Introduction to the Two-Sample T-Test
For research scientists who have already run an experiment and hold only summary statistics (mean, SD, n per arm) rather than raw data, and need the t-statistic and df for a two-group mean comparison without opening R or SPSS, this calculator is ideal. It performs an independent two-sample t-test computing the t-statistic and degrees of freedom for comparing two means. This saves valuable time by providing immediate results for preliminary analysis or quick verification.
How to Use This T-Test Calculator
- Enter Group 1's mean, standard deviation, and sample size in the first column.
- Enter Group 2's mean, standard deviation, and sample size in the second column.
- Keep "Welch" selected unless you have established that both groups share the same variance, in which case choose "Pooled / Student".
- Read the t-statistic, degrees of freedom, and method badge in the results panel; the formula line shows the SE and t computation with your numbers substituted.
FAQ
Q: Should I use the Welch or the pooled (Student) two-sample t-test?
A: Welch is the default here because it does not assume equal variances and computes a fractional df from each group's SD and n; choose pooled only when equal variances are a defensible assumption, in which case df = n1 + n2 − 2.
Q: Why are the degrees of freedom for the Welch test not a whole number?
A: Welch's df comes from the Welch–Satterthwaite expression SE⁴ ÷ ((SD1²/n1)²/(n1−1) + (SD2²/n2)²/(n2−1)), which is generally fractional; the pooled method instead uses the integer df = n1 + n2 − 2.
Q: Can I run a two-sample t-test with only means, SDs and sample sizes?
A: Yes — the t-statistic needs only each group's mean, standard deviation and n: SE = √(SD1²/n1 + SD2²/n2) and t = (mean1 − mean2)/SE, so raw observations are not required.
Q: What happens if one group has a sample size of 1?
A: The tool refuses to compute and flags the field, because both the Welch df term (n−1) and the pooled df = n1 + n2 − 2 require at least 2 observations per group; the results shown are estimates for educational and preliminary use, not a substitute for a full statistical package.