# Should I standardize all variables before a PCA separately if some share the same units

I have a matrix that contains >2000 variables which can be divided in 4 groups of ~500 variables with each group having a distinct unit. I need to standardize the matrix before running a PCA, but when doing so, should I:

a) Standardize each variable independently (calculate mean and std dev on each column-each column being a variable- and use those to calculate standardized values for all values in said column), or

b) Treat each group of the 4 ~500 variables as a group to standardize: calculate mean and std dev for all values contained in those ~500 columns (as a group) and use those to standardize the values for all those ~500 variables

I am leaning towards "b" since standarizing as "a" would lead to same starting values being converted to different values for different columns depending on the mean/std for each column (say, for the first observation/row variable 1 and 2 -variables with same units- have values of 5, after standarization I could get for the first observation/row values of 1 and 2 for variable 1 and 2, respectively... which, to me, is counterintuitive.

But I am not aware of any other PCA whose data was treated like this and thus unaware if this would be a proper/mathematically correct to pretreat the data before running the PCA

## 1 Answer

No I wouldn't normally do that. It doesn't change anything other than the scale of the coordinates of the PCs, and those are easier to interpret if kept on the original scale.

If the scales of the data are somewhat arbitrary and don't have any particular meaning to your audience, you might want to standardize them as they will then all be on the SD scale which you may find easier to interpret.

But that usually won't be the case.

• It would change the scale of coordinates for each group of the 4 different types of variables, but it would also prevent the groups of variables with higher magnitude units to weigh more than lower magnitude ones when doing the PCA, correct? – mem31 Apr 6 '19 at 0:10
• Yes that's true, the variables with higher SD would have more contribution to the PCs. – Helene Hoegsbro Thygesen Apr 12 '19 at 2:20