DIFFERENCE OF BIWEIGHT LOCATION

DIFFERENCE OF BIWEIGHT LOCATION (LET)

Let Subcommand

Compute the difference between the biweight locations for two response variables.

The biweight location estimate is defined as:
\( y* = \frac{\sum_{i=1}^{n}{w_{i}y_{i}}} {\sum_{i=1}^{n}{w_{i}}} \)

where

\( w_{i} = (1 - (\frac{y_{i} - y*}{cS})^{2})^{2} \hspace{0.5in} \mbox{for } (\frac{y_{i} - y*}{cS})^{2} < 1 \)

\( w_{i} = 0 \hspace{0.5in} \mbox{otherwise} \)

and

\( S = \mbox{median}\{|y_{i} - y*|\} \)

c = 6 (using 6 means that residuals up to approximately \( 4 \sigma \) are included)

Note that this is an iterative estimate since y* depends on w_i and w_i depends on y*.

Dataplot will compute up to 10 iterations (computation is terminated if the biweight location estimate does not change in value by more than 0.000001).

For the differeence of biweight locations, the biweight location is computed for each of two samples then their difference is taken.

LET <par> = DIFFERENCE OF BIWEIGHT LOCATION
                        <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 biweight locations is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = DIFFERENCE OF BIWEIGHT LOCATION Y1 Y2
LET A = DIFFERENCE OF BIWEIGHT LOCATION Y1 Y2 SUBSET X > 1

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

None

None

BIWEIGHT LOCATION	= Compute the biweight location.
DIFFERENCE OF MEDIAN	= Compute the difference of medians.
DIFFERENCE OF TRIMMED MEAN	= Compute the difference of trimmed means.
DIFFERENCE OF MIDMEAN	= Computes the difference of midmeans.
DIFFERENCE OF MEAN	= Compute the difference of means.
BIWEIGHT SCALE	= Compute a biweight scale estimate of a variable.
BIWEIGHT CONFIDENCE LIMITS	= Compute a biweight based confidence interval.

Data Analysis

3/2003

SKIP 25 
READ IRIS.DAT Y1 TO Y4 X 
. 
LET A = DIFFERENCE OF BIWEIGHT LOCATION Y1 Y2 
TABULATE DIFFERENCE OF BIWEIGHT LOCATION Y1 Y2 X 
. 
XTIC OFFSET 0.2 0.2
X1LABEL GROUP ID
Y1LABEL DIFFERENCE OF BIWEIGHT LOCATIONS
CHAR X 
LINE BLANK 
DIFFERENCE OF BIWEIGHT LOCATION PLOT Y1 Y2 X 
CHAR X ALL 
LINE BLANK ALL 
BOOTSTRAP DIFFERENCE OF BIWEIGHT LOCATION PLOT Y1 Y2 X  
    

The following output is generated.

       *****************************************************
       **  LET A = DIFFERENCE OF BIWEIGHT LOCATION Y1 Y2  **
       *****************************************************
  
  
 THE COMPUTED VALUE OF THE CONSTANT A             =  0.27841682E+01
  
  
       ********************************************************
       **  TABULATE DIFFERENCE OF BIWEIGHT LOCATION Y1 Y2 X  **
       ********************************************************
  
  
                 *    Y1       AND Y2
     X           *    DIFFERENCE OF BIWEIGHT LOCATION
 **********************************************
     1.00000     *     1.57608
     2.00000     *     3.14232
     3.00000     *     3.60915
  
       GROUP-ID AND STATISTIC WRITTEN TO FILE DPST1F.DAT