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Paired T-Test Calculator (With Steps)

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Paired T-Test Calculator

A paired t-test is used when each observation in one sample is naturally linked to one in the other: the same students before and after tutoring, the same patients on two treatments, or matched pairs of products. Instead of comparing two group means, it tests whether the mean of the pairwise differences is zero.

Enter the two samples in the same order. The calculator lists each difference, finds the mean and standard deviation of the differences, computes the standard error, the t statistic with n − 1 degrees of freedom and the p-value, and reports a confidence interval for the mean difference and the effect size dz. The conclusion is stated in plain language for the alternative you chose.

Pairing removes the variation between subjects, so a paired test is usually far more powerful than an independent two-sample t-test on the same numbers. If the differences are clearly non-normal with a small n, the Wilcoxon signed-rank test is the non-parametric alternative.

Separate values with commas, spaces or new lines.

Same order as sample 1, one value per pair.

Result and step-by-step solution

t(7) = −8.9188
p = < 0.0001
Reject H₀ at α = 0.05. The result is statistically significant: there is enough evidence at the 5% level to conclude that the mean difference (sample 1 − sample 2) is not zero.
  1. State the hypotheses
    H₀: μd = 0   H₁: μd ≠ 0 (two-tailed test) where d = sample 1 − sample 2
  2. Compute the differences
    PairSample 1Sample 2d
    17276−4
    26870−2
    37579−4
    48084−4
    56668−2
    67175−4
    77880−2
    87477−3
  3. Mean and SD of the differences
    d̄ = Σd ÷ n = −25 ÷ 8 = −3.125; sd = √(6.875 ÷ 7) = 0.991
  4. Standard error
    SE = sd ÷ √n = 0.991 ÷ √8 = 0.3504
  5. Test statistic
    t = d̄ ÷ SE = −3.125 ÷ 0.3504 = −8.9188, df = 7
  6. p-value
    2 × P(T ≥ |−8.9188|) = < 0.0001
  7. Decision
    p = < 0.0001 < α = 0.05. critical values ±2.3646 (reject when |t| > 2.3646).
95% CI for the mean difference−3.9535 to −2.2965
Effect size (Cohen’s dz)−3.153

Frequently asked questions

What is the difference between a paired and an independent t-test?
A paired test uses the differences within each pair, so it requires the two samples to be linked one-to-one and equal in size. An independent test compares two unrelated groups that can be different sizes.
Which way round should I subtract?
The calculator uses d = sample 1 − sample 2. For before-and-after data with sample 1 = before, a negative mean difference means values increased. One-tailed alternatives refer to this direction.
What are the degrees of freedom?
n − 1, where n is the number of pairs, not the total number of measurements.
What is Cohen's dz?
The mean difference divided by the standard deviation of the differences. It is the standard effect size for paired designs.

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Last reviewed: September 25, 2026. Calculations run in your browser and were validated against SciPy.

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