t-test with scipy.stats in Data Analysis Python - Step-by-Step Execution

Concept Flow - t-test with scipy.stats

Start: Two data samples

↓

Choose t-test type

↓

Calculate t-statistic and p-value

↓

Compare p-value to threshold

↓

Reject null

↓

End

We start with two data samples, choose the t-test type, calculate the t-statistic and p-value, then decide if the difference is significant by comparing p-value to a threshold.

Execution Sample

Data Analysis Python

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

This code runs an independent t-test on two small samples and prints the t-statistic and p-value.

Execution Table

Step	Action	Input	Output	Explanation
1	Import scipy.stats	None	scipy.stats module ready	Prepare to use t-test functions
2	Define sample1	[5,6,7,8,9]	sample1 list created	First data sample stored
3	Define sample2	[5,5,5,5,6]	sample2 list created	Second data sample stored
4	Call ttest_ind(sample1, sample2)	sample1, sample2	(t_stat=2.449, p_val=0.041)	Calculate t-statistic and p-value for independent samples
5	Print results	(2.449, 0.041)	2.449 0.041	Show t-statistic and p-value
6	Compare p_val < 0.05	0.041 < 0.05	True	p-value is less than 0.05, reject null hypothesis
7	End	Decision made	Reject null hypothesis	Samples differ significantly

💡 Execution stops after printing results and deciding significance based on p-value.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	Final
sample1	None	[5,6,7,8,9]	[5,6,7,8,9]	[5,6,7,8,9]	[5,6,7,8,9]
sample2	None	None	[5,5,5,5,6]	[5,5,5,5,6]	[5,5,5,5,6]
t_stat	None	None	None	2.449	2.449
p_val	None	None	None	0.041	0.041

Key Moments - 3 Insights

Why do we compare the p-value to 0.05?

The p-value tells us how likely the observed difference happened by chance. If it's less than 0.05 (5%), we say the difference is statistically significant and reject the null hypothesis. See execution_table step 6.

What does the t-statistic number mean?

The t-statistic measures how big the difference between samples is relative to their variation. A larger absolute t-statistic means a bigger difference. The exact number helps calculate the p-value. See execution_table step 4.

Can we use ttest_ind for samples that are related?

No, ttest_ind assumes samples are independent. For related samples, use ttest_rel instead. This example uses independent samples as shown in the code.

Visual Quiz - 3 Questions

Look at the execution_table at step 4, what are the values of t_stat and p_val?

A t_stat=5, p_val=6

B t_stat=0.041, p_val=2.449

C t_stat=2.449, p_val=0.041

D t_stat=1, p_val=0.5

💡 Hint

Check the Output column in execution_table row for step 4.

At which step does the code decide to reject the null hypothesis?

A Step 6

B Step 3

C Step 2

D Step 5

💡 Hint

Look for the step where p_val is compared to 0.05 in execution_table.

If the p-value was 0.1 instead of 0.038, what would change in the execution_table?

A Step 2 sample1 would change

B Step 6 would say 'False' and we would fail to reject null

C Step 4 t_stat would change

D No change at all

💡 Hint

Look at the comparison and decision in step 6 of execution_table.

Concept Snapshot

t-test with scipy.stats:
- Use stats.ttest_ind(sample1, sample2) for independent samples
- Returns t-statistic and p-value
- If p-value < 0.05, reject null hypothesis (samples differ)
- Use ttest_rel for related samples
- Helps test if two groups differ significantly

Full Transcript

This visual execution shows how to perform a t-test using scipy.stats in Python. We start by importing the module, then define two data samples. We run the independent t-test function which returns a t-statistic and a p-value. The p-value tells us if the difference between samples is statistically significant. If the p-value is less than 0.05, we reject the null hypothesis, meaning the samples differ significantly. The variable tracker shows how sample data and results change step-by-step. Key moments clarify why we compare p-value to 0.05 and what the t-statistic means. The quiz tests understanding of the execution steps and decision points.

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