Differential analysis & tests / Paired t-test
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The paired t-test is for two measurements on the same subjects (before/after treatment, left/right, matched case–control pairs). It tests whether the mean difference equals μ₀ (0 by default).
In the long layout the subject column links the two measurements; subjects missing either measurement are removed and the page reports how many. In the wide layout each row is one pair.
Difference = first group − second group; one-sided alternatives refer to this difference. Effect size Cohen’s d_z = mean difference / SD of the differences.
In the paired-line plot each line is one subject, coloured by increase or decrease. If the differences are clearly skewed or contain outliers, also check the Wilcoxon signed-rank test.
Student (1908) Biometrika 6:1–25. t, P and the confidence interval match scipy.stats.ttest_rel; the CI for d_z is the normal approximation d_z ± z·√(1/n + d_z²/(2n)).
Up to 100,000 rows.
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