Cochrane Armitage Trend Test Calculator

Analyze ordered binary outcomes with flexible rows. Check trend direction, variance, significance, and assumptions quickly. Download clean reports for audits, articles, and final decisions.

Calculator Inputs

Group 1

Group 2

Group 3

Group 4

Example Data Table

Exposure Group Score Successes Total Observed Rate
Low Dose 1 12 80 0.1500
Medium Dose 2 18 78 0.2308
High Dose 3 29 82 0.3537
Very High Dose 4 42 84 0.5000

Formula Used

Let xᵢ be successes, nᵢ be totals, and wᵢ be ordered scores. Let X be total successes and N be total observations.

Score mean: w̄ = Σ nᵢwᵢ / N

Numerator: T = Σ (wᵢ - w̄)(xᵢ - nᵢX / N)

Variance: Var(T) = X(N - X) / [N(N - 1)] × Σ nᵢ(wᵢ - w̄)²

Test statistic: Z = T / √Var(T)

Chi square form: χ² = Z² with one degree of freedom.

How To Use This Calculator

Enter each ordered group in the correct sequence. Add the number of successes and the total sample size for every group. Choose custom scores when group spacing is unequal. Choose rank scores when the groups are simply ordered. Select the alternative hypothesis before reading the p value. Press calculate to view the result above the form. Use CSV or PDF buttons to save the current analysis.

Why Ordered Proportion Testing Matters

Many studies compare a binary outcome across ordered groups. The groups may be dose levels, exposure bands, age classes, stages, or ranked scores. A simple chi square test can show that proportions differ. It does not focus on a steady ordered rise or fall. The Cochrane Armitage trend test targets that ordered pattern.

What The Test Measures

The method compares observed successes with expected successes under no trend. Each group receives a numeric score. Those scores define the order and spacing. The calculator centers the scores by the group totals. It then builds a z statistic from weighted deviations. A large positive z suggests increasing risk. A large negative z suggests decreasing risk.

Good Data Preparation

Use counts, not percentages. Enter the number of successes and the group total for every ordered category. The total must include successes and non successes. Keep the order meaningful. Low dose should appear before high dose. Early stage should appear before late stage. Scores can be simple ranks, such as 1, 2, 3, and 4. Unequal scores are useful when the categories have real distances.

Interpreting Results

The two sided p value checks for any linear trend. The greater p value checks an upward trend. The less p value checks a downward trend. Select the alternative before reading the result. Also review the group rates. A significant test can still hide one unusual group. Small counts may need exact or permutation methods.

Practical Uses

Researchers use this test in clinical trials, toxicology, screening studies, survey analysis, and quality control. It is helpful when the question is ordered by design. It is less helpful when categories have no natural rank. Always explain the scoring choice in reports. Clear scores make the result easier to audit. Use subject expertise when the trend size appears modest or uncertain overall.

Limits And Assumptions

The test assumes independent observations and binomial outcomes within groups. It also expects the chosen scores to represent the planned order. It is a large sample method, so very sparse tables can be unstable. Use it with charts, rates, and context. Statistical significance is not the same as practical importance. Report both the trend test and the observed proportions together.

FAQs

What is the Cochrane Armitage trend test?

It is a statistical test for a linear trend in proportions across ordered groups. It is often used when outcomes are binary and categories have a natural order.

What data does this calculator need?

It needs successes, total observations, and ordered scores for each group. The total should include both successes and failures for that group.

Can I use percentages instead of counts?

No. Use actual counts. Percentages lose sample size information, and the variance calculation depends on the number of observations in each ordered group.

What do positive and negative z values mean?

A positive z value suggests an increasing trend as scores rise. A negative z value suggests a decreasing trend as scores rise.

Which p value should I report?

Report the p value matching your planned hypothesis. Use two sided for any trend, greater for an increasing trend, and less for a decreasing trend.

What scores should I enter?

Use meaningful ordered scores. Simple ranks work for evenly ordered groups. Custom scores are better when group distances represent real exposure or dose spacing.

Is this test the same as a chi square test?

No. A general chi square test checks any difference among proportions. This test focuses on a linear trend across ordered categories.

When should I avoid this test?

Avoid it when categories are not ordered, observations are dependent, or expected counts are very sparse. In those cases, consider other methods.

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