Standardizing Variables

SAS

    Proc Standard is used to create a new SAS data set with standardized values for the specified variables. Here is a simple example:

options pageno=min nodate formdlim='-';
title 'Standardizing Variables.'; run;
data Sol; input x y @@; cards;
5 80 4 100 3 40 2 60 1 20
proc corr; var x; with y; run;
proc standard data=Sol mean=0 std=1 vardef=n out=zscores; var x y; run;
proc print; run;
data corr; set zscores;
xy=x*y;
proc means mean; var x y xy; run;
 

    The MEAN= sets the value for the mean of the standardized variable.  STD= sets the value for the standard deviation of the standardized variable.  VARDEF= tells SAS what to use for the denominator when computing the variances.  The default value is DF (N-1).  Specifying N indicates that you consider the available data to be the entire population of interest.

    In the program above I also demonstrate that a Pearson correlation coefficient is simply the average value of the cross products of the z-scores for the variables of interest.

    In the programs I used to calculate grades for my students I standardize each student's average (across exams etc.) score, but I do not use PROC STANDARD to do so.  Rather, I simply run the program (which includes PROC UNIVARIATE) once, note the mean and standard deviation, and then insert the values for mean and standard deviation in a data step statement like "Z_score=(average - 89.4)/6.83;" before I run the program a second time.

SPSS

    Analyze, Descriptive Statistics, Descriptives.  Scoot into the Variable(s) box the variables you wish to standardize to mean 0, std 1.  Check the box "Save standardized values as variables."  OK.

    Please note that SPSS uses DF (N-1) in the denominator for the variance when computing these z-scores.  Of course, you can always just find the mean and std of the variables to be transformed and then use the COMPUTE operation to do the transformation.

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This page most recently revised on 8. February 2006.