Welch's T-Test calculator

Perform an online Welch's t-test with unequal variances. Compute t-statistic, degrees of freedom, p-value, Hedges' g, and confidence intervals instantly.

What it does

Compares the means of two independent groups without assuming equal variances — the robust default (Delacre et al. 2017).

Cautions

• Assumes approximate normality within each group; robust to violations once n ≥ 30 per group AND the skew is mild (|skew| < 1) — the central limit theorem protects the mean, but n = 30 is not a threshold that rescues strong skew.
• Means and SDs are outlier-sensitive — one extreme point can create or destroy significance.

Alternatives

• Mann-Whitney U — if the outcome is ordinal, or clearly skewed with fewer than ~30 per group — at larger n the t-test's mean comparison is usually fine even under skew
• Student's t — only if variances are known equal and groups balanced

How to read the output

Group means and the difference between them

The two group means, in the outcome's own units. Their difference is the finding; everything else describes how firmly it is pinned down. Report the difference and its interval, in units. 'Significantly higher' without a number is not a result.

t-statistic and df

The difference expressed in standard errors. Welch's df is fractional (e.g. 41.7) because it is estimated rather than counted — that is correct, not a rounding fault. A whole-number df here would mean the equal-variance test was run. This module runs Welch by design: it costs almost nothing when variances are equal and protects you when they are not.

p-value

How surprising a difference at least this large would be IF the groups really were identical on this measure. A small p means the data would be surprising under that assumption. It is not the probability that the result is due to chance, and not the probability that the groups are the same — those read the conditional backwards. It also answers 'would this be surprising?', never 'is this big enough to matter?': with a large sample a trivial difference returns a small p, and the result looks identical to an important one.

How this calculator is validated · Which statistical test should I use?