Joseph -

I suggest you not use an hypothesis test. A p-value is changed, just by changing the sample size, so you'd need an idea of effect size, perhaps measurement of a type II error probability, or some sensitivity analysis. I think you are better served by looking at measurements and standard errors. Though standard errors are also changed by sample size, they are more easily interpretable. (Determing sample size needs are a matter of methodology and standard deviation to see what sample size achieves a desired standard error, perhaps for a confidence interval or a prediction interval. A population standard deviation, by the way, is a constant that you often try to estimate.)

If you have a list of characteristics for your 'soil elements,' and can measure them, then you might compare those measurements, where measurements are made multiple times. Graphics can be helpful. One important comparison could be to find a confidence interval around the difference in two means. Whatever confidence interval which barely does not include zero will tell you your "confidence," given your sample size, that one measure is larger than the other.

Best wishes - Jim

Hi Joseph,

If you want to group together elements which are similar based on some properties I would suggest you to try a classification algorithm based on trees. An advantage of this method is that you can plot the actual tree and observe how the different elements contribute to the classification, this is called 'variable importance ranking'. The solution is greatly facilitated by using package 'tree' of the R system.

A good explanation of the topic is presented in James et al. (2013) chap 8 (*)

Hope it helps,

Augusto

* Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani.

An Introduction to Statistical Learning with Applications in R. Springer Science+Business

Media New York 2013

You can use a correlation test with the response or the dependent Variable to test their effects.