DIFFERENCE OF WINSORIZED VARIANCE

DIFFERENCE OF WINSORIZED VARIANCE (LET)

Let Subcommand

Compute the difference between the Winsorized variances for two response variables.

The variance estimate can be heavily influenced by extreme values. The Winsorized variance compensates for this by setting the tail values equal to a certain percentile value. For example, for a 90% Winsorized variance, the bottom 5% of the values are set equal to the value corresponding to the 5th percentile while the upper 5% of the values are set equal to the value corresponding to the 95th percentile. Then the regular variance formula (HELP VARIANCE for details) is applied.

For the difference of Winsorized variances, the Winsorized variance is computed for each of two samples then their difference is taken.

LET <par> = DIFFERENCE OF WINSORIZED VARIANCE <y1> <y2>
                        <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
            <y2> is the first response variable;
            <par> is a parameter where the computed difference of the Winsorized variance is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = DIFFERENCE OF WINSORIZED VARIANCE Y1 Y2
LET A = DIFFERENCE OF WINSORIZED VARIANCE Y1 Y2 SUBSET X > 1

The analyst must specify the percentages to Winsorized in each tail. This is done by defining the internal variables P1 (the lower tail) and P2 (the upper tail). For example, to Winsorize 10% off each tail, do the following:
LET P1 = 10
LET P2 = 10
LET A = DIFFERENCE OF WINSORIZED VARIANCE Y1 Y2

Dataplot statistics can be used in a number of commands. For details, enter
HELP STATISTICS

None

None

WINSORIZED SD	= Compute the Winsorized sd.
WINSORIZED VARIANCE	= Compute the Winsorized variance.
WINSORIZED MEAN	= Compute the Winsorized mean.
BIWEIGHT MIDVARIANCE	= Compute the biweight midvariance.
VARIANCE	= Compute the variance.
MEDIAN ABSOLUTE DEVIATION	= Compute the median aboslute deviation.
AVERAGE ABSOLUTE DEVIATION	= Compute the average absolute deviation.
IQ RANGE	= Compute the interquartile range.
DIFFERENCE OF WINSORIZED MEAN	= Compute the difference of the Winsorized means.
DIFFERENCE OF WINSORIZED STANDARD DEVIATION	= Compute the difference of the Winsorized standard deviations.
DIFFERENCE OF WINSORIZED VARIANCE	= Compute the difference of the Winsorized variances.
DIFFERENCE OF BIWEIGHT MIDVARIANCE	= Compute the difference of the biweight midvariances.
STATISTICS PLOT	= Generate a statistic versus subset plot.
BOOTSTRAP PLOT	= Generate a bootstrap plot.
TABULATE	= Perform a tabulation for a specified statistic.

Data Analysis

2003/03

SKIP 25 
READ IRIS.DAT Y1 TO Y4 X 
. 
LET P1 = 10 
LET P2 = 10 
LET A = DIFFERENCE OF WINSORIZED VARIANCE Y1 Y2 
TABULATE DIFFERENCE OF WINSORIZED VARIANCE Y1 Y2 X 
. 
XTIC OFFSET 0.2 0.2 
X1LABEL GROUP ID 
Y1LABEL DIFFERENCE OF WINSORIZED VARIANCE 
CHAR X 
LINE BLANK 
DIFFERENCE OF WINSORIZED VARIANCE PLOT Y1 Y2 X 
CHAR X ALL 
LINE BLANK ALL 
BOOTSTRAP DIFFERENCE OF WINSORIZED VARIANCE PLOT Y1 Y2 X  
    

Dataplot generated the following output.

       *******************************************************
       **  LET A = DIFFERENCE OF WINSORIZED VARIANCE Y1 Y2  **
       *******************************************************
  
  
 THE COMPUTED VALUE OF THE CONSTANT A             =  0.38307112E+00
  
  
       **********************************************************
       **  TABULATE DIFFERENCE OF WINSORIZED VARIANCE Y1 Y2 X  **
       **********************************************************
  
  
                 *    Y1       AND Y2
     X           *    DIFFERENCE OF WINSORIZED VARIANCES
 **********************************************
     1.00000     *   -0.137959E-01
     2.00000     *    0.118057
     3.00000     *    0.261424
  
       GROUP-ID AND STATISTIC WRITTEN TO FILE DPST1F.DAT