If your data are in weight percent, they are compositional. Treating them as they are implies using methods that are prone to be misleading. Karl Pearson pointed at the problems with spurious correlations back in 1897, something that should be well known after more than 100 years. There is a lot of literature on the issue. Look at the web www.compositionaldata.com to begin with. There you can find references and hints.

The boring answer is that the treatment of the data depends on what you want to do with the data.

If the sheet you have is in weight percent oxide, you can assume that all the necessary treatment of the raw data (e.g., correction for escape peaks and pulse pile up) has been carried out.

If the lanthanides are present in detectable quantities, I would include them in data sheets that you are reporting. They were present during the treatment of the raw data and are a part of the quantification. Make sure that they are properly calibrated.

During data analysis you can treat the data in whatever way is appropriate. For example, removing stoichiometric oxygen, recalculating to atomic weight percent, or normalising to "dry weight" by removing Loss On Ignition.

Thanks Alex!

If your data are in weight percent, they are compositional. Treating them as they are implies using methods that are prone to be misleading. Karl Pearson pointed at the problems with spurious correlations back in 1897, something that should be well known after more than 100 years. There is a lot of literature on the issue. Look at the web www.compositionaldata.com to begin with. There you can find references and hints.

Percentage data in medical field, as I know, it treated with arcsin transformation. The major objection to treating percentage data as it is that they often come from different denominators which are not so comparable. Consider 70 out of 100 can not be taken similar to 7 out of 10. Hence, transformation is suggested. In one of my international paper, I have used percentages with transformation. You can refer Statistical Methods by Snedecor and Cochran where it is suggested to use arcsin transformation to percentage data. The details of the publication in which we have used the methods is given below(sorry pdf copy of the paper is not available with me).

Regarding removing the not so desired data, by choice is not appropriate. Removing the so called outliers may change totally the outcome. Hence, removal of data should be done with care. Long back I read a paper with title "Finding the outliers that matters". The paper stressed that outliers should not be removed by choice. 

Tyagi, B.K., Ramnath, T. and Sahi, A. K. : Evaluation of repellency effect of Tegitus minuta (family composited) against the vector mosquitoes Anopheles stephensi liston, Culex quinquefaciatus say and Aedes aegypti (L). Int Pest Control (U.K.) 39 (1997) 184.

Dear Tharanga and all contributors,

As I understand your question about the analysis of major oxides, the data set constitutes a typical example of compositional data (pointed out by V. Pawlowsky-Glahn in a previous answer). This kind of data cannot be treated without transformations to the price of obtaining confusing or spurious results. In Geology these problems were treated intensively in the sixties (e.g. Chayes 1960), but the solution only arrived in the eighties mainly due to the contributions of J. Aitchison (his 1986 book is a summary of the theoretical developments at that time). Nowadays, the theory has been developed and compositions can be treated using orthogonal coordinates (isometric log-ratio transformations (ilr), balances) of the simplex. Many of these contributions are published in Mathematical Geosciences (previously Mathematical Geology) or in the book edited by Pawlowsky-Glahn and Buccianti (2011), and published by Wiley.

However, I would like to center in the point of suppressing lanthanides. Translated to compositional language, the suppression of variables corresponds to analyse a "subcomposition". The fact that lanthanides appear with a lower concentration (trace elements) than the major oxides does not imply that they are outliers (generally they are not). The question is whether the elimination of some elements can affect the results obtained for the remaining oxides. The log-ratio transformations have been explicitly designed to fulfill the so-called principle of "subcompositional coherence", so that you can safely analyse a subcomposition using these techniques. For instance, to transform your data into a subcomposition (in proportions), you need to add up the remaining variables and then divide each of them by the sum. However, you do not need to do this in a compositional approach, as when you compute balances or ilr transformations all the constants cancel out.

Although I am not experienced with the arcsin transformation, I think it is not subcompositionally coherent. Ramnath, is it so?

I would recommend you to download the free software CoDaPack (search for CoDaPack, Universitat de Girona). There are also R packages like Compositions (general purpose), robCompositions (robust statistics), zCompositions (dealing with zeros).

There have been some interesting mathematical discussions on data treatment for this question. I am not an expert in that so I would just add these are quite good advise about data treatment & statistics from respectable academicians like Dr. Pawlowsky-Glahn, Dr. Juan Jose Egozcue, and Dr. Takiar.

Being from the XRF field, i would like to mention a technical point here: generally if rocks are analyzed as oxides we assume they have been subjected to fusion (oxidation) to find major elements (not the trace ones). The software (fundamental parameters) assumes the sum of oxides as 100 % (all metals detected as oxides and their sum). I don't know how trace lanthanides are introduced as oxides...unless they have analyzed the pressed pellet for the trace elements as well. Generally removing anything from the total may lead to biased results.

However XRF being a std. method used to analyze rocks you should ask for the reproduction of certified reference materials (CRMs) and cross-check your results with them...do similar treatment as the CRMs for your sample...see reproducibility....you can only build your confidence (quality control) for results that way.

Dear Tharanga,

indeed bulk-rock analyses are traditionally expressed in wt % oxides, even when the originally measured quantities were element concentrations. The good side is that good analysis totals normally indicate good quality analyses. And as Axel mentioned it, the way in which data have to be expressed depend on the intended use. As I suppose, your XRF results are expressed in oxide wt % for major elements and ppm for trace elements, and you have to leave them unchanged or convert them according to the diagrams or mathematical expressions in which you intend to use them. Please find attached two excel files which might help you transform oxide concentrations in element concentrations or viceversa, or atomic concentrations (chemical formulae) in either oxide or element concentrations. Please consider that 1 wt% element equals 10.000 ppm, or 1 ppm = 0.0001 wt %. I made the files for personal use, so might you experience difficulties in using them, please just ask for clarifications.

I may only add to what I have mentioned previously that the transformations are basically done to reduce the variance in the data in question. So one can do various transformations to data and should see whether these or any one of the transformation selected reduces the variability or not ? If the transformation reduces the variability then it should be believed that the transformation has done its job otherwise it is not so useful. 

I have knowledge of application of transformation to biological data or medical data. So whether arcsine transformation is beneficial or not can be seen with the reduction in variability. 

To me, the main purpose of a transformation is to assure that the models and methods can be applied without violating the assumptions on which they are based. If the assumptions are violated, than the variance or any other measure can be nonsensical. Most methods assume that data lie in real space, i.e. they can range from -infinity to +infinity, an assumption seldom satisfied in practice without a transformation.

Dear all, Thanks a lot for your invaluable comments.

Calculate the normative mineralogies of your rocks from the oxide analyses.  Either the CIPW NORM or Irvine's CATANORM will do.   See what you can learn from the results.

Thanks all