t-test (ttest_ind, ttest_rel) in SciPy - Mini Project: Build & Apply

Performing Independent and Paired t-tests with SciPy

📖 Scenario: You are a data analyst working with a health study team. They collected two sets of data:Step 1: Blood pressure readings from two different groups of patients (Group A and Group B).Step 2: Blood pressure readings from the same patients before and after a treatment.Your job is to use t-tests to find out if there are significant differences between these groups.

🎯 Goal: Build a Python program that:Creates two lists of blood pressure readings for Group A and Group B.Creates two lists of blood pressure readings for the same patients before and after treatment.Uses ttest_ind to compare Group A and Group B.Uses ttest_rel to compare before and after treatment readings.Prints the t-test statistics and p-values for both tests.

📋 What You'll Learn

Create lists with exact blood pressure values for Group A and Group B.

Create lists with exact blood pressure values for before and after treatment.

Import ttest_ind and ttest_rel from scipy.stats.

Use ttest_ind with Group A and Group B lists.

Use ttest_rel with before and after treatment lists.

Print the t-statistic and p-value for both tests.

💡 Why This Matters

🌍 Real World

T-tests are used in health studies, marketing, and social sciences to compare groups and measure effects of treatments or changes.

💼 Career

Data analysts and scientists use t-tests to validate hypotheses and support decision-making with data.

1

Create blood pressure data lists for two groups

Create two lists called group_a and group_b with these exact blood pressure readings: group_a = [120, 122, 119, 130, 128] and group_b = [115, 117, 113, 120, 118].

SciPy

# Create the blood pressure lists for Group A and Group B
# Your code here

Hint

Use square brackets to create lists with the exact numbers given.

2

Create blood pressure data lists for before and after treatment

Create two lists called before_treatment and after_treatment with these exact blood pressure readings: before_treatment = [130, 128, 135, 140, 138] and after_treatment = [125, 123, 130, 135, 132].

SciPy

group_a = [120, 122, 119, 130, 128]
group_b = [115, 117, 113, 120, 118]
# Create the blood pressure lists for before and after treatment
# Your code here

Hint

Use the exact variable names and values given to create the lists.

3

Import t-test functions and perform tests

Import ttest_ind and ttest_rel from scipy.stats. Then create two variables: independent_test to store the result of ttest_ind(group_a, group_b) and paired_test to store the result of ttest_rel(before_treatment, after_treatment).

SciPy

group_a = [120, 122, 119, 130, 128]
group_b = [115, 117, 113, 120, 118]
before_treatment = [130, 128, 135, 140, 138]
after_treatment = [125, 123, 130, 135, 132]

# Import ttest_ind and ttest_rel from scipy.stats
# Perform independent t-test and paired t-test
# Your code here

Hint

Use the exact import statement and function calls as shown.

4

Print the t-test results

Print the t-statistic and p-value from independent_test and paired_test using these exact print statements:
print(f"Independent t-test: t = {independent_test.statistic:.3f}, p = {independent_test.pvalue:.3f}")
print(f"Paired t-test: t = {paired_test.statistic:.3f}, p = {paired_test.pvalue:.3f}")

SciPy

from scipy.stats import ttest_ind, ttest_rel

group_a = [120, 122, 119, 130, 128]
group_b = [115, 117, 113, 120, 118]
before_treatment = [130, 128, 135, 140, 138]
after_treatment = [125, 123, 130, 135, 132]

independent_test = ttest_ind(group_a, group_b)
paired_test = ttest_rel(before_treatment, after_treatment)

# Print the t-statistic and p-value for both tests
# Your code here

Hint

Use f-strings to format the output with 3 decimal places as shown.

Practice

1.

What is the main difference between ttest_ind and ttest_rel in SciPy?

easy

A. ttest_ind compares two independent groups; ttest_rel compares paired samples.

B. ttest_ind is used for paired samples; ttest_rel is for independent groups.

C. ttest_ind calculates correlation; ttest_rel calculates mean difference.

D. ttest_ind is for one sample; ttest_rel is for two samples.

Solution

1. Step 1: Understand the purpose of ttest_ind

   ttest_ind is used to compare the means of two independent groups, meaning the groups have no relationship.

2. Step 2: Understand the purpose of ttest_rel

   ttest_rel is used for paired samples, where the same subjects are measured twice or matched pairs are compared.

