
Dear all,

I have a question about the 'sdev' value returned by the princomp function (which does principal components analysis).

On the help page for princomp it says 'sdev' is 'the standard deviations of the principal components'.

However, when I calculate the principal components for the USArrests data set, I don't find this to be the case:

Here is how I calculated the principal components and got the 'sdev' values:
> scaledUSArrests <- scale(USArrests) # standardise the variables to have variance 1 and mean 0
> myPCA <- princomp(scaledUSArrests)  # do the PCA
> myPCA$sdev
   Comp.1    Comp.2    Comp.3    Comp.4 
1.5590500 0.9848705 0.5911277 0.4122639 

As far as I understand, the principal components themselves are stored in the 'scores' value returned by princomp, so I calculated the standard deviations of those values to see if they agree with 'sdev':
> sd(myPCA$scores)
   Comp.1    Comp.2    Comp.3    Comp.4 
1.5748783 0.9948694 0.5971291 0.4164494 

I get different values than I got using sd(myPCA$scores) and myPCA$sdev, why is this?

As there are 4 standardised variables, and the variance of each standardised variable is 1, I would expect the variances of the principal components to add to 1. I find that this is true for the variances calculated using sd(myPCA$scores) but not myPCA$sdev:
> (1.5590500^2) + (0.9848705^2) + (0.5911277^2) + (0.4122639^2)
  3.92
> (1.5748783^2) + (0.9948694^2) + (0.5971291^2) + (0.4164494^2)
  4.00

I am wondering why are the values in 'sdev' not equal to the standard deviations of the principal components (as stored in 'scores'), and why is the total variance calculated by summing the squared 'sdev' values not equal to 4?

Sorry if I have misunderstood something obvious. I would be grateful for help as I'm a bit confused..

Kind regards,
Avril

Avril Coghlan
Cork, Ireland


	[[alternative HTML version deleted]]

