Cochran-Armitage test for trend

[Rey Yeo]

Hi,

I across across this webpage regarding the Cochran-Armitage test for trend in Stata and would like to check if my understanding is correct:

I used the ptrend command created by Patrick Royston.

Q trend (Pearson's correlation):
Null hypothesis (H0): There is no linear association.
If p < 0.05, reject H0 --> Linear association.

Q departure (Cochran-Armitage test):
Null hypothesis (H0): There is linear trend.
If p < 0.05, reject H0 --> No linear trend.

Thank you!

[Joseph Coveney]

From that FAQ: "The null hypothesis for the Cochran–Armitage test is that the trend is linear, and the test is for 'departures' from linearity; i.e., it’s simply a goodness-of-fit test for the linear model." The null hypothesis would be that the relationship is strictly linear, and the alternative would be that the relationship is not strictly linear, that is, it could be, for example, curvilinear, and could even have a zero linear component. (See the next paragraph in the FAQ.)

[Rey Yeo]

From that FAQ: "The null hypothesis for the Cochran–Armitage test is that the trend is linear, and the test is for 'departures' from linearity; i.e., it’s simply a goodness-of-fit test for the linear model." The null hypothesis would be that the relationship is strictly linear, and the alternative would be that the relationship is not strictly linear, that is, it could be, for example, curvilinear, and could even have a zero linear component. (See the next paragraph in the FAQ.)

Yes I saw this part. I wanted to check my understanding as null hypothesis would usually mean no association or trend. But the author did wrote that the null hypothesis for the Cochran-Armitage test is that there is linear trend. This will have implications for the interpretation of the p values. In some papers I came cross, the authors reported a trend with p < 0.05 or < 0.001 after performing the Cochran-Armitage test. That is strange to me, because if p is < 0.05 or < 0.001, the null hypothesis would have been rejected and the conclusion should be that there is no linear trend.

[Joseph Coveney]

The null hypothesis is that any trend is linear only. The alternative is the the trend has a nonlinear component, not that there is no linear trend.

[Rey Yeo]

The null hypothesis is that any trend is linear only. The alternative is the the trend has a nonlinear component, not that there is no linear trend.

Does that mean that in papers in which the authors report trends with significant p values, they are actually using results from the chi2 trend test (and not the Cochran-Armitage test)?

[Joseph Coveney]

Don't know what papers you're referring to, but, based upon what a commercial statistical software package does (see results from running the attached do file), that would be a good guess.

[Rey Yeo]

Don't know what papers you're referring to, but, based upon what a commercial statistical software package does (see results from running the attached do file), that would be a good guess.

Thank you for attached do file. Now I am convinced that the chi2 test for trend does report the Cochran-Armitage trend test results that I should be reporting.

[Laura Myles]

Following on from this, in both examples the p-value of the chi2 for departture is >.05. But what would you do if this had not been the case? would you still go ahead and report the chi2 for trend or would you consider reporting the overall chi2 or use a different approach?

In my data the chi2 for departure has p<.001 and when I plot the data I can see that rates decrease linearly over time but started to increase in 2016 and 2017.

Thank you.