Cochran-Armitage Trend Test

Coming soon

Categorical

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

Tests a MONOTONE TREND in event probabilities across ≥ 3 ordered predictor levels (binary outcome × ordered predictor).

Computes a trend score Z by regressing the binary outcome on scored predictor levels (default linearly-spaced 1, 2, …, k). Higher power than the unordered chi-square test when the true relationship IS monotone. Reports the trend Z, p, and the per-level event proportions with 95% CIs. The canonical dose-response test in clinical pharmacology, toxicology (NTP carcinogenicity assays), and any study with an a-priori ordered exposure.

Worked example

Does the response rate rise steadily with dose?

Response (yes/no) was recorded across four ordered dose groups; the Cochran-Armitage test looks specifically for a linear trend in the proportions.

Result

Response rose with dose (3% → 57%), Cochran-Armitage trend Z = 4.45, p < .001.

How you'd report it (APA)

A Cochran-Armitage test showed a significant increasing trend in response rate with dose, Z = 4.45, p < .001.

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • Dose-response with binary outcome
    A vaccine trial compares seroconversion (yes/no) across 4 dose levels (0, 10, 50, 100 μg).
  • Carcinogenicity / toxicology dose-response
    NTP carcinogenicity study: 50 rats per dose at 0, 50, 100, 200 ppm.

When NOT to — use instead

Hypotheses

H₀: the probability of the outcome event is constant across the ordered levels of the predictor — p_1 = p_2 = … = p_k.
Hₐ: there is a MONOTONE trend in the event probability across the ordered levels.

Parameter tested: linear trend in event probability across ordered levels

Assumptions (and what to do if they fail)

Each ordered level has an adequate number of observations and both outcome classes are represented.medium

Check: Report min per-level n and whether any level has 0 events or all events.

If violated: Sparse per-level cells reduce power; all-zero or all-one levels do not contribute to the trend.

The proportion of observations should be distributed across ordered levels rather than concentrated at one level.low

Check: Check the largest single level.

If violated: Skewed level distribution reduces sensitivity to trend in the sparse levels.

Ready to run a Cochran-Armitage Trend Test on your own data?

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

Run this test →