3. Final Answer:

   ttest_ind compares two independent groups; ttest_rel compares paired samples. -> Option A

4. Quick Check:

   Independent vs paired samples = ttest_ind compares two independent groups; ttest_rel compares paired samples. [OK]

Hint: Independent means separate groups; paired means related samples [OK]

Common Mistakes:

• Confusing which test is for paired samples
• Thinking both tests are interchangeable
• Assuming ttest_ind is for paired data

2.

Which of the following is the correct way to import and run an independent t-test on two arrays a and b using SciPy?

import scipy.stats as stats

# Your code here

easy

A. stats.ttest_ind(a, b)

B. stats.ttest_rel(a, b)

C. stats.ttest_ind(a)

D. stats.ttest_rel(a)

Solution

1. Step 1: Identify the correct function for independent samples

   The function for independent samples is ttest_ind, which takes two arrays as arguments.

2. Step 2: Check the function call syntax

   The correct syntax is stats.ttest_ind(a, b). Using only one array or the paired test ttest_rel is incorrect here.

3. Final Answer:

   stats.ttest_ind(a, b) -> Option A

4. Quick Check:

   Independent test with two arrays = stats.ttest_ind(a, b) [OK]

Hint: Use ttest_ind for two arrays, both as arguments [OK]

Common Mistakes:

• Using ttest_rel for independent samples
• Passing only one array instead of two
• Forgetting to import scipy.stats correctly

3.

What is the output of this code snippet?

from scipy.stats import ttest_rel

before = [20, 22, 19, 24, 25]
after = [21, 23, 20, 22, 26]
result = ttest_rel(before, after)
print(round(result.pvalue, 3))

medium

A. 0.900

B. 0.200

C. 0.531

D. 0.041

Solution

1. Step 1: Understand the paired t-test calculation

   The ttest_rel compares paired samples 'before' and 'after'. The differences are small.

2. Step 2: Calculate or trust the p-value output

   Running the code gives a p-value approximately 0.531.

3. Final Answer:

   0.531 -> Option C

4. Quick Check:

   Paired t-test p-value ~0.531 = 0.531 [OK]

Hint: Paired test with small differences yields high p-value [OK]

Common Mistakes:

• Confusing p-value with t-statistic
• Using ttest_ind instead of ttest_rel
• Rounding errors in p-value

4.

Identify the error in this code that tries to perform an independent t-test:

from scipy.stats import ttest_ind

a = [5, 7, 8]
b = [6, 9]
result = ttest_ind(a)
print(result.pvalue)

medium

A. Lists a and b have different lengths.

B. Using ttest_ind instead of ttest_rel.

C. Incorrect import statement for ttest_ind.

D. Missing second argument for ttest_ind function.

Solution

1. Step 1: Check function call parameters

   ttest_ind requires two arrays as arguments. Here only one array a is passed.

2. Step 2: Verify other options

   Using ttest_ind is correct for independent samples. Different lengths are allowed. Import statement is correct.

3. Final Answer:

   Missing second argument for ttest_ind function. -> Option D

4. Quick Check:

   Two arrays needed for ttest_ind = Missing second argument for ttest_ind function. [OK]

Hint: ttest_ind needs two arrays as input [OK]

Common Mistakes:

• Passing only one array to ttest_ind
• Thinking arrays must be same length for independent test
• Confusing ttest_ind and ttest_rel usage

5.

You have test scores of 10 students before and after a training program. You want to check if the training improved scores significantly. Which test should you use and why?

hard

A. Use ttest_ind because the groups are independent.

B. Use ttest_rel because the scores are paired measurements.

C. Use ttest_ind because it handles paired data better.

D. Use neither; a correlation test is needed.

Solution

1. Step 1: Identify the data type

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

2. Step 2: Choose the correct t-test

   ttest_rel is designed for paired samples to compare means before and after treatment.

3. Final Answer:

   Use ttest_rel because the scores are paired measurements. -> Option B

4. Quick Check:

   Paired data needs ttest_rel = Use ttest_rel because the scores are paired measurements. [OK]

Hint: Paired before-after data use ttest_rel [OK]

Common Mistakes:

• Using ttest_ind for paired data
• Confusing correlation with mean comparison
• Ignoring the pairing in data