t-test in R Programming - Mini Project: Build & Apply

Performing a t-test in R

📖 Scenario: You are a scientist studying the effect of a new fertilizer on plant growth. You have measured the heights of plants with and without the fertilizer. You want to check if the fertilizer makes a significant difference in plant height.

🎯 Goal: Learn how to perform a t-test in R to compare two groups of data and interpret the result.

📋 What You'll Learn

Create two numeric vectors with exact plant height values

Create a variable to hold the significance level

Use the t.test() function to compare the two groups

Print the p-value from the t-test result

💡 Why This Matters

🌍 Real World

Scientists and researchers use t-tests to check if two groups have different averages, like testing new medicines or fertilizers.

💼 Career

Data analysts and scientists often perform t-tests to make decisions based on data and prove if changes have real effects.

1

Create the plant height data

Create two numeric vectors called control and fertilized with these exact values: control = c(15, 16, 14, 15, 16), fertilized = c(18, 19, 17, 20, 18).

R Programming

# Create the plant height data vectors
# Your code here

Hint

Use the c() function to create numeric vectors with the exact values given.

2

Set the significance level

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

R Programming

control <- c(15, 16, 14, 15, 16)
fertilized <- c(18, 19, 17, 20, 18)
# Create the significance level variable alpha
# Your code here

Hint

Just assign the value 0.05 to a variable named alpha.

3

Perform the t-test

Use the t.test() function with control and fertilized as inputs and save the result in a variable called test_result.

R Programming

control <- c(15, 16, 14, 15, 16)
fertilized <- c(18, 19, 17, 20, 18)
alpha <- 0.05
# Perform the t-test and save the result
# Your code here

Hint

Use t.test(control, fertilized) and assign it to test_result.

4

Print the p-value

Print the p-value from test_result using print() and accessing the $p.value element.

R Programming

control <- c(15, 16, 14, 15, 16)
fertilized <- c(18, 19, 17, 20, 18)
alpha <- 0.05
test_result <- t.test(control, fertilized)
# Print the p-value from test_result
# Your code here

Hint

Use print(test_result$p.value) to show the p-value.

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