T-Test Calculator
Tests whether a difference in means is larger than sampling variation would explain.
Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
The formula
Welch: t = (x̄₁ − x̄₂) ÷ √(s₁²/n₁ + s₂²/n₂) Paired: t = d̄ ÷ (s_d ÷ √n) One sample: t = (x̄ − μ₀) ÷ (s ÷ √n)
Welch’s test does not assume equal variances and is a safe default for two independent groups. The test assumes each mean is close to normally distributed, which holds for roughly normal data or larger samples.
What to watch out for
Use a paired test when the two lists are matched, such as before and after on the same items. Use Welch’s test for separate groups. The p-value calculator explains how to read the result.
Frequently Asked Questions
Which t-test should I use?
One sample if comparing with a fixed value. Paired if each value in one list matches one in the other. Welch for two separate groups.
Why does pairing matter?
It removes the differences between individuals. The figures filled in above are Student’s sleep data. Paired, t is -4.0621. Treated as two separate groups, t is only -1.8608.
Does it matter if my data is skewed?
Less with larger samples. With a small and clearly skewed sample, treat the p-value with caution.