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Dataplot Vol 2 Vol 1

DIFFERENCE OF BIWEIGHT MIDVARIANCE

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

      \( s_{bi}^2 = \frac{\sum_{i=1}^{n}{(y - y')^2(1 - u^2)^4}} {(\sum_{i=1}^{n}{(1 - u^2)(1 - 5u^2)})^2} \)

    where the summation is restricted to \( u_{i}^2 \le 1 \) and

      \( y' = \mbox{median } y \)

    and

      \( u_{i} = \frac{y_{i} - y'}{9*MAD} \hspace{0.3in} \mbox{for } (\frac{y_{i} - y*}{cS})^{2} < 1 \)

    where MAD is the median absolute deviation.

    For the difference of biweight midvariances, the biweight midvariance is computed for each of two samples then their difference is taken.

Syntax:
    LET <par> = DIFFERENCE OF BIWEIGHT MIDVARIANCE <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 midvariances is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = DIFFERENCE OF BIWEIGHT MIDVARIANCE Y1 Y2
    LET A = DIFFERENCE OF BIWEIGHT MIDVARIANCE Y1 Y2 SUBSET X > 1
Note:
    Dataplot statistics can be used in a number of commands. For details, enter

Default:
    None
Synonyms:
    None
Related Commands: Applications:
    Data Analysis
Implementation Date:
    2003/03
Program:
    SKIP 25 
    READ IRIS.DAT Y1 TO Y4 X 
    . 
    LET A = DIFFERENCE OF BIWEIGHT MIDVARIANCE Y1 Y2 
    TABULATE DIFFERENCE OF BIWEIGHT MIDVARIANCE Y1 Y2 X 
    . 
    XTIC OFFSET 0.2 0.2 
    X1LABEL GROUP ID 
    Y1LABEL DIFFERENCE OF BIWEIGHT MIDVARIANCE 
    CHAR X 
    LINE BLANK 
    DIFFERENCE OF BIWEIGHT MIDVARIANCE PLOT Y1 Y2 X 
    CHAR X ALL 
    LINE BLANK ALL 
    BOOTSTRAP DIFFERENCE OF BIWEIGHT MIDVARIANCE PLOT Y1 Y2 X  
        
    Dataplot generated the following output.
           ********************************************************
           **  LET A = DIFFERENCE OF BIWEIGHT MIDVARIANCE Y1 Y2  **
           ********************************************************
      
      
     THE COMPUTED VALUE OF THE CONSTANT A             =  0.52265614E+00
      
      
           ***********************************************************
           **  TABULATE DIFFERENCE OF BIWEIGHT MIDVARIANCE Y1 Y2 X  **
           ***********************************************************
      
      
                     *    Y1       AND Y2
         X           *    DIFFERENCE OF BIWEIGHT MIDVARI
     **********************************************
         1.00000     *   -0.349338E-02
         2.00000     *    0.178072
         3.00000     *    0.310287
      
           GROUP-ID AND STATISTIC WRITTEN TO FILE DPST1F.DAT
        
    plot generated by sample program

    plot generated by sample program

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Date created: 03/27/2003
Last updated: 11/06/2015

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