Z-score
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Benjamin Otto ▴ 830
@benjamin-otto-1519
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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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@william-shannon-1787
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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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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 > > > >_______________________________________________ >Bioconductor mailing list >Bioconductor at stat.math.ethz.ch >https://stat.ethz.ch/mailman/listinfo/bioconductor >Search the archives: >http://news.gmane.org/gmane.science.biology.informatics.conductor Naomi S. Altman 814-865-3791 (voice) Associate Professor Dept. of Statistics 814-863-7114 (fax) Penn State University 814-865-1348 (Statistics) University Park, PA 16802-2111