Jonckheere-Terpstra (ordered trend)

Coming soon

Nonparametric ANOVA

This test is implemented and is currently going through StatMinds’ production verification: every statistic is independently checked against a trusted reference (scipy / R), locked with regression tests, and the screen is exercised across assumption-met/violated and significant/non-significant scenarios before it opens up.

See what’s live now

Ordered-alternative nonparametric omnibus test for k ≥ 3 independent groups.

Tests whether there is a monotone trend (θ_1 ≤ θ_2 ≤ … ≤ θ_k, or ≥) in the specified group order. Computes J = Σ_{i<j} U_{ij} (sum of pairwise Mann-Whitney U statistics in the assumed direction) and refers Z = (J − E[J])/SE(J) to the standard normal. Reports J, Z, p, and the per-group medians with 95% CIs. Typically 10-30% more powerful than Kruskal-Wallis when the a-priori ordering is correct; no power against non-monotone (inverted-U) patterns.

Worked example

Do the groups increase in a predicted order?

The Jonckheere-Terpstra test detects an ordered (monotonic) trend across a-priori-ordered groups — more powerful than Kruskal-Wallis for a trend.

Result

There was a significant increasing trend across dose groups, J-T z = 3.4, p < .001.

How you'd report it (APA)

A Jonckheere-Terpstra test showed a significant monotonic increase across the ordered groups, z = 3.4, p < .001.

When to use it

  • Dose-response or graded-intensity design
    A study compares anxiety reduction across four mindfulness training doses (0 hrs / 4 hrs / 8 hrs / 16 hrs).
  • Ordered severity / staging in clinical research
    Cancer-stage analysis: serum biomarker measured in n = 200 patients across 4 stages.

When NOT to — use instead

Hypotheses

H₀: the k group distributions are identical — F₁ = F₂ = … = F_k.
Hₐ: there is a MONOTONE trend in the specified order — θ_1 ≤ θ_2 ≤ … ≤ θ_k (or ≥), with at least one strict inequality.

Parameter tested: monotone trend in group central tendency

Assumptions (and what to do if they fail)

Total sample size is adequate (N ≥ 10 recommended) for the asymptotic normal approximation to J.medium

Check: Report total N and per-group n_j.

If violated: Small N makes the Z approximation unreliable.

Ties in the pooled sample do not dominate (adjustable via tie correction in the variance).low

Check: Report the largest tie block.

If violated: Heavy ties reduce power and may destabilise the variance estimate.

Ready to run a Jonckheere-Terpstra (ordered trend) on your own data?

Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.

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