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

Concept Flow - t-test with scipy.stats

Start: Two data samples

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Choose t-test type

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Calculate t-statistic and p-value

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Compare p-value to threshold

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Reject null

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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.