# Alternative data standardization procedures before PCA analysis

I'm working with morphometric data including 50 different variables (with very different scales) measured in 180 individuals (these 180 individuals belong to 4 different groups which received different treatments) and I'm trying to analyze these data by PCA in order to identify the variables, or combinaisons of variables, which are the most useful to discriminate these individuals.

If I understand things correctly, Z-Score is classically used to standardize data before PCA analysis in order to obtain variables with a mean = 0 and SD = 1. However, most of my data are not normally distributed. This will thus affect the "quality" of the standardization since Z-Scores are based on the mean and SD of the data. Therefore, I'm trying to use Robust Z-Scores (based on median and MAD) instead of the classical Z-Scores. After standardization by the Robust Z-Scores, all my variables have a median = 0 and a MAD = 0.67.

I'd like to know if the standardization based on Robust Z-Scores (Median & MAD) instead of classical Z-Scores (Mean & SD) is suitable for PCA analysis.

Thanks a lot for your precious help !

• The use of Z-scores for standardization means your PCA is based on correlations rather than covariances. There is no requirement in most PCA applications that the distribution by Normal and there is no requirement, period, for Z-scores to be useful and meaningful, apart from the need for the SD to be nonzero so that the Z-score can be defined.
– whuber
Commented Dec 2, 2021 at 13:52
• How are you intending to use the model? Will you be applying it to predictions on new data? If so, how will you apply the "robust z-score" transformation to the new data?
– EdM
Commented Dec 2, 2021 at 14:07
• The PCA will not be used for predictions on new data but to identify the variables, or combinaisons of variables, which are the most useful to discriminate the individuals (the 180 individuals belong to 4 groups which received different treatments).
– Erik
Commented Dec 3, 2021 at 16:33