Paired_Comparisons.md

Paired comparisons are used when observations are collected in matched pairs or from the same subjects at two time points. These tests account for the dependency between measurements.

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1. When to Use Paired Comparisons

• Before-and-after measurements (e.g., pre- and post-treatment)

• Matched subjects in a case-control study

• Repeated measures on the same subject

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2. Parametric Test: Paired t-test

• Compares the mean difference between two related groups

• Assumes differences are normally distributed

# Paired t-test in R
paired_result <- t.test(before, after, paired = TRUE)
summary(paired_result)

Assumptions

• Data are continuous

• Differences follow a normal distribution

• Observations are dependent within pairs but independent between pairs

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3. Non-parametric Alternative: Wilcoxon Signed-Rank Test

• Used when the assumption of normality is not met

# Wilcoxon test in R
wilcox.test(before, after, paired = TRUE)

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4. Visualization

• Line plots to show change per subject

• Boxplots of paired differences

# Line plot example
matplot(t(cbind(before, after)), type = "l", lty = 1, col = 1:n)

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5. Summary

Paired comparisons are essential for within-subject or matched designs. Use the paired t-test when assumptions are met and Wilcoxon test otherwise. Visualization helps reveal the direction and consistency of changes.