DIFFERENCE OF WINSORIZED MEAN

DIFFERENCE OF WINSORIZED MEAN (LET)

Let Subcommand

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

The mean is the sum of the observations divided by the number of observations. The mean can be heavily influenced by extreme values in the tails of a variable. The Winsorized mean compensates for this by setting the tail values equal to a certain percentile value. For example, for a 90% Winsorized mean, 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.

For the differeence of Winsorized means, the Winsorized mean is computed for each of two samples then their difference is taken.

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

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

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

None

None

WINSORIZED MEAN	= Compute the Winsorized mean.
TRIMMED MEAN	= Compute the trimmmed mean.
WINSORIZED SD	= Compute the Winsorized sd.
WINSORIZED VARIANCE	= Compute the Winsorized variance.
DIFFERENCE OF MEDIAN	= Compute the difference of medians.
DIFFERENCE OF MEAN	= Compute the difference of the means.
DIFFERENCE OF MIDMEAN	= Compute the difference of the midmeans.
DIFFERENCE OF BIWEIGHT LOCATION	= Compute the difference of the biweight locations.
DIFFERENCE OF WINSORIZED STANDARD DEVIATIONS	= Compute the difference of the Winsorized variances.
DIFFERENCE OF WINSORIZED VARIANCE	= Compute the difference of the Winsorized variances.
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 MEAN Y1 Y2 
TABULATE DIFFERENCE OF WINSORIZED MEAN Y1 Y2 X 
. 
XTIC OFFSET 0.2 0.2
X1LABEL GROUP ID
Y1LABEL DIFFERENCE OF WINSORIZED MEANS
CHAR X 
LINE BLANK 
DIFFERENCE OF WINSORIZED MEAN PLOT Y1 Y2 X 
CHAR X ALL 
LINE BLANK ALL 
BOOTSTRAP DIFFERENCE OF WINSORIZED MEAN PLOT Y1 Y2 X  
    

Dataplot generated the following output.

       ***************************************************
       **  LET A = DIFFERENCE OF WINSORIZED MEAN Y1 Y2  **
       ***************************************************
  
  
 THE COMPUTED VALUE OF THE CONSTANT A             =  0.27719998E+01
  
  
       ******************************************************
       **  TABULATE DIFFERENCE OF WINSORIZED MEAN Y1 Y2 X  **
       ******************************************************
  
  
                 *    Y1       AND Y2
     X           *    DIFFERENCE OF WINSORIZED MEANS
 **********************************************
     1.00000     *     1.58000
     2.00000     *     3.19600
     3.00000     *     3.63800
  
       GROUP-ID AND STATISTIC WRITTEN TO FILE DPST1F.DAT