Stats Question

Hi REG,I am a little confused with your question. Do you want to test whether the trees planted at different places are correlated? Basically, what do you have are variables related to the enviornment around the trees. However, these varialbes are like the INPUT, not your response. The relationship among these varialbes depends on how (where) do you choose your samples, right? So, I think what you need is to measure the trees from different aspects. Then, analyze where these trees are similar in someway.

Before we jump into analysis like ANOVA (which doesn’t seem appropriate given that quantitative inputs are described), we need to understand what the output is.
In the original inquiry, 8 total columns of data were indicated, and 8 quantative environmental variables were mentioned.  Consequently, you can’t compare whether one willow tree is different from another because we apparently don’t have an output measurement for them.  If we can get the trees’ height or circumference, for example, then we can understand whether the 8 inputs have some impact on the trees.
I’m curious whether one of these 8 variables is really an output. 

I think I understand you problem now. You want to see whether the environment for willow occurrences is different. Am I right? Of course, you first step shoulb be looking at each individual variable, and see whether there are special patterns exist among them.Then, I propose two possible ways to do the multivariate analysis:1. Use a multivariate T2 chart to plot your data. Although you are not really using the control chart to monitor anything, from the multivariate t2 chart, you can find the dispersion of your data. If all data points are very disperse, that means they are different. 2. Use clustering. Try to cluster you data into multiple groups, and check the distance between the groups. If the distance is large, then it suggests that there is significant differences exist in your data. One more thing, you can even work on your original variable first, use factor analysis or principle component to extract significant factors, then do the above two analysis based on the factors your extracted.