Dataplot Vol 2 Vol 1

QUARTILE COEFFICIENT OF DISPERSION

Name:
QUARTILE COEFFICIENT OF DISPERSION (LET)
Type:
Let Subcommand
Purpose:
Compute the quartile coefficient of dispersion of a variable.
Description:
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.

Syntax 1:
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.
Syntax 2:
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.
Examples:
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

Note:
Dataplot statistics can be used in a number of commands. For details, enter

Default:
None
Synonyms:
QCD
Related Commands:
 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.
Reference:
Bonett, D. G. (2006). "Confidence interval for a coefficient of quartile variation", Computational Statistics & Data Analysis, 50 (11): 2953–2957.
Applications:
Data Analysis
Implementation Date:
2017/01
2017/06: Added DIFFERENCE OF QUARTILE COEFFICIENT OF DISPERSION
Program 1:

SKIP 25
LET QCD = QUARTILE COEFFICIENT OF DISPERSION Y

Program 2:

. Step 1:   Create the data
.
skip 25
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

Program 3:

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


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Date created: 01/24/2017
Last updated: 06/30/2017