Statistics
T-test Calculator
Compare two independent samples, reporting the t statistic, degrees of freedom, and two-tailed p-value.
Compare two independent samples with unequal variances.
Welch’s t statistic
t = (ȳ₁ − ȳ₂) / √(s₁²/n₁ + s₂²/n₂) ν ≈ (s₁²/n₁ + s₂²/n₂)² / [s₁⁴/(n₁²(n₁ − 1)) + s₂⁴/(n₂²(n₂ − 1))]
Welch’s adjustment is robust when variances differ or sample sizes are unequal, making it a safe default.
How to use
- Enter the two samples as comma-separated lists.
- Ensure each sample has at least two observations.
- Review the mean difference, t statistic, degrees of freedom, and p-value.
Example
Input: Sample A = 23,21,25,20,27; Sample B = 18,19,17,20,16
Output: t ≈ 4.03, ν ≈ 7.8, p ≈ 0.0041
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for T-test Calculator: t test calculator, welch t test calculator, two sample t test calculator, t test p value calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
T-test Calculator: Performs Welch’s two-sample t-test with p-value. It's built around t-test, hypothesis test, p-value, so you can go from a raw question to a checked answer without switching tools.
The math behind it: Welch’s adjustment is robust when variances differ or sample sizes are unequal, making it a safe default. The core relationship is t = (ȳ₁ − ȳ₂) / √(s₁²/n₁ + s₂²/n₂) ν ≈ (s₁²/n₁ + s₂²/n₂)² / [s₁⁴/(n₁²(n₁ − 1)) + s₂⁴/(n₂²(n₂ − 1))], shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Enter the two samples as comma-separated lists. (2) Ensure each sample has at least two observations. (3) Review the mean difference, t statistic, degrees of freedom, and p-value. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering Sample A = 23,21,25,20,27; Sample B = 18,19,17,20,16 returns t ≈ 4.03, ν ≈ 7.8, p ≈ 0.0041. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
Is this a paired test?
No. The calculator runs Welch’s unpaired test. Pair your data manually if observations are matched.
How accurate is the p-value?
P-values rely on the Student’s t CDF via the incomplete beta function, giving accurate probabilities for common degrees of freedom.
What formula does the T-test Calculator use?
Welch’s adjustment is robust when variances differ or sample sizes are unequal, making it a safe default.
How do I use the T-test Calculator?
Enter the two samples as comma-separated lists. Ensure each sample has at least two observations. Review the mean difference, t statistic, degrees of freedom, and p-value.