Help with problem involving Euclidean distances

[cathsouza]

Hi,

I'm a biologiste and I'm not good at all in Math so I'm not even sure if this is the correct section to post this question (sorry if it's not the correct place!).

I'm using Euclidean distances to calculate the environmental heterogeneity bewteen two sampling sites (based in some environmental variables) using this formula:

At that point, everything is ok. The problem is that I need to estimate how much each one of these variables contributed to the Euclidean distance (that means, I need to know which variable was the main source of heterogeneity).

At first, I tried to estimate the contribution of each variable by calculating the Euclidean distance without a given variable and then the obtained value was subtracted from the Euclidean distance considering all the variables. Doing so, I obtained one value for each variable. But, later when I add all the values I don't get the exact value of the initial Euclidean distance (the one calculated with all variables).

Probably, it's a very easy solution but I cannot figure this out by myself! Could someone help me please? I need that to finish my analyses for a scientific article.

Thanks in advance!

 

[stapel]

I'm using Euclidean distances to calculate the environmental heterogeneity between two sampling sites (based in some environmental variables) using this formula:

At that point, everything is ok. The problem is that I need to estimate how much each one of these variables contributed to the Euclidean distance (that means, I need to know which variable was the main source of heterogeneity).

What is the precise, mathematical definition of this "distance" thing?

Assuming the p_i 's and q_i 's are corresponding values for each of the sites P and Q, why can't you just use whatever of the squared diff erences is largest?

Thank you!