Welch Two-Sample T-Test
Compare two sample means without assuming equal variance.
How the welch two-sample t-test works
Welch’s t-test compares two independent sample means without requiring equal population variances. Each list gets its own sample variance, and those variance-over-size terms form the standard error. The difference in means divided by that error gives t. Welch–Satterthwaite degrees of freedom adjust for unequal uncertainty, and the Student t distribution supplies the two-tailed p value.
The default samples have means 14 and 10, sample variances 10 and 2.5, and equal sizes five. Their verified t statistic is 2.529822 with approximately 5.882353 degrees of freedom. Numerical integration of the matching t tail gives a two-sided p near 0.04546, just below the conventional 0.05 threshold.
Reading welch two-sample t-test results privately
The test assumes independent observations and targets a difference in means. Strong outliers, dependence, or highly non-normal tiny samples can make interpretation unreliable. A small p value does not measure effect size or practical importance, and it does not prove a causal relationship. This page does not pair rows; paired measurements require a paired t-test. This welch two-sample t-test calculation runs entirely in your browser, so the numbers you enter never leave your device.
Frequently Asked Questions
Why use Welch’s test instead of the pooled t-test?
Welch’s version remains valid when sample variances or sizes differ and does not require an equal-variance assumption.
What does the two-tailed p value test?
It measures evidence against equal population means in either direction under the model assumptions.
Is the welch two-sample t-test private?
Yes. Its inputs and results stay in your browser. Bushe.co does not upload or store the values used in this calculation.
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