On 12-Aug-2014 21:41:52 Rolf Turner wrote: > On 13/08/14 07:57, Ron Michael wrote: >> Hi, >> >> I would need to get a clarification on a quite fundamental statistics >> property, hope expeRts here would not mind if I post that here. >> >> I leant that variance-covariance matrix of the standardized data is equal to >> the correlation matrix for the unstandardized data. So I used following >> data. > > <SNIP> > >> (t(Data_Normalized) %*% Data_Normalized)/dim(Data_Normalized)[1] >> >> Point is that I am not getting exact CORR matrix. Can somebody point >> me what I am missing here? > > You are using a denominator of "n" in calculating your "covariance" > matrix for your normalized data. But these data were normalized using > the sd() function which (correctly) uses a denominator of n-1 so as to > obtain an unbiased estimator of the population standard deviation. > > If you calculated > > (t(Data_Normalized) %*% Data_Normalized)/(dim(Data_Normalized)[1]-1) > > then you would get the same result as you get from cor(Data) (to within > about 1e-15). > > cheers, > Rolf Turner
One could argue about "(correctly)"! >From the "descriptive statistics" point of view, if one is given a single number x, then this dataset has no variation, so one could say that sd(x) = 0. And this is what one would get with a denominator of "n". But if the single value x is viewed as sampled from a distribution (with positive dispersion), then the value of x gives no information about the SD of the distribution. If you use denominator (n-1) then sd(x) = NA, i.e. is indeterminate (as it should be in this application). The important thing when using pre-programmed functions is to know which is being used. R uses (n-1), and this can be found from looking at ?sd or (with more detail) at ?cor Ron had assumed that the denominator was n, apparently not being aware that R uses (n-1). Just a few thoughts ... Ted. ------------------------------------------------- E-Mail: (Ted Harding) <ted.hard...@wlandres.net> Date: 12-Aug-2014 Time: 23:22:09 This message was sent by XFMail ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.