[BioC] Z-score

[Wolfgang Huber]

Dear Benjamin,

the range of the z-score is minus infinity to plus infinity, and the
distribution will have mean 0 and standard deviation 1. If S
is Normal (with some mean and variance), then z is N(0,1).

I don't agree that z-transformation induces Normality, the distribution
of z will be just the same as that of S, but shifted and scaled.

 Best wishes
  Wolfgang



William Shannon wrote:
> Yes, it will scale the sd up to 1 and you can expect most data to fall between -3 and 3.  
>    
>   The more important question is why are you transforming.  A z-transformation is done to induce normality (usually) which is important for certain statistical tests.
>    
>    
>   Bill Shannon, PhD
> Associate Professor of Biostatistics in Medicine
> Washington University School of Medicine
> http://ilya.wustl.edu/~shannon 
> 
> Founder and President
> BioRankings, LLC
> 314-704-8725
> 
> 
> 
> Benjamin Otto <b.otto at uke.uni-hamburg.de> wrote:
>   Hi,
> 
> Just a stupid statistical question to z-scores:
> 
> Given a set "S" of numeric values the z-score of these values is given by:
> 
> (S - mean(S))/sd(S)
> 
> ??? What range of values do I expect afterwards? -1 to 1 mainly? When my
> standard deviation is smaller than one, then I get my range scaled up rather
> than down, but in any case and that is the main thing my standard deviation
> is scaled to 1. So do I have to worry if my new value range is scaled up?
> 
> Benjamin
>