Chi-squared test in R Programming - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the purpose of the Chi-squared test?

The Chi-squared test checks if there is a significant association between two categorical variables by comparing observed data with expected data under the assumption of independence.

beginner

In R, which function is commonly used to perform a Chi-squared test on a contingency table?

The chisq.test() function is used to perform the Chi-squared test on a contingency table in R.

beginner

What kind of data is required to use the Chi-squared test?

The data must be categorical and organized in a contingency table showing counts or frequencies for each category combination.

intermediate

What does a low p-value from a Chi-squared test indicate?

A low p-value (usually less than 0.05) suggests that the observed data is unlikely under the assumption of independence, so we reject the null hypothesis and conclude there is an association between variables.

intermediate

How do you interpret the Chi-squared statistic value?

The Chi-squared statistic measures how much the observed counts deviate from the expected counts. Larger values indicate greater difference and stronger evidence against independence.

Which R function performs the Chi-squared test?

A t.test()

B chisq.test()

C lm()

D cor()

The chisq.test() function is designed for Chi-squared tests on categorical data.

What type of data is needed for a Chi-squared test?

A Categorical data in a contingency table

B Numerical continuous data

C Time series data

D Text data

Chi-squared tests require categorical data arranged in a contingency table showing counts.

A p-value less than 0.05 in a Chi-squared test means:

A Variables are associated

B Data is numerical

C Test is invalid

D Variables are independent

A low p-value means we reject independence and conclude variables are associated.

What does the Chi-squared statistic measure?

A Correlation coefficient

B Mean of the data

C Difference between observed and expected counts

D Variance of the data

It measures how much observed counts differ from expected counts under independence.

Which of these is NOT a requirement for the Chi-squared test?

A Data must be categorical

B Expected counts should be sufficiently large

C Data arranged in a contingency table

D Data must be normally distributed

Normal distribution is not required for the Chi-squared test.

Explain how to perform a Chi-squared test in R using a contingency table.

Think about how you organize data and call the test function.

Describe what a significant Chi-squared test result tells you about two categorical variables.

Focus on what the test result means for the relationship between variables.

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