t-test (ttest_ind, ttest_rel) in SciPy - Step-by-Step Execution

Concept Flow - t-test (ttest_ind, ttest_rel)

Start: Two Data Samples

↓

Choose Test Type

↓

Independent

↓

Calculate t-statistic and p-value

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Compare p-value to alpha

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Reject H0

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Conclude groups differ

Start with two data samples, choose independent or related t-test, calculate statistics, then decide if groups differ based on p-value.

Execution Sample

SciPy

from scipy.stats import ttest_ind, ttest_rel

# Sample data
sample1 = [5, 7, 8, 6, 9]
sample2 = [6, 9, 7, 10, 8]

# Independent t-test
result = ttest_ind(sample1, sample2)
print(result)

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

Execution Table

Step	Action	Calculation/Condition	Result
1	Input samples	sample1 = [5,7,8,6,9], sample2 = [6,9,7,10,8]	Samples ready
2	Choose test	Independent samples test	ttest_ind selected
3	Calculate means	mean1=7.0, mean2=8.0	Means computed
4	Calculate variances	var1=2.5, var2=2.5	Variances computed
5	Calculate t-statistic	t = (7.0-8.0)/sqrt(2.5/5 + 2.5/5) = -1.0	t = -1.0
6	Calculate degrees of freedom	df = 8	df = 8
7	Calculate p-value	p ≈ 0.34	p ≈ 0.34
8	Compare p-value to alpha=0.05	0.34 > 0.05	Fail to reject H0
9	Conclusion	No evidence groups differ	End

💡 p-value is greater than 0.05, so we fail to reject the null hypothesis.

Variable Tracker

Variable	Start	After Step 3	After Step 4	After Step 5	After Step 7	Final
sample1	[5,7,8,6,9]	[5,7,8,6,9]	[5,7,8,6,9]	[5,7,8,6,9]	[5,7,8,6,9]	[5,7,8,6,9]
sample2	[6,9,7,10,8]	[6,9,7,10,8]	[6,9,7,10,8]	[6,9,7,10,8]	[6,9,7,10,8]	[6,9,7,10,8]
mean1	N/A	7.0	7.0	7.0	7.0	7.0
mean2	N/A	8.0	8.0	8.0	8.0	8.0
var1	N/A	N/A	2.5	2.5	2.5	2.5
var2	N/A	N/A	2.5	2.5	2.5	2.5
t-statistic	N/A	N/A	N/A	-1.0	-1.0	-1.0
p-value	N/A	N/A	N/A	N/A	0.34	0.34

Key Moments - 3 Insights

Why do we choose between independent and related t-tests?

Because independent t-tests compare two separate groups, while related t-tests compare paired or matched samples. This choice affects how the test calculates differences, as shown in Step 2 of the execution_table.

What does the p-value tell us in the t-test?

The p-value shows the chance of seeing the data if the groups are actually the same. If p is less than 0.05 (Step 8), we say groups differ; otherwise, we say no evidence of difference.

Why do we calculate degrees of freedom (df)?

Degrees of freedom help determine the shape of the t-distribution used to find the p-value. It depends on sample sizes and is calculated in Step 6.

Visual Quiz - 3 Questions

Look at the execution_table at Step 5, what is the approximate t-statistic value?

A -1.0

B 0.707

C -1.5

D 1.5

💡 Hint

Check the 'Result' column in Step 5 of the execution_table.

At which step does the test decide to fail to reject the null hypothesis?

A Step 7

B Step 8

C Step 6

D Step 9

💡 Hint

Look for the comparison of p-value to alpha in the execution_table.

If sample sizes increased, how would the degrees of freedom change in the execution_table?

A Degrees of freedom would decrease

B Degrees of freedom would stay the same

C Degrees of freedom would increase

D Degrees of freedom would become zero

💡 Hint

Degrees of freedom depend on sample sizes, see Step 6 in execution_table.

Concept Snapshot

t-test compares means of two samples.
Use ttest_ind for independent groups.
Use ttest_rel for paired samples.
Calculate t-statistic and p-value.
If p < 0.05, groups differ significantly.
Otherwise, no evidence of difference.

Full Transcript

A t-test compares two groups to see if their averages differ. We start with two data samples. We pick the test type: independent if groups are separate, related if paired. Then we calculate the t-statistic, which measures difference size relative to variation. We find the p-value, which tells us how likely the difference is by chance. If p-value is less than 0.05, we say the groups differ. Otherwise, we say there is no evidence they differ. This process helps us make decisions about data differences.