
COEFFICIENT OF DISPERSIONName:
where \( \eta \) and \( \tau \) are the median and median absolute deviation, respectively. This statistic has been suggested as a robust alternative to the coefficient of variation.
<SUBSET/EXCEPT/FOR qualification> where <y> is a response variable; <par> is a parameter where the coefficient of dispersion value is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
<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 coefficient of dispersion values is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET COD = COEFFICIENT OF DISPERSION Y1 SUBSET TAG > 2
LET DIFFCOD = DIFFERENCE OF COEFFICIENT OF DISPERSION Y1 Y2
It is sometimes defined as
To compute this statistic in Dataplot, use the command
Another definition is
where AAD is the average absolute deviation. In this case, we are computing the AAD as
where \( \tilde{X} \) denotes the median. That is, we compute absolute differences from the median rather than from the mean. This statistic can be computed in Dataplot using the command
Basically, you can define a dispersion index based on a scale statistic (standard deviation, average absolute deviation, median absolute deviation, etc.) divided by a location statistic (mean, median, etc.). So there are additional possibilities not discussed here.
Gastwirth (1982), "Statistical properties as a measure of tax assessment uniformity", Journal of Statistical Planning Inference, Vol. 6, pp. 112.
SKIP 25 READ ZARR13.DAT Y LET COD = COEFFICIENT OF DISPERSION YProgram 2: . 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 Coefficient of Dispersion x1label Group title 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 coefficient of dispersion plot y x . set write decimals 5 tabulate coefficient of dispersion y x
Cross Tabulate COEFFICIENT OF DISPERSION (Response Variables: Y )  X  COEFFICIENT OF  1.00000  0.00300 2.00000  0.00250 3.00000  0.00251 4.00000  0.00301 5.00000  0.00402 6.00000  0.00702 7.00000  0.00400 8.00000  0.00200 9.00000  0.00251 10.00000  0.00201Program 3: SKIP 25 READ IRIS.DAT Y1 TO Y4 X . LET A = DIFFERENCE OF COEFFICIENT OF DISPERSION Y1 Y2 SET WRITE DECIMALS 4 TABULATE DIFFERENCE OF COEFFICIENT Y1 Y2 XCross Tabulate DIFFERENCE OF COEFFICIENT OF DISPERSION (Response Variables: Y1 Y2 )  X  DIFFERENCE OF C  1.0000  0.0335 2.0000  0.0121 3.0000  0.0051. XTIC OFFSET 0.2 0.2 X1LABEL GROUP ID Y1LABEL DIFFERENCE OF COEFFICIENT OF DISPERSION CHAR X LINE BLANK DIFFERENCE OF COEFFICIENT OF DISPERSION PLOT Y1 Y2 X  
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Date created: 01/24/2017 