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:
 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.
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


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