Jonckheere-Terpstra Trend Test

The Jonckheere-Terpstra test is a rank-based test of whether an outcome tends to increase or decrease across three or more groups arranged in a prespecified order.

Jonckheere-Terpstra 검정은 미리 정한 순서가 있는 셋 이상의 집단에서 결과값이 그 순서대로 커지거나 작아지는 경향이 있는지 순위로 검정하는 방법이다.

How do I test whether scores rise steadily across low, medium and high dose groups without assuming normality?

용량이 낮음, 중간, 높음 순서인 세 집단에서 점수가 점점 올라가는지 정규성 가정 없이 검정하려면 어떻게 해야 하나요?

Use the Jonckheere-Terpstra test, which sums pairwise Mann-Whitney counts across the ordered groups into a statistic J and compares it with its null mean and tie-corrected variance. Because it targets a monotone trend, it has more power than the Kruskal-Wallis test when the ordering hypothesis is correct.

When to use Jonckheere-Terpstra Trend Test

• The groups have a natural order, such as dose levels or education stages.
• The hypothesis is a monotone trend rather than any difference.
• The outcome is ordinal or continuous but not normally distributed.

When to use something else

• The groups have no meaningful order; use the Kruskal-Wallis test instead.
• The outcome is normal and the trend is linear; use a linear contrast in ANOVA or regression instead.

Assumptions and requirements

• Observations are independent within and between groups.
• The group order is specified before looking at the data.
• Group distributions differ, if at all, by a shift in location.

What the analysis reports

• J statistic
• Expected J and its tie-corrected variance
• Standardized z and p-value
• Trend effect size (concordance from -1 to 1)

How to report it

A Jonckheere-Terpstra test indicated a [increasing/decreasing] trend across the ordered groups, J = [value], z = [value], p = [value].

Related methods

• Kruskal-Wallis Test
• Cochran-Armitage Trend Test
• Mann-Whitney U Test

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