What is the name of this normalization?

Question

This may be a stupid question but... is there a specific name for normalizing some data so that it has mean=0 and sd=1?

Or do I just say "data was normalized to have mean=0 and sd=1"?

thanks nico

Just a comment on the tag. Right now we have one question tagged "nomenclature" and another question tagged "terminology". I personally prefer "terminology" - it's much more common in everyday language than nomenclature, but I see nomenclature potentially being used. Could someone consider a tag synonym or just a rename one way or the other?
@Thomas Owens: you are right, terminology is better, I changed it. I guess "nomenclature" sounds better to people in biology :)
btw, this is special case of "whitening" which takes data and makes it's empirical covariance matrix identity

ars · Accepted Answer · 2010-08-20 08:42:39Z

up vote 6 down vote accepted

The quantity $z = \frac{X - \mu}{\sigma}$ is a standard score. So, standardization is a common way to refer to it.

answered Aug 20 '10 at 8:42

ars
7,07111130

	wtf. you are to fast. i was still typing. nevertheless +1 for the correct answer. – Henrik Aug 20 '10 at 8:45
	Thank you ars! :) – nico Aug 20 '10 at 8:49

mbq · Answer 2 · 2010-08-20 09:24:29Z

up vote 3 down vote

I think it is just called z-score.

edited Aug 20 '10 at 9:24

answered Aug 20 '10 at 8:45

mbq♦
12.2k32166

	no, it is called z-score (small letter), big letter Z-scores refer to mean = 100 and sd = 10. – Henrik Aug 20 '10 at 8:46
	@Henrik I have never heard of something like this; nevertheless I've made the change, it seems lowercase z is used more often. – mbq♦ Aug 20 '10 at 9:25
	could be that it is a psychology specific distinction. browsing the web i realized that it could even be specific German. At least I only found it in the German wikipedia (not surprisingly i learned it in a German university): de.wikipedia.org/wiki/Normskala – Henrik Aug 20 '10 at 9:50
	Let's not confuse the z-score with the process of standardization. The former is described in ars' answer: it is a statistic. Standardization consists of replacing each of the X[i] by (X[i]-m)/s for further analysis. That's what nico was asking about. – whuber♦ Aug 20 '10 at 15:58

2 Answers