t-test with scipy.stats in Data Analysis Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a t-test used for in data analysis?

A t-test helps us compare the average values of two groups to see if they are different in a meaningful way.

beginner

Which function in scipy.stats is commonly used to perform a t-test for independent samples?

The function scipy.stats.ttest_ind() is used to compare the means of two independent groups.

beginner

What does the p-value from a t-test tell us?

The p-value shows the chance that the difference between groups happened by random chance. A small p-value (like less than 0.05) means the difference is likely real.

intermediate

How do you perform a paired t-test using scipy.stats?

Use scipy.stats.ttest_rel() to compare two related samples, like measurements before and after a treatment on the same subjects.

intermediate

What assumptions must be met to correctly use a t-test?

The data should be roughly normally distributed, the samples should be independent (except for paired tests), and variances should be similar for independent t-tests.

Which scipy.stats function is used for an independent two-sample t-test?

A ttest_1samp

B ttest_rel

C anova

D ttest_ind

ttest_ind compares means of two independent groups. ttest_rel is for paired samples, ttest_1samp compares one sample to a known value, and ANOVA is a different test.

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

A There is strong evidence the groups differ

B The groups are definitely the same

C The test was done incorrectly

D The sample size is too small

A p-value below 0.05 suggests the difference between groups is statistically significant, meaning it is unlikely due to chance.

Which t-test should you use to compare measurements before and after treatment on the same people?

A ttest_ind

B ttest_rel

C ttest_1samp

D chi-square test

ttest_rel is for paired samples, like before-and-after measurements on the same subjects.

Which assumption is NOT required for a t-test?

A Data is normally distributed

B Samples are independent (for independent t-test)

C Data is categorical

D Variances are similar between groups

T-tests require numerical data, not categorical data.

What does scipy.stats.ttest_1samp() do?

A Tests if a sample mean differs from a known value

B Compares two related groups

C Compares two independent groups

D Tests for correlation between variables

ttest_1samp tests if the average of one sample is different from a specific number.

Explain how to perform an independent t-test using scipy.stats and interpret the results.

Think about comparing two groups like test scores from two classes.

Describe the main assumptions behind using a t-test and why they matter.

Consider what could go wrong if data is very skewed or samples are related but treated as independent.

Practice

1.

What does a t-test help you find out in data analysis?

easy

A. If two groups have different average values

B. The total number of data points in a dataset

C. The exact values of all data points

D. How to sort data in ascending order

Solution

1. Step 1: Understand the purpose of a t-test

   A t-test compares the means (averages) of two groups to see if they are different.

2. Step 2: Identify what the t-test does not do

   It does not count data points, show exact values, or sort data.

3. Final Answer:

   If two groups have different average values -> Option A

4. Quick Check:

   T-test checks mean difference = A [OK]

Hint: T-test compares averages between groups [OK]

Common Mistakes:

• Thinking t-test counts data points
• Confusing t-test with sorting methods
• Assuming t-test shows exact data values

2.

Which of the following is the correct way to import the t-test function for independent samples from scipy.stats?

?

easy

A. from scipy.stats import ttest_ind

B. import scipy.stats.ttest_ind

C. from scipy import ttest_ind

D. import ttest_ind from scipy.stats

Solution

1. Step 1: Recall Python import syntax

   To import a specific function, use 'from module import function'.

2. Step 2: Match the correct import statement

   'from scipy.stats import ttest_ind' correctly imports the independent t-test function.

3. Final Answer:

   from scipy.stats import ttest_ind -> Option A

4. Quick Check:

   Correct import syntax = A [OK]

Hint: Use 'from module import function' to import specific functions [OK]

Common Mistakes:

• Using 'import scipy.stats.ttest_ind' which is invalid
• Trying 'from scipy import ttest_ind' missing 'stats'
• Writing 'import ttest_ind from scipy.stats' which is wrong syntax

3.

What will be the output of this code snippet?

import numpy as np
from scipy.stats import ttest_1samp

data = np.array([5, 7, 8, 6, 9])
test_stat, p_value = ttest_1samp(data, popmean=6)
print(round(p_value, 3))

medium

A. 0.045

B. 0.100

C. 0.500

D. 0.317

Solution

1. Step 1: Understand the t-test 1 sample function

   ttest_1samp tests if the sample mean differs from the population mean (6 here).

2. Step 2: Calculate the p-value for the data

   Using the data, the p-value is approximately 0.317, meaning no strong evidence against mean=6.

3. Final Answer:

   0.317 -> Option D

4. Quick Check:

   p-value from ttest_1samp = 0.317 [OK]

Hint: Round p-value to 3 decimals to compare easily [OK]

Common Mistakes:

• Confusing test statistic with p-value
• Using wrong population mean in function
• Not rounding p-value before comparing

4.

Identify the error in this code that tries to perform a paired t-test:

from scipy.stats import ttest_rel

data1 = [10, 12, 14, 16]
data2 = [11, 13, 15]

result = ttest_rel(data1, data2)
print(result.pvalue)

medium

A. Missing import for numpy

B. ttest_rel is not the correct function for paired tests

C. The two data lists have different lengths

D. print statement syntax is incorrect

Solution

1. Step 1: Check input data lengths for paired t-test

   Paired t-test requires both data arrays to have the same length because it compares pairs.

2. Step 2: Identify the mismatch in data lengths

   data1 has 4 elements, data2 has 3 elements, causing an error.

3. Final Answer:

   The two data lists have different lengths -> Option C

4. Quick Check:

   Paired t-test needs equal length arrays = C [OK]

Hint: Paired t-test needs equal length data arrays [OK]

Common Mistakes:

• Using different length arrays for paired test
• Confusing ttest_rel with independent t-test
• Assuming print syntax error without checking data

5.

You have two groups of exam scores:

group1 = [78, 85, 90, 88, 76]
group2 = [82, 79, 88, 91, 77]

You want to check if their average scores differ significantly. Which code correctly performs this test and interprets the result?

hard

A. from scipy.stats import ttest_ind
stat, p = ttest_ind(group1, group2)
if p > 0.05:
print('Different averages')
else:
print('No difference')

B. from scipy.stats import ttest_ind
stat, p = ttest_ind(group1, group2)
if p < 0.05:
print('Different averages')
else:
print('No difference')

C. from scipy.stats import ttest_rel
stat, p = ttest_rel(group1, group2)
if p < 0.01:
print('Different averages')
else:
print('No difference')

D. from scipy.stats import ttest_1samp
stat, p = ttest_1samp(group1, group2)
if p < 0.05:
print('Different averages')
else:
print('No difference')

Solution

1. Step 1: Choose the correct t-test for two independent groups

   ttest_ind is used for comparing two independent samples like group1 and group2.

2. Step 2: Interpret the p-value correctly

   If p-value is less than 0.05, we say averages differ; otherwise, no difference.

3. Final Answer:

   Use ttest_ind and check if p < 0.05 to decide difference -> Option B

4. Quick Check:

   Independent t-test + p < 0.05 means difference [OK]

Hint: Use ttest_ind for independent groups and p < 0.05 for difference [OK]

Common Mistakes:

• Using ttest_1samp for two groups
• Using ttest_rel for independent groups
• Reversing p-value condition for significance