Why statistical tests validate hypotheses in R Programming - See It in Action

Why Statistical Tests Validate Hypotheses

📖 Scenario: Imagine you are a scientist testing if a new medicine changes blood pressure. You collect data from patients and want to check if the medicine really works or if the changes happened by chance.

🎯 Goal: You will write a simple R program that uses a statistical test to check if the average blood pressure after medicine is different from before. This helps you understand how statistical tests validate hypotheses.

📋 What You'll Learn

Create a numeric vector called before with exact values: 120, 122, 119, 130, 125

Create a numeric vector called after with exact values: 115, 118, 117, 128, 120

Create a variable called alpha and set it to 0.05

Use t.test() with before and after to perform a paired t-test

Print the p-value from the test result

💡 Why This Matters

🌍 Real World

Scientists and researchers use statistical tests to check if their ideas about data are true or just random chance.

💼 Career

Understanding hypothesis testing is important for data analysts, scientists, and anyone working with data to make informed decisions.

1

Create the blood pressure data vectors

Create a numeric vector called before with values 120, 122, 119, 130, 125 and another numeric vector called after with values 115, 118, 117, 128, 120.

R Programming

# Create vectors before and after with given values
# Your code here

Hint

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

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

before <- c(120, 122, 119, 130, 125)
after <- c(115, 118, 117, 128, 120)
# Create alpha and set it to 0.05
# Your code here

Hint

Just assign 0.05 to a variable named alpha.

3

Perform the paired t-test

Use the t.test() function with before and after vectors to perform a paired t-test. Save the result in a variable called test_result.

R Programming

before <- c(120, 122, 119, 130, 125)
after <- c(115, 118, 117, 128, 120)
alpha <- 0.05
# Perform paired t-test and save to test_result
# Your code here

Hint

Use t.test(before, after, paired = TRUE) to compare paired samples.

4

Print the p-value from the test

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

R Programming

before <- c(120, 122, 119, 130, 125)
after <- c(115, 118, 117, 128, 120)
alpha <- 0.05
test_result <- t.test(before, after, paired = TRUE)
# Print the p-value
# Your code here

Hint

Use print(test_result$p.value) to show the p-value. The exact output will be close to 0.0027.

Practice

1. Why do we use statistical tests in R when working with data?
t.test() is an example of such a test. What is its main purpose?

easy

A. To create graphs and charts from data

B. To clean and organize data before analysis

C. To check if the data supports a specific idea or hypothesis

D. To store data in a database

Solution

1. Step 1: Understand the role of statistical tests

   Statistical tests like t.test() are used to check if the data supports a hypothesis or if observed results could be due to chance.

2. Step 2: Identify the main purpose of t.test()

   The t.test() compares means between groups to validate if differences are statistically significant, supporting or rejecting a hypothesis.

3. Final Answer:

   To check if the data supports a specific idea or hypothesis -> Option C

4. Quick Check:

   Statistical tests validate hypotheses = To check if the data supports a specific idea or hypothesis [OK]

Hint: Statistical tests check if data supports your idea [OK]

Common Mistakes:

• Thinking tests create graphs
• Confusing data cleaning with hypothesis testing
• Assuming tests store data

2. Which of the following is the correct way to perform a t-test in R to compare two groups stored in vectors group1 and group2?

easy

A. t.test(group1, group2)

B. t_test(group1, group2)

C. ttest(group1, group2)

D. test.t(group1, group2)

Solution

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

   The correct function for a t-test in R is t.test(), with a dot between 't' and 'test'.

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

   Calling t.test(group1, group2) compares the two vectors correctly.

3. Final Answer:

   t.test(group1, group2) -> Option A

4. Quick Check:

   Correct t-test syntax = t.test(group1, group2) [OK]

Hint: Remember R uses dot in function names like t.test() [OK]

Common Mistakes:

• Using underscores instead of dots in function names
• Misspelling the function name
• Using incorrect function order

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

set.seed(123)
group1 <- rnorm(10, mean=5)
group2 <- rnorm(10, mean=5.5)
test_result <- t.test(group1, group2)
round(test_result$p.value, 3)

medium

A. 0.001

B. 0.500

C. 0.900

D. 0.406

Solution

1. Step 1: Understand the code generating data

   Two groups of 10 random numbers are created with means 5 and 5.5, so they differ slightly.

2. Step 2: Perform t-test and check p-value

   The t-test compares these groups; the p-value shows the chance difference is random. With these means, p-value is about 0.406.

3. Final Answer:

   0.406 -> Option D

4. Quick Check:

   p-value ≈ 0.406 means difference likely due to chance = 0.406 [OK]

Hint: p-value > 0.05 means groups do not differ significantly; check rounded p-value [OK]

Common Mistakes:

• Ignoring set.seed causing different results
• Confusing p-value with test statistic
• Rounding incorrectly

4. Identify the error in this R code that tries to validate a hypothesis using a t-test:

data1 <- c(2, 3, 5, 7)
data2 <- c(3, 4, 6, 8)
test <- t.test(data1 + data2)

medium

A. Missing parentheses around vectors

B. Using '+' inside t.test instead of two separate vectors

C. t.test cannot be used with numeric vectors

D. Data vectors are too short for t.test

Solution

1. Step 1: Analyze the t.test function call

   The code uses t.test(data1 + data2), which adds vectors element-wise, producing a single vector.

2. Step 2: Understand correct usage of t.test

   t.test expects two separate vectors as arguments to compare groups, not their sum.

3. Final Answer:

   Using '+' inside t.test instead of two separate vectors -> Option B

4. Quick Check:

   t.test needs two groups, not their sum [OK]

Hint: Pass two vectors separately to t.test, not their sum [OK]

Common Mistakes:

• Adding vectors inside t.test
• Thinking t.test works on one combined vector
• Ignoring function argument rules

5. You want to check if a new teaching method improves test scores. You have scores before and after the method for 15 students stored in vectors before and after. Which R code correctly validates the hypothesis that scores improved?

hard

A. t.test(before, after, paired=TRUE, alternative='greater')

B. t.test(before, after, paired=FALSE, alternative='two.sided')

C. t.test(before, after, paired=FALSE, alternative='greater')

D. t.test(before, after, paired=TRUE, alternative='less')

Solution

1. Step 1: Identify paired data and hypothesis direction

   Scores before and after for same students means paired data. Improvement means after > before, so test if after is greater than before.

2. Step 2: Choose correct t.test parameters

   Use paired=TRUE for paired data. Since we want to check if scores improved (after > before), use alternative='greater'.

3. Final Answer:

   t.test(before, after, paired=TRUE, alternative='greater') -> Option A

4. Quick Check:

   Paired test with 'greater' alternative = t.test(before, after, paired=TRUE, alternative='greater') [OK]

Hint: Use paired=TRUE and alternative='greater' to test improvement [OK]

Common Mistakes:

• Not using paired=TRUE for same subjects
• Choosing wrong alternative hypothesis
• Using unpaired test for paired data