Paired t-Test Calculator

A paired t-test checks whether the average difference between two related measurements is meaningfully different from zero, which is exactly what you want when the same people or items are measured twice. This calculator takes a list of paired differences, for example each person's after value minus their before value, and works out the mean difference, the standard deviation of those differences, and the t statistic. The t statistic is the mean difference divided by the standard error, where the standard error is the standard deviation divided by the square root of the number of pairs. It also reports the degrees of freedom, which is the number of pairs minus one. New Zealand students, researchers, and quality and health analysts use the paired t-test for before and after studies, matched comparisons, and repeated measures, because pairing removes a lot of the noise that comes from differences between individuals. To use it, enter the differences separated by commas; if a person scored 70 then 72, enter 2. A positive mean difference suggests an increase and a negative one a decrease, while a t statistic far from zero, compared against a t table at your degrees of freedom, points to a real effect rather than chance. For trustworthy results, keep the pairs in a consistent order, make sure the differences are roughly symmetric without extreme outliers, and report the sample size alongside the t value. The paired test is more powerful than an unpaired test when a genuine pairing exists, so always pair your data when the design allows it. Pair only genuinely linked observations.

t = mean(diff) / (sd(diff) / sqrt(n)), with df = n - 1 and sd using n - 1.