👥 Two-Sample T-Test Calculator
Compare two independent sample means using Welch’s t-test, which does not assume equal variances.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
Please enter valid values.
Formula and Explanation
Compare two independent sample means using Welch’s t-test, which does not assume equal variances.
| Concept | Formula or rule |
|---|---|
| Two-Sample T-Test Calculator | t = (x̄₁−x̄₂) / √(s₁²/n₁ + s₂²/n₂) |
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: Compare means 72 and 66 with their sample standard deviations and sizes.
✓ Welch’s test adjusts degrees of freedom for unequal variances.
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
⚠️
Using paired data as independent
Repeated measures require a paired analysis.
Repeated measures require a paired analysis.
⚠️
Assuming equal variances unnecessarily
Welch’s test is generally safer.
Welch’s test is generally safer.
⚠️
Ignoring unequal measurement quality
A formula cannot fix biased or incomparable groups.
A formula cannot fix biased or incomparable groups.
Practice Questions
1. If both means are equal, what is t?
Answer: 0
2. Are paired observations appropriate here?
Answer: No; use a paired t-test.
3. Does Welch’s test require equal variances?
Answer: No.
Frequently Asked Questions
What is the null hypothesis?▾
The population means are equal.
Why can df be non-integer?▾
Welch–Satterthwaite approximation adjusts for unequal variances.
Can sample sizes differ?▾
Yes.