Paired t-Test Calculator
Run a paired (dependent) t-test on before-and-after measurements to see whether their mean difference is statistically significant.
Tail
p-value = 0.0002 · df = 7
- 1
Mean difference (d̄)
(sum of 8 differences) ÷ 8 = 4.625Each difference dᵢ = before − after. - 2
Std dev of differences (s_d)
√(Σ(dᵢ − d̄)² ÷ (8 − 1)) = 1.8468 - 3
Standard error (SE)
s_d ÷ √n = 1.8468 ÷ √8 = 0.6529 - 4
t statistic
d̄ ÷ SE = 4.625 ÷ 0.6529 = 7.083
How does this calculator work?
A paired t-test compares two related measurements (like before vs after) by analyzing their differences. It computes t = d̄ / (s_d / √n) with df = n − 1, where d̄ is the mean difference. The resulting p-value tells you whether the average change is statistically significant rather than random noise.
Formula
How this is calculated
Enter two equal-length lists: the "before" values (xᵢ) and the "after" values (yᵢ). Each pair belongs to the same subject or matched unit, which is what makes the test "paired." The calculator forms the paired differences dᵢ = xᵢ − yᵢ for the n pairs, then computes the mean difference d̄ = Σdᵢ / n and the sample standard deviation of the differences s_d = √(Σ(dᵢ − d̄)² / (n − 1)).
The test statistic is t = d̄ / (s_d / √n), which follows a Student-t distribution with df = n − 1 degrees of freedom under the null hypothesis that the true mean difference is zero. The p-value is obtained from the Student-t CDF: a two-tailed test reports 2·P(T > |t|), while one-tailed tests report the relevant single-tail probability. The Tail selector switches between testing for any difference (≠), an increase, or a decrease.
Assumptions: the differences are approximately normally distributed and the pairs are independent of one another. Values are unitless to the calculator, so keep both lists in the same measurement units. Edge cases: the two lists must have equal length and at least 2 pairs, and if every difference is identical (s_d = 0) the statistic is undefined and no result is shown.
Frequently asked questions
Use a paired t-test when each observation in one group is naturally linked to a specific observation in the other, such as the same person measured before and after a treatment. The pairing removes between-subject variability, making the test more powerful than an independent-samples t-test.
It is the probability of observing a mean difference at least as extreme as yours if the true mean difference were zero. A small p-value (commonly below 0.05) suggests the before-and-after change is unlikely to be due to chance alone.
Each value in the "before" list is subtracted from its partner in the "after" list to form a single difference per pair. Unequal lengths mean some measurements have no partner, so the paired difference cannot be defined.
Also known as
TG we-Calculate Editorial Team. (2026). Paired t-Test Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/paired-t-test-calculator
TG we-Calculate Editorial Team. "Paired t-Test Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/paired-t-test-calculator.
TG we-Calculate Editorial Team, "Paired t-Test Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/paired-t-test-calculator
@misc{wecalculate_paired_t_test_calculator, title = {Paired t-Test Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/paired-t-test-calculator}}, year = {2026}, note = {TG we-Calculate} }
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