XLSTAT: Cochran-Armitage trend test in Excel

 

Background

The Cochran-Armitage trend test, also referred to as the trend on proportions test, allows to test if a series of proportions (or the corresponding counts, stored in an Rx2 contingency table), can be considered as varying linearly with an ordinal or continuous score variable. It is related to the Chi-square independence test that allows to test if there is relationship between the rows and the columns of a contingency table. The Cochran-Armitage test allows to take into account a ranking among the rows, based on scores.

 

Dataset for Example

The data used in this tutorial have been published in [Cochran W.G. (1954). Some methods on strengthening the common Chi-square tests. Biometrics, 10, 417-451] and are also used in [Agresti A. (1990), Categorical Data Analysis. Wiley]. The data correspond to a study where drugs have been given to patients with leprosy at two different levels (Low/High).

The clinical impact of the drugs is recorded on a five-level scale (Worse, Stationary, Slight improvement, Moderate improvement, Marked improvement). Our goal is to determine whether there is a linear dependence between the impact and the level of drugs.

 

Setting Up

• Open XLSTAT.

• Click on the Correlation-Association tests menu and select the Cochran-Armitage trend test feature:

• Once you have clicked on the button, the dialog box appears.

In the General tab:

• Select the data corresponding to the two columns containing the counts for each level.

• In the Data format field, select the Contengency table option. 

• Do not select the scores (e.g., clinical impact) since they are ordinal and already sorted.

• Check the Column labels option if the column headers were included in the selection.

In the Options tab:

• Select the two-sided alternative hypothesis to test for the presence of a linear trend.

• Activate the Monte Carlo method to get results that better approximate an exact test, improving upon the classical Cochran-Armitage approximation.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

The first result is a summary based on the selected data.

A scatter plot is displayed so that you can visually see if there is a trend or not. We can see here that there is a trend, and that it is almost perfectly linear.

Last, the results of the two tests (approximated, and simulations based) are displayed. The two results are close and lead us to conclude, with a very low risk of being wrong, that there is a linear trend in the proportions.

 

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