Paired t-test: the same subjects measured twice

When every subject is measured under both conditions — the same ten patients before and after a treatment, the same twelve loaves scored by two panels — the two values belong together. A paired t-test works on the differences within each pair, which removes the subject-to-subject spread that an independent test would have to fight through.

The data

Extra sleep (hours) under two drugs for the same ten patients (R’s classic sleep data): one row per condition, one column per subject.

r = replicate: r1 is replicate 1, r2 replicate 2, and so on.

Paired layout: the same subject occupies the same column in both rows — column r1 is patient 1 under each drug.

In MinutePlot

Choose t-test (paired), paste the two rows, and run. MinutePlot pairs the columns, tests the mean difference, and reports the effect size (Hedges’ g with its confidence interval) alongside t, df and p.

The result

t(9) = −4.06, p = 0.003: drug 2 gives about 1.6 hours more sleep than drug 1 in the same patients. An independent t-test on the same numbers gives p = 0.08 — the pairing is what finds the effect.

The figure MinutePlot produces for this analysis: the two drug means with error bars and the letters marking their difference.

Styling and exporting this figure: see Figure styling and Exporting & downloading.

Report it like this

“Sleep gain differed between the drugs in the same patients (paired t-test, t(9) = −4.06, p = 0.003; mean difference 1.58 h).”