SED navigation bar go to SED home page go to Dataplot home page go to NIST home page SED Home Page SED Contacts SED Projects SED Products and Publications Search SED Pages
Dataplot Vol 2 Auxiliary Chapter

DIFFERENCE OF BIWEIGHT LOCATION

Name:
    DIFFERENCE OF BIWEIGHT LOCATION (LET)
Type:
    Let Subcommand
Purpose:
    Compute the difference between the biweight locations for two response variables.
Description The biweight location estimate is defined as:

    y* = SUM[i=1 to n][w(i)*y(i)]/SUM[i=1 to n][w(i)]

where

    w(i) = (1 - ((y(i)-y*)/(c*S))**2)**2  for (Y(i)-y*)/(c*S)**2 < 1

    w(i) = 0             otherwise

    and

    S = 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 wi and wi 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. Syntax:

    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.
Examples:
    LET A = DIFFERENCE OF BIWEIGHT LOCATION Y1 Y2
    LET A = DIFFERENCE OF BIWEIGHT LOCATION Y1 Y2 SUBSET X > 1
Note:
    The difference of biweight locations statistic is also supported for the following commands:

      DIFFERENCE OF BIWEIGHT LOCATIONS PLOT Y1 Y2 X
      CROSS TABULATE DIFFERENCE OF BIWEIGHT LOCATIONS PLOT Y1 Y2 X
      BOOTSTRAP DIFFERENCE OF BIWEIGHT LOCATIONS PLOT Y1 Y2
      TABULATE DIFFERENCE OF BIWEIGHT LOCATIONS Y1 Y2 X
      CROSS TABULATE DIFFERENCE OF BIWEIGHT LOCATIONS Y1 Y2 X
      LET Z = CROSS TABULATE DIFFERENCE OF BIWEIGHT LOCATIONS Y1 Y2 X1 X2

    Enter

      HELP STATISTIC PLOT
      HELP CROSS TABULATE PLOT
      HELP BOOTSTRAP PLOT
      HELP TABULATE
      HELP CROSS TABULATE
      HELP CROSS TABULATE (LET)

    for more information on these plots and commands.

Default:
    None
Synonyms:
    None
Related Commands:
    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.
    STATISTICS PLOT = Generate a statistic versus subset plot.
    CROSS TABULATE PLOT = Generate a statistic versus two subsets plot.
    BOOTSTRAP PLOT = Generate a bootstrap plot.
Applications:
    Data Analysis
Implementation Date:
    3/2003
Program:
    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
        
    plot generated by sample program

    plot generated by sample program

Date created: 3/21/2003
Last updated: 4/4/2003
Please email comments on this WWW page to alan.heckert@nist.gov.