Paired T-Test Calculator
Isolating the Effect of a Change on the Same Subjects
Comparing before-and-after measurements on the same subjects is more statistically powerful than comparing two separate groups, because each subject serves as their own control — individual variation between people cancels out, leaving only the effect of whatever changed between the two measurements. The paired t-test formalizes this by working entirely with the differences between paired observations.
The Formula
where d = before − after for each pair, df = n − 1
Worked Example
Before: 10, 12, 9, 14. After: 8, 10, 7, 13.
| Quantity | Value |
|---|---|
| Differences | 2, 2, 2, 1 |
| Mean difference | 1.75 |
| SD of differences | 0.50 |
| t statistic | 7.00 |
| df | 3 |
| Two-tailed p-value | 0.0060 |
Computed directly from the calculator's formula.
With every subject improving and very little variation in the size of that improvement, the test returns a small p-value even with just four pairs — a good illustration of how consistent within-subject differences give the paired design its statistical power.
Where This Calculation Matters
- Pre/post treatment comparisons — measuring the same patients, employees, or products before and after an intervention, and testing whether the average change is different from zero.
- Matched-pairs experiments — comparing two conditions applied to deliberately matched pairs (e.g., twin studies, or left-foot vs. right-foot in a shoe comfort trial).
- Repeated measures on the same unit — testing a product's performance metric before and after a design change, using the same test units for both measurements.
How to Use This Calculator
- Enter the "before" values as a comma-separated list.
- Enter the matching "after" values as a comma-separated list, in the same order (at least 2 pairs required).
- Select Calculate to get the t statistic, degrees of freedom, and two-tailed p-value.
Related Calculations
When the paired differences are not normally distributed, use the non-parametric Wilcoxon Signed-Rank Calculator instead. For two independent (unpaired) samples, see the Welch's T-Test Calculator.