Concept: Cochran-Armitage Test for Trend

Introduction

The Cochran Armitage test is a method of directing chi squared tests toward narrow alternatives. The test is sensitive to the linearity between response variable and experimental variables and detects trends that would not be noticed by more crude methods.

When the linear probability model holds, the statistic z ² , based on df = 1, tests for a linear trend in the proportions. The trend test may give strong evidence of positive or increasing linear trends, of constant or stable trends over time, or of negative or decreasing trends. Results of the trend test are similar to those obtained by testing that the slope is zero in a linear logit model.

In Roos et al. (1999), the trend statistic was used to measure the growth in screening mammography over time (an increasing linear trend) among both urban and rural women.

On-Line Documentation

There are several web sites available that detail statistical information about the trend test and how to apply it using SAS® software. The following two sites are accessible from this page to assist in this description and to provide working examples of this statistical test:

• SAS OnLineDoc® 9.1.3 - Search using the phrase "Cochran Armitage" (accessed September 5, 2008).
  
  
• Hui Liu. Cochran-Armitage Trend Test Using SAS, Paper SP05, Merck Research Labs, Merck & Co., Inc, Rahway, NJ (2007) (accessed September 5, 2008).

SAS Code Example

The SAS® system provides procedures for calculating various "trend" statistics. One application of the Cochran Armitage trend test is an option within Proc Freq . Specifying 'trend' within the Tables statement will generate the statistic.

Example:

/*Produce a cross tab with display of Cochran Armitage trend statistic*/
proc freq data= name_of_data ;
tables var1 * var2 /trend ;
run;