t-test (ttest_ind, ttest_rel) in SciPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the purpose of a t-test in statistics?

A t-test helps us compare the means of two groups to see if they are different in a meaningful way, considering the variation in data.

beginner

What is the difference between ttest_ind and ttest_rel in scipy?

ttest_ind compares means of two independent groups (like two different classes). ttest_rel compares means of two related groups (like before and after measurements on the same people).

beginner

In a t-test, what does the p-value tell us?

The p-value shows the chance that the difference we see happened by random luck. A small p-value (usually less than 0.05) means the difference is likely real.

beginner

When should you use a paired t-test (ttest_rel)?

Use a paired t-test when the two sets of data are linked or matched, like measuring the same people before and after a treatment.

intermediate

What assumptions do t-tests make about the data?

T-tests assume the data is roughly normally distributed and that the groups have similar variances. For ttest_ind, the groups should be independent.

Which scipy function compares means of two independent samples?

A chi2_contingency

B ttest_rel

C anova

D ttest_ind

ttest_ind is used for independent samples.

When should you use ttest_rel?

A Comparing more than two groups

B Comparing two unrelated groups

C Comparing two related or paired groups

D Testing categorical data

ttest_rel is for related or paired samples.

What does a p-value less than 0.05 usually mean in a t-test?

A No difference between groups

B Strong evidence of a difference

C Data is not normal

D Test failed

A p-value below 0.05 suggests the difference is statistically significant.

Which assumption is NOT required for a t-test?

A Data must be categorical

B Groups have equal variances

C Data is normally distributed

D Samples are independent for <code>ttest_ind</code>

T-tests require numerical data, not categorical.

If you measure the same group twice, which test is best?

A ttest_rel

B correlation test

C chi-square test

D ttest_ind

Repeated measures on the same group use ttest_rel.

Explain the difference between ttest_ind and ttest_rel and give an example of when to use each.

Think about whether the data points in the two groups are connected or not.

Describe what a p-value means in the context of a t-test and how you decide if the difference is significant.

Consider how confident you are that the groups truly differ.

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