One-sample: comparing a single group's mean against a known or hypothesized value. Independent two-sample: comparing two separate, unrelated groups. Paired: comparing two measurements on the SAME subjects, like before/after — using an independent test on paired data is a common, genuine error that gives a wrong answer, not just a less powerful one.
Why does this calculator use Welch's t-test for two samples, not the classic pooled version?+−
Welch's t-test doesn't assume the two groups have equal variances, which makes it more robust — it performs nearly identically to the pooled test when variances genuinely are equal, and considerably better when they aren't. It's now widely recommended as the safer default.
What does the degrees of freedom number mean?+−
Degrees of freedom relates to how much independent information your sample provides after estimating the mean(s) from the data itself. For a one-sample or paired test, df = n − 1. For Welch's two-sample test, df is calculated from both sample sizes and variances using the Welch-Satterthwaite equation, and is often not a whole number.
Is this a one-tailed or two-tailed test?+−
This calculator reports the two-tailed p-value, appropriate when your alternative hypothesis is simply "different from," not specifically "greater than" or "less than." For a one-tailed test, divide the reported p-value by 2 (and check the direction of the difference matches your predicted direction) before comparing to your significance level.