t-test with scipy.stats in Data Analysis Python

Introduction

A t-test helps us check if two groups have different average values. It tells us if the difference is real or just by chance.

Comparing average test scores of two classes to see if one did better.

Checking if a new medicine changes blood pressure compared to no treatment.

Seeing if sales before and after a promotion are different.

Comparing average heights of plants grown with two different fertilizers.

Syntax

Data Analysis Python

from scipy import stats

# For one sample t-test
t_statistic, p_value = stats.ttest_1samp(sample_data, population_mean)

# For two independent samples t-test
t_statistic, p_value = stats.ttest_ind(sample1, sample2)

# For two related samples t-test (paired)
t_statistic, p_value = stats.ttest_rel(sample1, sample2)

Use ttest_1samp to compare one group to a known value.

Use ttest_ind for two separate groups.

Use ttest_rel for paired or matched groups.

Examples

One sample t-test: Check if sample average differs from 6.

Data Analysis Python

from scipy import stats
sample = [5, 7, 8, 6, 9]
result = stats.ttest_1samp(sample, 6)
print(result)

Two independent samples t-test: Compare averages of two groups.

Data Analysis Python

from scipy import stats
sample1 = [5, 7, 8, 6, 9]
sample2 = [4, 6, 7, 5, 8]
result = stats.ttest_ind(sample1, sample2)
print(result)

Paired t-test: Compare measurements before and after treatment on same subjects.

Data Analysis Python

from scipy import stats
before = [20, 22, 19, 24, 20]
after = [21, 23, 20, 25, 22]
result = stats.ttest_rel(before, after)
print(result)

Sample Program

This program compares average scores of two classes to see if they differ significantly.

Data Analysis Python

from scipy import stats

# Sample data: test scores of two classes
class_a = [88, 92, 85, 91, 87]
class_b = [78, 81, 79, 74, 77]

# Perform independent t-test
result = stats.ttest_ind(class_a, class_b)

print(f"t-statistic: {result.statistic:.3f}")
print(f"p-value: {result.pvalue:.3f}")

Important Notes

A small p-value (usually < 0.05) means the groups are likely different.

Make sure your data is roughly normal and samples are independent for best results.

Paired t-test is for related samples, like before and after measurements.

Summary

T-tests check if two averages are different.

Use scipy.stats functions: ttest_1samp, ttest_ind, ttest_rel.

Look at p-value to decide if difference is real.

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