Dear Gustavo, most important thing in multivariate analysis is number of subjects/or plots. If your data met this criterion that you have subjects 5 times your items, or at least 100 subjects, there is no need of normality. But if your data have severe abnormal distribution the number of subjects should be increased.

Refer to these articles for sample size in PCA:

https://www.encorewiki.org/display/~nzhao/The+Minimum+Sample+Size+in+Factor+Analysis

http://pareonline.net/getvn.asp?v=9&n=11

Refer to this book for central theorem for sample size:

Regression Methods in Biostatistics Linear, Logistic, Survival, and Repeated Measures Models

Eric Vittinghoff Stephen C. Shiboski

David V. Glidden Charles E. McCulloch

Page 33, 3.1.7 Robustness to Violations of Assumptions

EK

PCA has different interpretations and different applications. From a strictly rigorous statistical point of view, PCA consists of eigenvalue decomposition of the covariance matrix of Gaussian distributed random variables, and obtaining uncorrelated linear combinations of these r.v. starting with the highest variance to the lowest. In this paradigm, since the original r.v.'s are Gaussian distributed, their linear combinations will also be Gaussian distributed, and uncorrelated principal components will also be independent. In statistical process control, for instance, this approach is widely adopted, and Hotelling's T2 and Q-residual tests can be used with established confidence limits. On the other hand, PCA has also the interpretation of projecting the given data into a reduced linear subspace (or onto a reduced plane), which most explains the data. In this paradigm, PCA is mainly used as a data compression, dimension reduction, or even filtering method for non-Gaussian distributed and/or nonlinear data. When PCA is used for these purposes, the above mentioned standard statistical tests cannot be used. Nevertheless the dimension reduction capability and particularly robustness of PCA is, IMHO, still unmatched, though many nonlinear techniques like Isomap, Independent Component Analysis, Local Linear Embedding have come out in the recent years. So to sum it all, the answer to your question depends on your field of application of PCA, and what you hope to achieve with it. I'd say, whatever your distribution of multivariate data, using PCA initially is a very practical and good way of starting your analysis. Then you may continue with more sophisticated tools.

Normal distribution is not necessary, read more in http://f3.tiera.ru/2/M_Mathematics/MV_Probability/MVsa_Statistics%20and%20applications/Jolliffe%20I.%20Principal%20Component%20Analysis%20(2ed.,%20Springer,%202002)(518s)_MVsa_.pdf

Hello, I agree with you Vesna, it'is not necessary because he is an exploratory approach.

Thank you for your answers. It is clear now after having dealt with both Gaussian and non-Gaussian distributed data. I often see people zscoring the data without checking the normality. Would you say this is a bad practice or it is suppressed by having enough subjects? The kind of data I am going to deal from now is not necessary Gaussian distributed, so perhaps would it be better if I used a scaling factor instead of zscoring?