Statistics & probability
Welch two-sample t test
Compare independent sample means without assuming equal variances.
A clear answer. Here’s how.
Uses (mean₁−mean₂)/sqrt(s₁²/n₁+s₂²/n₂) and Welch–Satterthwaite degrees of freedom. Each independent sample needs at least two values and the combined standard error must be positive. Assumes suitable sampling and normal/large-sample behaviour. The directional alternative refers to first minus second; p-values do not establish causation.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- First sample
- 10, 12, 9, 11, 13
- Second sample
- 8, 9, 11, 7, 10
- Alternative hypothesis
- Different (two-sided)
Example result
- First sample mean
- 11
- Second sample mean
- 9
- Mean difference (first − second)
- 2
- t statistic
- 2
- Degrees of freedom
- 8
- p-value
- 0.0805162379573
A p-value is conditional on the stated null model and sampling assumptions; it is not the probability that the null hypothesis is true.