Chi-squared test in R Programming - Mini Project: Build & Apply

Chi-squared Test in R

📖 Scenario: You are a researcher studying if two categorical variables are related. For example, you want to check if gender and preference for a product are independent.

🎯 Goal: Build a simple R program that creates a contingency table, sets up a significance level, performs a chi-squared test, and prints the test result.

📋 What You'll Learn

Create a contingency table with exact counts

Set a significance level variable

Perform a chi-squared test using the table

Print the test result

💡 Why This Matters

🌍 Real World

Chi-squared tests are used in research to check if two categories are related, like gender and product preference.

💼 Career

Data analysts and scientists use chi-squared tests to analyze survey data and make decisions based on categorical data relationships.

1

Create the contingency table

Create a matrix called data_matrix with these exact values and dimensions: 2 rows and 2 columns. The values are 30, 10 in the first row and 20, 40 in the second row. Set the row names to c("Male", "Female") and column names to c("Like", "Dislike").

R Programming

# Create the matrix data_matrix with given values and row/column names
# Your code here

Hint

Use matrix() with byrow = TRUE to fill rows first. Then assign row and column names with rownames() and colnames().

2

Set the significance level

Create a variable called alpha and set it to 0.05 to represent the significance level for the test.

R Programming

data_matrix <- matrix(c(30, 10, 20, 40), nrow = 2, byrow = TRUE)
rownames(data_matrix) <- c("Male", "Female")
colnames(data_matrix) <- c("Like", "Dislike")
# Create alpha variable and set to 0.05
# Your code here

Hint

Just assign 0.05 to a variable named alpha.

3

Perform the chi-squared test

Use the chisq.test() function on data_matrix and save the result in a variable called test_result.

R Programming

data_matrix <- matrix(c(30, 10, 20, 40), nrow = 2, byrow = TRUE)
rownames(data_matrix) <- c("Male", "Female")
colnames(data_matrix) <- c("Like", "Dislike")
alpha <- 0.05
# Perform chi-squared test and save to test_result
# Your code here

Hint

Use chisq.test() with the matrix as input and assign the output to test_result.

4

Print the test result

Print the variable test_result to display the chi-squared test output.

R Programming

data_matrix <- matrix(c(30, 10, 20, 40), nrow = 2, byrow = TRUE)
rownames(data_matrix) <- c("Male", "Female")
colnames(data_matrix) <- c("Like", "Dislike")
alpha <- 0.05
test_result <- chisq.test(data_matrix)
# Print the test_result
# Your code here

Hint

Use print(test_result) to show the test output.

Practice

1. What does the Chi-squared test in R primarily check for?

easy

A. Whether two categorical variables are related

B. Whether two numerical variables have the same mean

C. Whether a variable follows a normal distribution

D. Whether the data contains missing values

Solution

1. Step 1: Understand the purpose of the Chi-squared test

   The Chi-squared test is used to check if there is an association between two categorical variables.

2. Step 2: Compare with other options

   Options A and B relate to numerical data tests, and D is about data quality, not relationships.

3. Final Answer:

   Whether two categorical variables are related -> Option A

4. Quick Check:

   Chi-squared test checks categorical variable relationship = C [OK]

Hint: Chi-squared tests relationships between categories, not numbers [OK]

Common Mistakes:

• Confusing Chi-squared with t-test or ANOVA
• Thinking it tests numerical data means
• Assuming it checks data normality

2. Which of the following is the correct way to perform a Chi-squared test on a table named tbl in R?

easy

A. chisq(tbl)

B. chisq.test(tbl)

C. chi.test(tbl)

D. test.chisq(tbl)

Solution

1. Step 1: Recall the correct function name in R

   The function to perform a Chi-squared test in R is chisq.test().

2. Step 2: Check the syntax

   The correct syntax is calling chisq.test() with the table as the argument.

3. Final Answer:

   chisq.test(tbl) -> Option B

4. Quick Check:

   Correct function is chisq.test() = B [OK]

Hint: Use chisq.test() function for Chi-squared test in R [OK]

Common Mistakes:

• Using incorrect function names like chisq() or chi.test()
• Placing the function name after the table
• Forgetting parentheses after function name

3. What will be the output of the following R code?

tbl <- matrix(c(10, 20, 30, 40), nrow=2)
result <- chisq.test(tbl)
round(result$p.value, 3)

medium

A. 0.504

B. 0.025

C. 0.000

D. Error: object 'result' not found

Solution

1. Step 1: Understand the input table

   The matrix has counts: 10, 20 in first row and 30, 40 in second row.

2. Step 2: Perform Chi-squared test and check p-value

   Running chisq.test on this table gives a p-value around 0.504, meaning no strong association.

3. Final Answer:

   0.504 -> Option A

4. Quick Check:

   Chi-squared p-value rounded = 0.504 [OK]

Hint: Check p-value from chisq.test() to judge significance [OK]

Common Mistakes:

• Confusing p-value with test statistic
• Expecting zero p-value for small counts
• Mistaking error message for output

4. Identify the error in this R code snippet for Chi-squared test:

data <- matrix(c(5, 15, 20, 10), ncol=2)
chisq.test(data)

medium

A. Matrix should have rows and columns swapped

B. chisq.test() requires a data frame, not a matrix

C. No error, code runs correctly

D. Matrix must be named 'tbl' to work

Solution

1. Step 1: Check matrix creation

   The matrix is created with 4 values and 2 columns, which is valid.

2. Step 2: Check chisq.test() input type

   chisq.test() accepts a matrix of counts, so this input is valid and runs without error.

3. Final Answer:

   No error, code runs correctly -> Option C

4. Quick Check:

   chisq.test() accepts matrix input = A [OK]

Hint: chisq.test() works with matrices or tables of counts [OK]

Common Mistakes:

• Thinking chisq.test() only accepts data frames
• Assuming matrix dimensions must be square
• Believing variable name affects function

5. You have survey data of 3 groups choosing among 3 products. How do you apply a Chi-squared test in R to check if product preference depends on group?

group <- c('A', 'A', 'B', 'B', 'C', 'C')
product <- c('X', 'Y', 'X', 'Z', 'Y', 'Z')
# What next?

hard

A. Convert group and product to numeric and run chisq.test()

B. Run chisq.test(group, product) directly without table

C. Use t.test() on group and product vectors

D. Create a table with table(group, product) then run chisq.test() on it

Solution

1. Step 1: Create a contingency table

   Use table(group, product) to get counts of each group-product combination.

2. Step 2: Apply Chi-squared test on the table

   Run chisq.test() on the table to test independence between group and product preference.

3. Final Answer:

   Create a table with table(group, product) then run chisq.test() on it -> Option D

4. Quick Check:

   Table then chisq.test() = A [OK]

Hint: Always make a table before chisq.test() for categorical data [OK]

Common Mistakes:

• Trying to run chisq.test() on raw vectors
• Using t.test() instead of chisq.test() for categories
• Converting categories to numbers incorrectly