t-test (ttest_ind, ttest_rel) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of independent t-test on two samples

What is the output of the following code snippet that performs an independent t-test between two groups?

SciPy

from scipy.stats import ttest_ind
import numpy as np
np.random.seed(0)
group1 = np.random.normal(10, 2, 30)
group2 = np.random.normal(12, 2, 30)
result = ttest_ind(group1, group2)
print((round(result.statistic, 2), round(result.pvalue, 3)))

A (0.45, 0.655)

B (4.03, 0.000)

C (-4.03, 0.000)

D (-0.45, 0.655)

💡 Hint

Remember that ttest_ind returns a statistic and p-value. The sign of the statistic depends on which group mean is larger.

The independent t-test compares means of two independent samples. Since group2 has a higher mean, the t-statistic is negative. The p-value is very small, indicating a significant difference.

❓ data_output

intermediate

Number of significant paired differences

Given the paired samples below, how many pairs show a significant difference at alpha=0.05 using a paired t-test?

SciPy

from scipy.stats import ttest_rel
import numpy as np
np.random.seed(1)
before = np.array([20, 22, 19, 24, 30, 28, 25, 27])
after = np.array([21, 23, 18, 25, 29, 30, 26, 28])
result = ttest_rel(before, after)
print((round(result.statistic, 3), round(result.pvalue, 3)))

A Statistic: -1.414, p-value: 0.197

B Statistic: 1.414, p-value: 0.197

C Statistic: -2.828, p-value: 0.025

D Statistic: 2.828, p-value: 0.025

💡 Hint

Paired t-test compares means of differences. The sign depends on which sample is larger on average.

The paired t-test statistic is negative because the 'before' values are slightly greater than 'after' values on average. The p-value is above 0.05, so differences are not significant.

🔧 Debug

advanced

Identify the error in t-test code

What error will this code raise when run?

SciPy

from scipy.stats import ttest_ind
import numpy as np
a = np.array([1, 2, 3])
b = np.array([4, 5])
result = ttest_ind(a, b)
print(result)

A TypeError: unsupported operand type(s) for -: 'int' and 'str'

B ValueError: operands could not be broadcast together

C IndexError: index out of bounds

D No error, outputs t-statistic and p-value

💡 Hint

Check if ttest_ind requires equal length arrays.

ttest_ind works with arrays of different lengths because it compares independent samples. No error occurs.

🧠 Conceptual

advanced

Choosing between ttest_ind and ttest_rel

Which situation correctly describes when to use ttest_rel instead of ttest_ind?

A Comparing test scores of students before and after a training program

B Comparing heights of men and women in a population

C Comparing sales of two different stores in different cities

D Comparing average temperatures of two different months

💡 Hint

ttest_rel is for paired or related samples.

ttest_rel is used when samples are related or paired, like measurements before and after treatment on the same subjects.

🚀 Application

expert

Interpreting t-test results for clinical trial data

A clinical trial measures blood pressure before and after treatment for 15 patients. The paired t-test returns statistic=3.25 and p-value=0.006. What is the correct interpretation?

A There is no significant change in blood pressure because p-value is greater than 0.01.

B The treatment caused a significant change in blood pressure (p < 0.05), so we reject the null hypothesis.

C The treatment has no effect because the t-statistic is positive.

D The sample size is too small to conclude anything from the test.

💡 Hint

Check the p-value against common significance levels.

A p-value of 0.006 is less than 0.05, indicating a statistically significant difference. The positive t-statistic shows the direction of change.

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