Determining significance of correlations with second matrix

[Maria Garcia]

Hello Bruce,

I ran my data in PC ORD and created an NMS ordination graph overlayed joint plot vectors. I also generated a table using the "correlations with second matrix feature."  Someone on my committee wanted to know if the correlations were significant. I am stumped by that question.  Is there a way for me to determine whether the correlations are significant using the features in PC ORD?  Are p-values typically reported for the correlations with the second matrix in the literature?

I appreciate your insight.
-Maria

[Bruce McCune]

Maria,

We address this a bit in the built-in Help system under the topic "Correlations with second matrix"

"This procedure is identical to correlations with the main matrix, except that it uses the variables in the secondary matrix. See example output under that topic. Only variables in the secondary matrix that you designated as quantitative are used.

A frequently asked question is how to test the significance of relationships between environmental variables and ordination axes. Application of standard inferential statistics to these correlations has a number of problems, as described by McCune and Grace (2002). To some extent these problems are alleviated by using a randomization test. The Mantel test in PC-ORD can be used for this purpose. For more information, see the topic, Mantel Test for Correlations with Ordination Axes."

For more information, please see p. 107 in McCune & Grace.

Bruce

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[Alin Van]

Bruce,

I had the same problem. And I read about Mantel  and Monte Carlo tests.
Still in some papers I have found that people are giving p-values for the correlation between the axes and variables, using Monte Carlo approach.
Is it really possible to do in PC-ORD?

Thanks,
Alina

[Alin Van]

Actually, I have found the answer - you can find a p-value from the MONTE CARLO test at the end of CCA results, if you click "randomization" when you start it.

Maria,
i hope it helps, at least one p-value for the correlation results...

[Bruce McCune]

I think a couple of issues are intertwined here. The checkbox for a randomization test with CCA --that tests the overall relationship between the second matrix and the first -- is it stronger than expected by chance?

The other issue is testing the strength of individual variables with an ordination. Yes, you can do this in PC-ORD, but it takes a few extra steps. PC-ORD de-emphasized this for reasons explained on p. 107 of McCune & Grace (2002).  Still, you can do it if you want to. To do it see the built-in Help topic, "Mantel Test for Correlations with Ordination Axes." The first part of this says,

"The Mantel test can be used to evaluate correlations between environmental variables and scores on ordination scores. This is a randomization test, so it does not depend on assumptions of normality of errors, but it the test statistic represents a linear relationship between the scores and the environmental variables.

Steps:

1. Graph ordination | Save scores as | spreadsheet.

2. Open this spreadsheet as the main matrix.

3. Delete all environmental variables but one.

4. Groups | Mantel Test. Choose Euclidean distance for both matrices.

-Bruce McCune