QUARTILE COEFFICIENT OF DISPERSION

QUARTILE COEFFICIENT OF DISPERSION (LET)

Let Subcommand

Compute the quartile coefficient of dispersion of a variable.

The sample quartile coefficient of dispersion is defined as
\( \mbox{QCD} = \frac{\mbox{Q3} - \mbox{Q1}} {\mbox{Q1} + \mbox{Q3}} \)

where Q1 is the lower quartile (25-th percentile) and Q3 is the upper quartile (75-th percentile).

This statistic has been suggested as a robust alternative to the coefficient of variation.

LET <par> = QUARTILE COEFFICIENT OF DISPERSION <y>
                        <SUBSET/EXCEPT/FOR qualification>
where <y> is a response variable;
            <par> is a parameter where the quartile coefficient of dispersion value is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET <par> = DIFFERENCE OF QUARTILE COEFFICIENT OF DISPERSION <y1> <y2>
                        <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
            <y2> is the second response variable;
            <par> is a parameter where the difference of the quartile coefficient of dispersion values is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET QCD = QUARTILE COEFFICIENT OF DISPERSION Y1
LET QCD = QUARTILE COEFFICIENT OF DISPERSION Y1 SUBSET TAG > 2


LET DIFFQCD = DIFFERENCE OF QUARTILE COEFFICIENT OF DISPERSION Y1 Y2

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

None

QCD

COEFFICIENT OF VARIATION	=	Compute the coefficient of variation of a variable.
COEFFICIENT OF DISPERSION	=	Compute the coefficient of dispersion of a variable.
SIGNAL TO NOISE RATIO	=	Compute the signal to noise ratio of a variable.
RELATIVE STANDARD DEVIATION	=	Compute the standard deviation of a variable.
MEAN	=	Compute the mean of a variable.
STANDARD DEVIATION	=	Compute the standard deviation of a variable.

Bonett, D. G. (2006). "Confidence interval for a coefficient of quartile variation", Computational Statistics & Data Analysis, 50 (11): 2953–2957.

Data Analysis

2017/01
2017/06: Added DIFFERENCE OF QUARTILE COEFFICIENT OF DISPERSION

 
SKIP 25
READ ZARR13.DAT Y
LET QCD = QUARTILE COEFFICIENT OF DISPERSION Y
    

 
. Step 1:   Create the data
.
skip 25
read gear.dat y x
skip 0
set write decimals 6
.
. Step 2:   Define plot control
.
title case asis
title offset 2
label case asis
.
y1label Quartile Coefficient of Dispersion
x1label Group
title Quartile Coefficient of Dispersion for GEAR.DAT
let ngroup = unique x
xlimits 1 ngroup
major x1tic mark number ngroup
minor x1tic mark number 0
tic mark offset units data
x1tic mark offset 0.5 0.5
.
character X
line blank
.
set statistic plot reference line average
quartile coefficient of dispersion plot y x
.
set write decimals 5
tabulate quartile coefficient of dispersion y x
    



            Cross Tabulate QUARTILE COEFFICIENT OF DISPERSION
 
(Response Variables: Y        )
---------------------------------------------
       X          |   QUARTILE COEFFI
---------------------------------------------
       1.000000   |          0.003385
       2.000000   |          0.003125
       3.000000   |          0.002886
       4.000000   |          0.003631
       5.000000   |          0.007318
       6.000000   |          0.007866
       7.000000   |          0.004746
       8.000000   |          0.002749
       9.000000   |          0.003378
      10.000000   |          0.003143
    

 
SKIP 25
READ IRIS.DAT Y1 TO Y4 X
.
LET A = DIFFERENCE OF QUARTILE COEFFICIENT OF DISPERSION Y1 Y2
SET WRITE DECIMALS 4
TABULATE DIFFERENCE OF QUARTILE COEFFICIENT OF DISPERSION Y1 Y2 X

            Cross Tabulate DIFFERENCE OF QuARTILE COEFFICIENT OF DI
 
(Response Variables: Y1       Y2      )
---------------------------------------------
       X          |   DIFFERENCE OF Q
---------------------------------------------
         1.0000   |           -0.0364
         2.0000   |           -0.0321
         3.0000   |           -0.0096


.
XTIC OFFSET 0.2 0.2
X1LABEL GROUP ID
Y1LABEL DIFFERENCE OF QUARTILE COEFFICIENT OF DISPERSION
CHAR X
LINE BLANK
DIFFERENCE OF COEFFICIENT OF DISPERSION PLOT Y1 Y2 X



CHAR X ALL
LINE BLANK ALL
BOOTSTRAP DIFFERENCE OF QUARTILE COEFFICIENT OF DISPERSION PLOT ...
          Y1 Y2 X