Independent t-Test — StatReason

Mean A - Mean B
95% CI of the difference
Welch t
Degrees of freedom (Welch-Satterthwaite)
p-value
Hedges' g (effect size)
Equal-variance (pooled) comparison

What this answers

This test answers "do these two independent groups have different means, and how confident should I be in that difference?" It compares Group A and Group B assuming they represent two separate, unrelated samples (unlike a paired t-test, which is for the same subjects measured twice). By default this calculator uses Welch's t-test, which does not require the two groups to have equal variance, a safer default than the classic Student's pooled-variance test since real groups rarely have exactly equal spread.

When to use it, and when not to

Use this when you have two genuinely independent groups (different people, different units, no natural pairing between a row in Group A and a row in Group B) and a roughly continuous outcome. Do not use it for matched pairs or repeated measures on the same subjects (use the Paired t-Test for that), and do not use it when your data is heavily skewed with a small sample, where the Mann-Whitney U Test is a safer choice.

How it is calculated

Welch's t statistic is the difference in group means divided by the standard error of that difference, computed from each group's own variance divided by its own sample size (not a shared pooled variance). Its degrees of freedom use the Welch-Satterthwaite approximation, which adjusts downward when the two groups have unequal variance or unequal sample sizes. This calculator also reports the classic equal-variance pooled result as an explicit, clearly labeled comparison, since some fields still expect to see it, but it is never the default interpretation.

Worked example

For Group A of 1, 2, 3 and Group B of 3, 4, 5: both groups have a mean difference of negative 2 and identical variance of 1, so Welch and the pooled test agree exactly here, giving a t statistic of about negative 2.449 on 4 degrees of freedom. The interval and p-value reported by the calculator for this input are independently checkable against any standard statistical package.

Assumption audit

Calculated from your data: each group's sample size, the observed variance ratio between groups, and whether either group has fewer than 2 values (which blocks the calculation).

Evidence to review: whether each group's distribution looks roughly symmetric (check with the Histogram Maker), since the t-test is more robust to non-normality with larger, more balanced samples and less robust with small, skewed ones.

You must verify: that observations within each group are independent of one another, that group assignment was not itself influenced by the outcome, and that the two groups are genuinely comparable except for whatever you are testing.

What this result does not mean

A p-value below your alpha threshold means the data provide evidence against the stated null model at that threshold, not that the difference is large or practically important; check Hedges' g for that. A p-value at or above alpha means the analysis was inconclusive at that threshold, not proof that the two groups are truly equal. Neither result tells you why a real difference exists, only whether the data are consistent with there being none.

Limitations

This test assumes your two groups were validly sampled and assigned; no test statistic can detect a confound or a biased comparison from the numbers alone. With very small samples, confidence intervals widen substantially and the test has limited power to detect a real but modest difference.