Page's Trend Test (ordered repeated measures)

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

Paired analogue of the Jonckheere-Terpstra trend test.

Detects a MONOTONE trend across ≥ 3 ordered within-subjects conditions. Computes L = Σ c_j · T_j where c_j = (1, 2, …, k) are the a-priori condition scores and T_j is the column-j rank-sum within subject, then refers a Z-transform to the standard normal. Reports L, Z, p, and per-condition within-subject median ranks. Typically 10-30% more powerful than Friedman when the within-subject ordering is correctly specified; no power against non-monotone within-subject trajectories.

Worked example

Do repeated conditions follow a predicted order?

Page's trend test checks for a pre-specified ordered trend across matched (repeated) conditions — the ranked-trend counterpart to Friedman.

Result

Rankings followed the predicted order, Page's L = 148, p = .006.

How you'd report it (APA)

Page's trend test confirmed the predicted ordered trend across conditions, L = 148, p = .006.

When to use it

  • Longitudinal repeated measures with a priori ordering
    A clinical study measures depression score on the same 20 patients at baseline, 1 month, 3 months, and 6 months post-treatment.
  • Within-subjects ordered dose / intensity
    Pain-tolerance study: 25 subjects exposed to 4 ascending stimulus intensities (counterbalanced order).

When NOT to — use instead

Hypotheses

H₀: the within-subject distributions of the k conditions are identical — no trend across ordered conditions.
Hₐ: there is a MONOTONE trend in the within-subject rank across the ordered conditions (θ_1 ≤ θ_2 ≤ … ≤ θ_k or the reverse).

Parameter tested: monotone trend across the k ordered within-subjects conditions

Assumptions (and what to do if they fail)

Each subject has a measurement at every one of the k ordered conditions (listwise deletion).high

Check: Tabulate missing-per-condition; report n_dropped.

If violated: Subjects with missing conditions are dropped by listwise deletion, reducing power and potentially biasing if missingness is not random.

At least ~8 subjects (rule of thumb) for the normal approximation to Page's L.medium

Check: Report n_subjects and k.

If violated: Small n makes the asymptotic Z approximation coarse.

Ready to run a Page's Trend Test (ordered repeated measures) on your own data?

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

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