Independent Samples t-Test Calculator
Enter two independent groups to test whether their means differ significantly. Uses Welch's t-test, which does not assume equal variances. Values can be comma or newline-separated.
Frequently asked questions
What is Welch's t-test and how does it differ from Student's t-test?
Student's t-test assumes both groups have equal population variances. Welch's t-test removes this assumption by using a separate variance estimate for each group and adjusting the degrees of freedom via the Welch-Satterthwaite equation. In practice, Welch's test performs at least as well as Student's when variances are equal and considerably better when they are not. Modern practice recommends Welch's as the default for independent samples.
What does the p-value tell me?
The p-value is the probability of observing a t-statistic at least as extreme as yours if the two population means were actually equal. A p-value below 0.05 is the conventional threshold for statistical significance, but a significant result does not tell you the difference is large or practically important. It only means the difference is unlikely to be zero. Always report the mean difference and confidence interval alongside p.
What does the 95% confidence interval mean?
The 95% CI gives a range of plausible values for the true difference in population means (Group A minus Group B). If you repeated the study many times, roughly 95% of such intervals would contain the true difference. An interval that does not include 0 is consistent with a statistically significant result at α = 0.05.
What are the assumptions of this test?
Independence: the two groups must be unrelated. Each group's values should be independent of one another (no repeated measures, no matched pairs). Approximate normality: the test is robust for moderate departures from normality when n > 15 per group, due to the central limit theorem. The test is not appropriate for very small samples with heavily skewed data. For matched pairs or repeated measures, use a paired t-test instead.
What is effect size and should I report it?
A statistically significant p-value only says the difference is unlikely to be zero, not that it is large. Cohen's d measures practical magnitude: d = mean difference / pooled SD. Conventional thresholds are 0.2 (small), 0.5 (medium), 0.8 (large), though these are rough guides. The mean difference shown above, interpreted in the units of your measurement, is often the most interpretable effect size.