DIFFERENCE OF WINSORIZED SD

DIFFERENCE OF WINSORIZED SD (LET)

Let Subcommand

Compute the difference between the Winsorized standard deviations for two response variables.

The standard deviation estimate can be heavily influenced by extreme values. The Winsorized standard deviation compensates for this by setting the tail values equal to a certain percentile value. For example, for a 90% Winsorized standard deviation, 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 standard deviation formula (HELP STANDARD DEVIATION for details) is applied.

For the difference of Winsorized standard deviations, the Winsorized standard deviation is computed for each of two samples then their difference is taken.

LET <par> = DIFFERENCE OF WINSORIZED SD <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 standard deviation is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = DIFFERENCE OF WINSORIZED SD Y1 Y2
LET A = DIFFERENCE OF WINSORIZED SD 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 SD Y1 Y2

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

None

DIFFERENCE OF WINSORIZED STANDARD DEVIATION is a synonym for DIFFERENCE OF WINSORIZED VARIANCE.

WINSORIZED SD	= Compute the Winsorized sd.
WINSORIZED VARIANCE	= Compute the Winsorized variance.
WINSORIZED MEAN	= Compute the Winsorized mean.
BIWEIGHT MIDVARIANCE	= Compute the biweight midvariance.
STANDARD DEVIATION	= Compute the standard deviation.
MEDIAN ABSOLUTE DEVIATION	= Compute the median absolute deviation.
AVERAGE ABSOLUTE DEVIATION	= Compute the average absolute deviation.
DIFFERENCE OF WINSORIZED MEAN	= Compute the difference of the Winsorized means.
DIFFERENCE OF WINSORIZED VARIANCE	= Compute the difference of the Winsorized variances.
DIFFERENCE OF AAD	= Compute the difference of the aad.
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 SD Y1 Y2 
    

The following Dataplot output is generated.

       *************************************************
       **  LET A = DIFFERENCE OF WINSORIZED SD Y1 Y2  **
       *************************************************
  
  
 THE COMPUTED VALUE OF THE CONSTANT A             =  0.36153185E+00