Paired T Test Calculator
paired t-test calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Paired T Test Calculator
Calculator
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Formula: t = d̄ / (s_d / √n)
Worked example — t statistic
Formula
t = d̄ / (s_d / √n)
Tests whether the mean difference between paired observations is significantly different from zero.
Worked Examples
Example 1: Before/After
Problem:Before:[200,210,190,220,205] After:[180,195,185,200,190]
Solution:d̄=15, t with df=4
Result:t statistic
Frequently Asked Questions
What does the paired t-test measure?
The paired t-test determines whether the mean difference (d̄) between two related measurements is significantly different from zero. By working on the differences rather than the raw values, it controls for between-subject variability, making it more powerful than an independent t-test when the same subjects or matched pairs are measured twice.
How do you interpret the t-statistic and p-value in a paired t-test?
Compare the absolute value of t to the critical value from a t-distribution with df = n − 1 at your chosen significance level α. If |t| exceeds the critical value (e.g., approximately 2.0 for df > 20 at α = 0.05, two-tailed), you reject the null hypothesis H₀: μ_d = 0 and conclude that there is a significant mean difference between the paired measurements.
When should I use a paired t-test vs. an independent t-test?
Use the paired t-test when each observation in one group is directly linked to a corresponding observation in the other group — such as before/after measurements on the same subjects, or matched participants. Use the independent t-test when the two groups consist of entirely different, unrelated subjects. Incorrectly using the independent t-test on paired data wastes statistical power.
What are the assumptions of the paired t-test?
The differences between paired observations must be approximately normally distributed (not the raw data themselves); each pair must be independent of other pairs; the data must be measured on a continuous interval or ratio scale; and pairs should be meaningful (i.e., each before value is truly related to its corresponding after value). For non-normal differences, use the Wilcoxon signed-rank test instead.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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