Chi-squared test in R Programming

Introduction

The Chi-squared test helps us check if two groups are related or independent by comparing counts in categories.

You want to see if a new medicine affects recovery rates differently between men and women.

You want to check if people prefer different ice cream flavors based on their age group.

You want to find out if a survey response depends on the city where people live.

Syntax

R Programming

chisq.test(x, y = NULL, correct = TRUE, ...)

x can be a table or matrix of counts.

If y is given, it should be a factor or vector to compare with x.

Examples

Test independence on a 2x2 table of counts.

R Programming

counts <- matrix(c(10, 20, 30, 40), nrow = 2)
chisq.test(counts)

Test if counts in one group differ from expected.

R Programming

group <- factor(c('A', 'A', 'B', 'B'))
result <- chisq.test(table(group))

Sample Program

This program tests if liking or disliking something depends on gender using a 2x2 table.

R Programming

counts <- matrix(c(12, 5, 7, 10), nrow = 2, byrow = TRUE)
rownames(counts) <- c('Male', 'Female')
colnames(counts) <- c('Like', 'Dislike')
result <- chisq.test(counts)
print(result)

Important Notes

The test works best with counts, not percentages.

Expected counts should be at least 5 for reliable results.

Yates' correction is applied by default for 2x2 tables to avoid overestimating significance.

Summary

The Chi-squared test checks if two categorical variables are related.

Use it with tables of counts, like survey results or group preferences.

Look at the p-value to decide if the relationship is significant or not.

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