T-Test Calculator
Perform a one-sample or two-sample t-test with t statistic, degrees of freedom and p-value.
About T-Test Calculator
The t-test determines whether a sample mean (or the difference between two sample means) is statistically significantly different from a hypothesised value. This calculator uses Welch's t-test for two samples, which does not assume equal variances.
Formulas
One-sample t
t = (x̄ − μ₀) / (s / √n)
- x̄
- Sample mean
- μ₀
- Hypothesised mean
- s
- Sample SD
- n
- Sample size
Two-sample t (Welch)
t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂)
- x̄₁,x̄₂
- Sample means
- s₁²,s₂²
- Sample variances
- n₁,n₂
- Sample sizes
Worked example
With the default values below, T-Test Calculator returns t Statistic of 3.0000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Test typeone of One-sample (test mean vs μ₀), Two-sample (compare two means)
- Two-sample (compare two means)
- Sample 1 (comma separated)
- 5, 7, 9, 6, 8
- Sample 2 (comma separated)
- 3, 5, 4, 6, 2
- Hypothesised mean μ₀
- 5
Results
- t Statistic
- 3.0000
- P-value (two-tailed)
- 0.017072
- Degrees of Freedom
- 8.00
Step by step
- 1Values used
- 2One-sample t
- 3Two-sample t (Welch)
- 4t Statistic= 3.0000
- 5P-value (two-tailed)= 0.017072
- 6Degrees of Freedom= 8.00
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
When should I use a one-sample vs two-sample t-test?
Use one-sample when testing if a single group's mean equals a known value. Use two-sample when comparing the means of two independent groups.
What is Welch's t-test?
Welch's t-test is a modification of the two-sample t-test that does not assume equal variances between the two groups, making it more generally applicable.