How to Calculate Paired t-Test
What is Paired t-Test?
The paired t-test compares means of two related groups (e.g., before and after measurements on the same subjects). It tests whether the mean difference is significantly different from zero.
Formula
t = (d̄ − μ₀) / (sₐ / √n) where d̄ is mean difference, sₐ is std of differences
- d
- difference between paired measurements
- d̄
- mean of differences
- sₐ
- standard deviation of differences
- n
- number of pairs
- t
- t-statistic
Step-by-Step Guide
- 1Calculate differences d = before − after
- 2Mean difference d̄ and standard deviation s_d
- 3t = d̄ / (s_d/√n)
- 4Compare t to critical value for df = n−1
Worked Examples
Input
Before: [20,22,19], After: [18,20,18]
Result
Mean diff = 1.67, t = 1.53, df = 2, not significant
Frequently Asked Questions
When do I use paired t-test vs. independent t-test?
Paired: same subjects measured twice (before/after). Independent: different subjects in two groups.
What is the null hypothesis for paired t-test?
H₀: mean difference = 0 (no difference between paired measurements).
Is paired t-test more powerful than independent t-test?
Yes, because pairing reduces variability (within-subject variation less than between-subject).
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