DIFFERENCE OF BIWEIGHT MIDVARIANCE

DIFFERENCE OF BIWEIGHT MIDVARIANCE (LET)

Let Subcommand

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

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.

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.

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

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

None

None

BIWEIGHT MIDVARIANCE	= Compute the biweight midvariance.
MAD	= Compute the median absolute deviation.
AAD	= Compute the average absolute deviation.
PERCENTAGE BEND MIDVARIANCE	= Compute the percentage bend midvariance.
STANDARD DEVIATION	= Compute the standard deviation.
DIFFERENCE OF AAD	= Compute the difference of average absolute deviations.
DIFFERENCE OF SD	= Compute the difference of standard deviations.
DIFFERENCE OF BIWEIGHT SCALE	= Compute the difference of biweight scales.
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 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