One-sided p-values for the Cochran-Armitage trend test (Version 1.2)

Hypothesis: All response probabilities are equal.

$$H_0: p_0=p_1=\ldots = p_k$$

Alternative: The dose responses are monotonically increasing with strict monotone increase in at least one dose step.

$$H_1: p_0 \leq p_1 \leq \ldots \leq p_k \text{ with } p_k > p_0 $$

Author: Dominic Edelmann


Dose scores

Group sizes

Cases per group

Dose 1
Dose 2
Dose 3
Dose 4
Dose 5
Dose 6
Dose 7
Dose 8
Dose 9
Dose 10

p-value of asymptotic test:

p-value of exact test:

Brief Description:

This app computes the one-sided p-values of the Cochran-Armitage trend test for the asymptotic and the exact conditional test. The test statistic used for the asymptotic test can e.g. be found in the paper by Portier and Hoel. The exact conditional test has been established by Williams. The computation of its p-value is performed using an algorithm following an idea by Mehta, et al.

Armitage, P. Tests for linear trends in proportions and frequencies. Biometrics 11.3 (1955): 375-386.
Cochran, W. G. Some methods for strengthening the common χ ² tests. Biometrics 10.4 (1954): 417-451.
Mehta, C. R., Nitin P., and Pralay S. Exact stratified linear rank tests for ordered categorical and binary data. Journal of Computational and Graphical Statistics 1.1 (1992): 21-40.
Portier, C., and Hoel D. Type 1 error of trend tests in proportions and the design of cancer screens. Communications in Statistics-Theory and Methods 13.1 (1984): 1-14.
Williams, D. A. Tests for differences between several small proportions. Applied Statistics (1988): 421-434.