Permutation Test for Paired Data

The paired permutation test assesses a within-unit difference by randomly flipping the signs of the paired differences to build the null distribution of their mean or median.

대응 자료 순열 검정은 짝지은 차이의 부호를 무작위로 뒤집어 평균 또는 중앙값 차이의 영분포를 만들고 단위 안의 변화를 검정하는 방법입니다.

I measured the same people before and after training, but the differences are skewed; how can I test the change without a paired t test?

같은 사람을 훈련 전후로 측정했는데 차이가 한쪽으로 치우쳐 있어요. 대응 t 검정 없이 변화를 검정하려면 어떻게 하나요?

Compute each person's difference, then flip the signs of the differences in all possible or many random patterns and recompute the mean (or median) each time. The p-value is the share of sign patterns giving a statistic at least as extreme as the observed one.

When to use Permutation Test for Paired Data

• Each unit is measured under two conditions and the differences are not normal.
• The sample is small, so an exact test over all 2^n sign patterns is possible.
• You want to test the median difference as well as the mean.

When to use something else

• The two samples are independent; use the permutation test for two groups instead.
• There are three or more conditions per unit; use the Friedman test or a repeated-measures permutation approach.

Assumptions and requirements

• Pairs are independent of each other.
• Under the null hypothesis the differences are symmetric around zero.

What the analysis reports

• Mean or median difference (second minus first condition)
• Exact (n <= 20) or Monte Carlo p for the chosen alternative
• Paired t, SD of differences and Cohen's dz for context
• Condition means, medians and SDs

How to report it

A paired permutation test on the mean difference indicated a change, mean difference = [value], n = [value] pairs, p = [value].

Related methods

• Paired t Test
• Wilcoxon Signed-Rank Test
• Permutation Test for Two Groups

Run Permutation Test for Paired Data on Quorant