Welch Two-Sample t-Test

Statistics

Welch Two-Sample t-Test with explicit assumptions and reproducible inputs.

Formula

t=(mean₁−mean₂)/√(s₁²/n₁+s₂²/n₂); use Welch–Satterthwaite degrees of freedom.

Use the units shown beside each field.
Results update automatically whenever you change an input.
Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
Independent groups and observations; approximate normality or suitable sample sizes. Does not assume equal variances. Paired observations require a paired test, which this tool does not perform. Numerical results are approximate. Extremely small probabilities can underflow to zero. No personal, clinical or financial decision rule is inferred.

Example Calculation

Example inputs

Group 1 mean: 12
Group 1 SD: 2
Group 1 n: 10
Group 2 mean: 10
Group 2 SD: 2
Group 2 n: 10
Alternative: Two-sided

Means12 and10, both SD2 and n10, give t=√5≈2.2361 and df18.

Method references

itl.nist.gov — method reference

Frequently asked questions

How do I use this calculator?

Enter group 1 mean, group 1 sd, group 1 n, group 2 mean, group 2 sd, group 2 n, alternative. The result updates automatically. Use Reset to restore the example values.

What method does it use?

t=(mean₁−mean₂)/√(s₁²/n₁+s₂²/n₂); use Welch–Satterthwaite degrees of freedom.. Independent groups and observations; approximate normality or suitable sample sizes. Does not assume equal variances. Paired observations require a paired test, which this tool does not perform. Numerical results are approximate. Extremely small probabilities can underflow to zero. No personal, clinical or financial decision rule is inferred.

Why might a rounded result differ?

The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.

Are my inputs saved online?

No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.

Check the assumptions and units before using this result. Read about calculation methods.