How to Perform
Chi-Square Test
of Independence in R

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What is a Chi-Square Test?

The chi-square test is a statistical test that can be used when we want to determine whether some observed frequencies deviate from the frequencies we would expect under a certain hypothesis. With this test, we examine whether there is an association between two variables, and it shows the probability of association. The Chi-square test is used when we have two categorical variables with two or more groups.

When Should a Chi-Square be Used?

You can use a chi-square test of independence when you have two categorical variables. It allows you to test whether the two variables are related to each other. If two variables are independent (unrelated), the probability of belonging to a certain group of one variable isn’t affected by the other variable

An Example Of a Chi-Square Test

For example, a researcher wants to check if there is a relationship between gender and math exam results. In that case, we have two categorical variables: gender (male, female) and math exam result (passed the exam or not).

Therefore, we test the following hypotheses:

Null hypothesis: There is no association between gender and math exam scores.

Alternative hypothesis: There is an association between gender and math exam scores.

R function to Compute Chi-Square Test

The code to run a Chi-Square Test using R is as follows:

chisq.test(V1, V2, data = dataframe)

For this, the chisq.test() the function is used.

Running Chi-Square Test in Rstudio

In this section, we will show you how to run the chi-square test using the r studio program and how to interpret the test results after we obtain the result of the test. In the first part, we present the r program code and function for the chi-square test. Next, you will see the outputs as a result of running the r codes. In the last section, you can find the interpretation of the chi-square test in APA format.

# LOAD DATA
library(readxl)
Data <- read_excel(“Data.xlsx“)
# VIEW DATA
View(Data)
# NAME VARIABLES
data <- Data
gender <- data$gender
mathexam <- data$mathexam

#CHI-SQUARE TEST OF INDEPENDENCE

chisq <- chisq.test(gender, mathexam)

chisq

chisq$observed
round(chisq$expected,2)

> chisq <- chisq.test(gender, mathexam)
> chisq

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  gender and mathexam
## X-squared = 1.9423, df = 1, p-value = 0.1634

> chisq$observed

##         mathexam
## gender   NO YES
##   female 17  27
##   male   13  42

> round(chisq$expected,2)

##         mathexam
## gender      NO   YES
##   female 13.33 30.67
##   male   16.67 38.33

Reporting Chi-Square Test in R

A Chi-square test of independence was conducted to determine whether success on math exam scores (yes, no) is related to gender (male, female). The results are non-significant, X-squared (1) = 1.94,p = 0.163. We, therefore, fail to reject the null hypothesis and conclude that there is no association between success on math exam scores (yes, no) and gender (male, female). There were 17 females who did not pass the math exam (13.33%), and 27 who pass (30.67%). There were 13 males who did not pass the math exam (16.67%), and 42 who pass (38.33%).

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How to Perform Chi-Square Test of Independence in R