T-Test Calculator
Compare a sample mean with a target, compare two independent means with Welch’s unequal-variance test, or test paired observations from matched data.
Match the t-test mode to the data structure before reading the p-value
One-sample mode compares one sample mean with a stated null mean. Welch mode compares two independent sample means without requiring equal population variances, while paired mode first turns matched observations into within-pair differences and tests the mean difference against zero.
Lynara reports the two-tailed p-value, t statistic and degrees of freedom without turning a threshold into an automatic conclusion. Sampling design, independence or pairing, outliers and distribution shape still determine whether the model is appropriate.
Privacy: calculator inputs are processed in your browser; Lynara does not need to upload these values to calculate the result.
Formula
one sample: t = (x̄ − μ₀)/(s/√n); Welch: t = (x̄₁ − x̄₂)/√(s₁²/n₁ + s₂²/n₂); paired: run one-sample t on pair differences
Example
For x̄ = 12, s = 2, n = 25 and μ₀ = 10, t = 5 with 24 degrees of freedom and a two-tailed p-value below 0.001.
Useful for
- One-sample t-test homework
- Welch two-sample comparison
- Paired before-and-after data
- Checking a two-tailed p-value
Questions
Why does Lynara use Welch for two independent samples?
Welch’s test does not require equal population variances and uses the Welch–Satterthwaite degrees-of-freedom approximation.
When should I use paired mode?
Use paired mode only when each value in the first list is meaningfully matched to the value in the same position in the second list, such as before-and-after measurements.