Welch Independent Samples t-Test Calculator
Welch’s t-test compares two independent sample means while allowing unequal variances. It uses group sample sizes, means and sample standard deviations.
How to use this calculator
- Enter each group’s sample size, mean and sample SD from independent observations.
- Check that all inputs use the same units, period and population scope.
- Change one assumption at a time when comparing scenarios.
Formula used by independent samples t test calculator
t = (mean₁ − mean₂) ÷ √(s₁²/n₁ + s₂²/n₂), with Welch–Satterthwaite degrees of freedom.
- t = (mean₁ − mean₂) ÷ √(s₁²/n₁ + s₂²/n₂), with Welch–Satterthwaite degrees of freedom.
- Requires independent observations and a design appropriate for comparing means. Very small samples and severe outliers can undermine the approximation.
- The tool validates inputs and rounds displayed figures for readability; it does not validate assumptions against external records.
Worked examples
Worked example
Group means are 52.4 and 47.9, with sample SDs 8.1 and 7.4 for sample sizes 30 and 28.
The standard error is √(8.1²/30 + 7.4²/28); the test uses estimated Welch degrees of freedom.
The calculator reports Welch’s t statistic, degrees of freedom and two-sided p-value.
Understanding the result
Welch’s t-test compares two independent sample means while allowing unequal variances. It uses group sample sizes, means and sample standard deviations.
Requires independent observations and a design appropriate for comparing means. Very small samples and severe outliers can undermine the approximation.
Important notes
Requires independent observations and a design appropriate for comparing means. Very small samples and severe outliers can undermine the approximation.
Treat the result as an estimate from the entered assumptions. For commercial, statistical, engineering or health-related decisions, verify relevant specifications and professional guidance.
Frequently asked questions
Why use Welch rather than pooled t?
Welch’s method does not require equal group variances.
Does this compare paired observations?
No. Use a paired test for matched or repeated observations.
How should I interpret this result?
Requires independent observations and a design appropriate for comparing means. Very small samples and severe outliers can undermine the approximation.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Percent Error — Learn the percent error formula and how to compare an experimental value with a reference or accepted value.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- Percentage Change — Learn what percentage change means, how to calculate increases and decreases, and how the original value affects the result.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.