estimates:

odds ratio

*4.294116*

The p-value output will be examined for significance. It is this value which is analyzed to assess the stated hypothesis, which is as follows:

**H0: The association is random.**

HA: The association is NOT random.

HA: The association is NOT random.

Since the p-value contained within the output (0.0001467), is less than our assumed alpha (.05), we will reject the null hypothesis, and assume that the association is not random.

The odds ratio is calculated in the following manner:

**a <- (130 / 20)**

b <- (30 / 20)

c <- a/b

c

b <- (30 / 20)

c <- a/b

c

Which produces the output:

*[1] 4.333333*

That’s it for now, Data Heads. Stay subscribed for more interesting articles!

## No comments:

## Post a Comment

Note: Only a member of this blog may post a comment.