Paired t-Test — StatReason

n pairs
Mean change (after - before)
95% CI of the mean change
t
Degrees of freedom
p-value
dz (effect size)

What this answers

This test answers "did the average value change between these two matched measurements, and how confident should I be in that change?" It works on the differences within each pair, which is what makes it more powerful than an independent t-test when your measurements are genuinely linked (the same subject before and after, or naturally matched pairs), since it removes variation between subjects from the comparison entirely.

When to use it, and when not to

Use this when each observation in one group has a genuine, meaningful match in the other group, most commonly the same subject measured twice. Never pair rows by position alone without confirming the pairing is real; a spreadsheet coincidence is not a matched design. For two genuinely independent groups, use the Independent t-Test instead.

How it is calculated

The difference (after minus before) is computed for every pair, then a one-sample t-test is run on those differences against a null value of 0. The reported t statistic, degrees of freedom (n minus 1 pairs), p-value, and confidence interval for the mean change all follow directly from that one-sample logic. Cohen's dz, the effect size reported here, is the mean difference divided by the standard deviation of the differences.

Worked example

For before values 1, 2, 3 and after values 2, 3, 4: every pair increases by exactly 1, so the mean change is exactly 1 with zero variability across pairs, the most extreme possible result a paired test can produce (every single pair agrees perfectly on both the direction and size of the change).

Assumption audit

Calculated from your data: the number of pairs, whether both lists have matching length, and whether the differences are constant (zero variability).

Evidence to review: whether the differences look roughly symmetric rather than heavily skewed, which affects how reliable the t-based p-value is, especially with a small number of pairs.

You must verify: that the pairing between before and after values is genuine (the same subject or a truly matched unit in both lists) and that the two measurements were taken in a way that makes comparing their difference meaningful.

What this result does not mean

A significant result means the data provide evidence that the average paired difference is not zero at your chosen threshold, not that every individual pair changed, and not that whatever happened between the two measurements caused the change on its own; other factors occurring over the same period cannot be ruled out by the test itself.

Limitations

This test assumes the differences, not the raw before/after values themselves, are reasonably close to normally distributed. A small number of pairs limits its power to detect a real but modest change.