Dear Hussein,

I am not aware if there is a specific limit, but the truth is the bigger your statistical population (more samples) is the more reliable are the results you get. The number of samples you refer is small but I guess you can apply some multivariate methods as those you refer; however, results should be treated with caution.

Communality and correlation are two different things. Communality refers to the degree by which a parameter’s contribution is explained by the extracted factors (e.g. in PCA or R-mode analysis), whilst correlation (coefficient I guess) accounts for the correlation matrix applied in a simple correlation analysis.

Regarding communalities, normally should be higher than 0.70 (70%) to interpret sufficiently the contribution of the variable parameters in the existing factors. Otherwise there are processes which cannot be explained and the general interpretation is weak.

Regarding correlation coefficient, 0.5 is the least threshold for the co-variance of two parameters, which means if positive a common source of enrichment and if negative a competitive process between them. Personally I don’t consider this value as safe; in literature higher thresholds are used (e.g. 0.7-0.8) to indicate a strong relationship between two parameters.

Below find attached some of my publications dealing with the application of multivariate statistics. You may find a lot more in literature.

 Regards

Article Environmental monitoring of Micro Prespa Lake basin (Western...

Article Assessing the hydrogeochemistry of groundwaters in ophiolite...

Article The use of hydrogeochemical analyses and multivariate statis...

Dear Evangelos,

Thank you so much  for your valuable comments and ideas are very interesting and important, would you add some reference which help me?

 Hi Hussein:

Evangelos has given you a really clear and cogent explanation.

Check your data too - you shouldn't really include any unstable parametric values in the MSA; so, drop out pH, DO, EC, temp etc.

A really useful and statistically robust approach is to use computational data analysis initially to reduce bias in the data; this is a really good preprocessing step before dumping the data into the MSA (here's a really good book on it: http://link.springer.com/book/10.1007/978-3-642-36809-7).

Use of CoDA allows means that you can deal adequately with any censored data and then you can scale and log transform the data before using PCA, HCA etc.

Tiernan

Thanks a lot for your valuable comments, would you add reference which help me

https://stats.stackexchange.com/questions/45820/minimum-sample-size-for-pca-or-fa-when-the-main-goal-is-to-estimate-only-few-com

Here are the discussion and few resources that should help in evaluating the sample size.

HTH

this will be helpful https://www.reneshbedre.com/blog/principal-component-analysis.html#sample-size-recommendations-for-pca

For the application of Multivariate analysis, The number of samples should be greater than number of variables quantified. Also Before conducting PCA, HCA or any other statistical test. Check the dataset for commonalities, KMO adequacy and perform bartletts' test.