T-Test Calculator

In short A t-test asks whether a difference in means is larger than the noise in the data can comfortably explain. It divides the difference by its standard error, and the result is compared with the t distribution on the appropriate degrees of freedom. This tool runs all three versions: one sample against a fixed value, two independent samples, and paired measurements. Two choices matter more than the arithmetic. The two-sample test here is Welch's, not Student's, because Student's version assumes the two groups have equal variances and almost nobody checks. Welch does not assume it, its degrees of freedom come out fractional as a result, and when the variances happen to be equal it loses almost nothing — so it is the better default in every direction. And if each value in one group is naturally matched with one in the other, before-and-after on the same subjects, use the paired test: it looks only at the differences, so variation between subjects cancels entirely and the test is far more sensitive. Read the confidence interval alongside the p-value, because they are two views of one fact. A 95% interval excludes a value exactly when the test rejects it at α = 0.05 — that is a definitional equivalence, not a coincidence. The p-value tells you the direction is probably real; the interval tells you how large the effect might be, which is the part anyone has to act on.