You may try to quantify a correlation between them using non-parametric correlation coefficients, like the Spearman or the Kendall's one.

You can also explore this graphically, and see if something seems visible.

Last, if you have other covariate, you may try more complex models of your values using for instance tools suggested by Jacek.

I didn't expect normality in the distribution, my interest is related to investigate if the concentration distribution of this two chemical compound my follow a statistical description or law in terms of reciprocal correlation. I know that the nature of the aquifer is the strong reason that drive the chemical composition of the groundwater, especially for the metals and metalloids.

best will be Karl pearson

Data from groundwater are not normally distributed,try Pearson correlation or PCA

> Ayedun Hassan : tests based on Pearson (linear) correlation assume nomality of the data...

'cause I'm too inexperienced with respect of statistical results, I've tried to examine the possible correlation with the Kendall and Spearman tests (are they appropriate for the non parametric distribution?). so one of the result I've obtained using R is paste below, can you help me to read this results? ("cor" means correlation value? p-value=0 are related to significativity of the test and so I can reject the null-hypotesis?)

Kendall's rank correlation tau

Mn Fe

Mn cor 1 0.5122

N 134 134

stat** 7.087

p-value 0.0000

---------

Fe cor 0.5122 1

N 134 134

stat** 7.087

p-value 0.0000

---------

** z

HA: two.sided

Is it the direct output of the cor.test( x, y, method = "spearman" ) of R ? Does not look like the usual output...

But basically, yes, if p-value is below your alpha, you can reject the hypothesis of uncorrelation.

Seems strange that the "stat" and "cor" is the same for the two tests; the output is not very readable...

I use the Deducer GUI for R, so I've noted some differences through out the output, anyway the test is one Mn-Fe. I think it is such a double answer like a matrix reader. Finally the two results are identically because the test is the same one. So the very strange value aren't the p-value=0?

Not, if this is a kind of matrix view and the two tests are in fact the same, it is quite normal. And with a stat of 7, p-value almost null is coherent & there is a significant correlation between Mn & Fe.

But I suggest to carefully read that part of the doc to really understand the output & be sure it really does what you need --- I personnaly do not know this GUI for R so can't help on that point.

For quantitative data, the best is to use the correlation ratio as the measure of strength of correlation. Previously, there is a sense to build graphs, as recommended Jacek Pietraszek.

I've decided to attache a screenshot of the result. The two tests (Kendall e Spearman) reject the null-hypotesis. Some delucided (any help are welcome)

(the file is here)

following the Jacek contribution I've tested the distribution of the two datasets in a 2D diagram (scatter plot) so the data not follow such "plume or cloud" geometry nor a curvilinear trend

I'm indebted with you and yours comments and technical support, the chemical characterization of groundwater almost do not have a statistical correlation, too much factor are dependant. So maybe this confirm the anisotropic nature of the subsurface, even if this is a nature "dictact". Finally i think that in addiction to the chemical compound concentration I need to consider other physico-chemical characteristics such as pH, conducibility etc.

These parameters will only correlate at very negative redox. You might break the data up in this regard if you have ORP or DO measurements.