t-test in R Programming

Introduction

A t-test helps you check if two groups have different average values. It tells you if the difference is real or just by chance.

Comparing average test scores of two classes to see if one did better.

Checking if a new medicine changes blood pressure compared to no treatment.

Seeing if two machines produce parts with different average sizes.

Testing if a diet plan changes average weight before and after.

Syntax

R Programming

t.test(x, y = NULL, alternative = c("two.sided", "less", "greater"), paired = FALSE, var.equal = FALSE, mu = 0)

x is the first group of numbers.

y is the second group (optional for one-sample test).

Examples

Compare two groups to see if their averages differ.

R Programming

t.test(group1, group2)

Compare measurements before and after on the same subjects.

R Programming

t.test(before, after, paired = TRUE)

Check if the average of x is different from 10.

R Programming

t.test(x, mu = 10)

Sample Program

This program compares two groups of numbers and prints the p-value. The p-value shows if the difference in averages is likely real.

R Programming

group1 <- c(5, 6, 7, 8, 9)
group2 <- c(7, 8, 9, 10, 11)
result <- t.test(group1, group2)
print(result$p.value)

Important Notes

A small p-value (usually less than 0.05) means the groups are likely different.

Use paired = TRUE when the same subjects are measured twice.

Set var.equal = TRUE if you believe both groups have the same variance.

Summary

A t-test checks if two groups have different averages.

It gives a p-value to help decide if the difference is real.

Use it for comparing groups or before/after measurements.

Practice

1.

What does a t-test primarily compare in two groups?

easy

A. The difference between their medians

B. The difference between their averages

C. The total number of observations

D. The variance of each group

Solution

1. Step 1: Understand the purpose of a t-test

   A t-test is used to compare the means (averages) of two groups to see if they are different.

2. Step 2: Identify what is compared

   The test focuses on the average values, not medians, counts, or variances.

3. Final Answer:

   The difference between their averages -> Option B

4. Quick Check:

   t-test compares means = A [OK]

Hint: Remember: t-test checks averages, not medians or counts [OK]

Common Mistakes:

• Confusing mean with median
• Thinking it compares counts
• Assuming it compares variances

2.

Which of the following is the correct way to run a t-test in R comparing two numeric vectors x and y?

easy

A. t_test(x, y)

B. ttest(x, y)

C. t.test(x, y)

D. test.t(x, y)

Solution

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

   The built-in function for t-test in R is t.test().

2. Step 2: Check the syntax for comparing two vectors

   Using t.test(x, y) compares the two numeric vectors correctly.

3. Final Answer:

   t.test(x, y) -> Option C

4. Quick Check:

   Correct function is t.test() = A [OK]

Hint: Use exact function name t.test() with dot [OK]

Common Mistakes:

• Misspelling the function name
• Using underscores instead of dots
• Confusing function with other test names

3.

What will be the output of this R code snippet?

group1 <- c(5, 7, 8, 6, 9)
group2 <- c(10, 12, 11, 13, 14)
test <- t.test(group1, group2)
round(test$p.value, 3)

medium

A. 0.001

B. 0.05

C. 0.5

D. 1.0

Solution

1. Step 1: Understand the data groups

   Group1 has smaller values around 5-9, Group2 has larger values around 10-14, so means differ.

2. Step 2: Interpret the p-value from t.test()

   Since the groups differ clearly, the p-value will be very small, close to 0.001 after rounding.

3. Final Answer:

   0.001 -> Option A

4. Quick Check:

   Distinct groups give low p-value = B [OK]

Hint: Big difference in groups means very small p-value [OK]

Common Mistakes:

• Assuming p-value is large for different groups
• Confusing p-value with test statistic
• Ignoring rounding in output

4.

Identify the error in this R code for a t-test:

data1 <- c(4, 5, 6)
data2 <- c(7, 8, 9)
test <- t.test(data1 + data2)

medium

A. t.test() cannot compare numeric vectors

B. Missing parentheses in t.test()

C. Vectors data1 and data2 must be data frames

D. Using '+' instead of ',' to separate vectors

Solution

1. Step 1: Check the function call syntax

   The t.test() function expects two separate vectors as arguments separated by a comma.

2. Step 2: Identify the mistake in argument passing

   The code uses '+' to add vectors instead of separating them with a comma, which is incorrect.

3. Final Answer:

   Using '+' instead of ',' to separate vectors -> Option D

4. Quick Check:

   Arguments must be comma-separated = D [OK]

Hint: Separate vectors with comma, not plus sign [OK]

Common Mistakes:

• Adding vectors instead of passing separately
• Confusing function arguments syntax
• Thinking t.test needs data frames

5.

You have two groups of exam scores: before and after a training program. Which t-test is best to check if the training improved scores?

hard

A. Paired t-test using t.test(before, after, paired=TRUE)

B. Two-sample t-test using t.test(before, after)

C. One-sample t-test using t.test(after)

D. Variance test using var.test(before, after)

Solution

1. Step 1: Understand the data relationship

   Scores are from the same students before and after training, so data are paired.

2. Step 2: Choose the correct t-test type

   A paired t-test compares matched pairs to see if scores changed after training.

3. Final Answer:

   Paired t-test using t.test(before, after, paired=TRUE) -> Option A

4. Quick Check:

   Paired data needs paired=TRUE = C [OK]

Hint: Use paired=TRUE for before-after same subjects [OK]

Common Mistakes:

• Using two-sample test for paired data
• Using one-sample test incorrectly
• Confusing variance test with t-test