What Is a T Test?

The t-test is the standard tool for comparing the means of two independent groups. It answers a precise question: given the observed difference and the variability within each group, how likely is it that this difference arose purely by chance? The answer is the p-value — the probability of seeing a difference this large if the two groups actually share the same mean.

How the Calculation Works

This calculator uses the Welch two-sample t-test. The t-statistic is the mean difference divided by its standard error:

t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂)

The degrees of freedom are adjusted with the Welch–Satterthwaite equation rather than the simpler n₁+n₂−2, because the two samples are not assumed to share a common variance. The p-value is then computed exactly from the Student's t distribution using the regularized incomplete beta function — no normal approximation is used, even for small samples.

Interpreting the Result

If the p-value falls below your significance level (typically 0.05), the difference is declared statistically significant: it is unlikely to be explained by sampling noise. Remember that significance is not the same as importance — a significant result only tells you the difference is real, not that it is large. Report the mean difference and its 95% confidence interval alongside the p-value to convey both.