Track 8 · Hypothesis Testing · Lesson 8 of 14
Paired t-test
Recognise paired data, analyse it with a paired t-test on the differences, and explain why pairing can make a test far more powerful.
The courier company measured the same 60 routes before and after its routing change. Routes differ enormously — a rural route takes twice as long as a city one — but each route is compared with itself. Treating such data as two independent samples throws that advantage away; the paired t-test keeps it.
Data are paired when each observation in one set is naturally linked to exactly one observation in the other: the same person before and after a treatment, the same route in two periods, two measurement methods applied to the same sample, twins, or deliberately matched pairs. For paired data the question is about the mean of the differences, .
The method is simple: compute the difference for every pair, then run a one-sample t-test on the differences against .
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It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Recognise paired designs: the same units measured twice, or matched pairs
- Run a paired t-test as a one-sample t-test on the differences with (pairs − 1) df
- Explain why pairing removes between-unit variation and increases power
- Distinguish a before/after change from a treatment effect, which needs a control group