T-Test Calculator
Perform a one-sample or two-sample t-test with t statistic, degrees of freedom and p-value.
Inputs
Used only for two-sample test
Used only for one-sample test
t Statistic
3.0000
P-value (two-tailed)
0.017072
Degrees of Freedom
8.00
Step by step
Values used
Test type = 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
One-sample t
t = (x̄ − μ₀) / (s / √n)
Two-sample t (Welch)
t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂)
t Statistic
= 3.0000
P-value (two-tailed)
= 0.017072
Degrees of Freedom
= 8.00
How it works
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
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.