[BioC] Z-score

[Naomi Altman]

To clarify and summarize the remarks of Bill and Wolfgang,

Taking z-scores does not induce normality.  However,
if the data are close to normal, most of the z-scores will fall 
between -3 and 3.

Regards,
Naomi

At 08:53 AM 2/8/2007, Wolfgang Huber wrote:

>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
> >
>
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Naomi S. Altman                                814-865-3791 (voice)
Associate Professor
Dept. of Statistics                              814-863-7114 (fax)
Penn State University                         814-865-1348 (Statistics)
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