@Glen_b Interesting point about z-scores. They get everywhere. I've seen Bradman (batting average) vs Pele (goals per game) (sometimes vs Gretzky or vs Ty Cobb) "greatest sportsman ever" discussions that have been "settled" by means of z-score. I wondered if the authors of such arguments were ever tempted to add an entirely spurious p-value, just to "prove the point"...

... as to whether force-feeding younger students with z-scores is a good idea or not, it's quite good as an introduction to transforming your data, perhaps, and does give some intuition as to how a normal distribution works when you don't have mean 0 and SD 1.

The bigger problem, it strikes me, is getting it into people's heads that "just because you can calculate a z-score, doesn't mean you can treat it as normally distributed".

Does speaking of z-scores imply some context? I had to google the term (shows my lack of formal stats education I suppose), but I've always seen this concept as a way of creating a dimensionless measurement out of univariate data. In that context, it doesn't seem too harmful.

In good news: I received my copy of Feller Volume II in the mail today!

@Matthew The issue mostly applies in particular areas, where the first thing that's often done with any set of numbers is to subtract their mean and divide by their standard deviation. ... I give you the results of an experiment (control-group, treatment group), and following the z-scores mantra, you find z-scores... Now go ahead and do a two-sample t-test on those.

Of course it makes no sense, but that's because there was no reason to find z-scores in the first place; they're a means to an end in some situations but they're seemingly viewed as desirable in and of themselves.

@SIlverfish... oh my. Of course that's pointless [it's definitely Bradman ;) ]. I don't object to the notion of standardization as an idea at all; it's obviously very important in a variety of situations. My objection is simply to the notion that one must necessarily standardize data by computing z-scores ("get data, compute z-scores of everything, ... ").

@MatthewDrury ... it's so long since I looked at Feller. I should borrow it.

If I write a text, I may draw a picture of small hordes of shambling undead, shuffling about moaning "z-scores, z-scores"

I've a set of integer sequences. Is there any measure to get which sequence is the most unique among the set?

@Glen_b That image is awesome.

@user Strictly speaking "unique" is not a matter of degree (if it's one-of-a-kind it's unique, otherwise it isn't - there are degrees of rarity or unusualness, by contrast) -- but in any case, how would you define a scale of whatever it is you regard as unique/rare/unusual? There's an infinite number of ways one might define such a thing, but many of them won't be relevant for whatever it is you're doing.

@Glen_b @Silverfish @Matthew Drury The problem with z-scores seems often linked with the inconsistent terminological morass over what is meant by standardize, normalize, etc. and confusion between wide and narrow senses of transformation. We know that (value - mean)/SD is just a linear rescaling or transformation, but there are many uses of normalise to mean "make more nearly normal (Gaussian)".

There also seems a widespread misunderstanding that transformations always change distributions or even always are, or should be, capable of producing normal distributions. I recollect questions on how to transform indicator variables (0, 1) to normality....

I have a column of Customer Numbers with about 200k unique numbers that I want to use as input for a neural network. Do I need to convert them to 1-of-C Dummy Variable? Is there a better way than having 200k columns?

@Adam12344, please ask that on the main site; it isn't a chat item. When you ask, be sure to provide sufficient context & make it clear.

@Glen_b Thanks for the reply. Actually I'm newbie, so I am not sure how I want to define degree of unusualness. Maybe reading some existing metric can help me. Can you please point me to some.

@user @Glen_b has explained that "There's an infinite number of ways one might define such a thing" so we really, really need some hints from you. More positively, it seems that you may mean which is most unusual compared with the others; if so, it is naturally to start by plotting them. Are they monotonic? Is there some science behind this? If not, what is the interest?

@user can you say more about the situation, perhaps? It might give us some clues about what kinds of unusualness might be useful to you

@NickCox Yes, what you said about Z-scores was insightful. I'd add to that, that its often unclear which S.D. we "should" be dividing by...