🔁 Paired T-Test Calculator
Test whether the average within-pair difference is zero using paired observations.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
Please enter valid values.
Formula and Explanation
Test whether the average within-pair difference is zero using paired observations.
| Concept | Formula or rule |
|---|---|
| Paired T-Test Calculator | t = d̄ / (s_d/√n) |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: Compute each before−after difference, then test whether their mean differs from zero.
✓ Pairing removes between-subject variability from the comparison.
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
⚠️
Reordering one list
Each position must describe the same subject or matched unit.
Each position must describe the same subject or matched unit.
⚠️
Using independent t-test for repeated measurements
That discards the pairing information.
That discards the pairing information.
⚠️
Ignoring extreme differences
The t-test applies to the distribution of differences.
The t-test applies to the distribution of differences.
Practice Questions
1. With 12 pairs, what is df?
Answer: 11
2. What is the null mean difference?
Answer: 0
3. Which values must align?
Answer: Measurements from the same pair.
Frequently Asked Questions
What is analyzed?▾
The list of pairwise differences.
What are degrees of freedom?▾
Number of pairs minus 1.
Can pairs have missing values?▾
Incomplete pairs need a defined handling plan and usually cannot be used directly.