
INDEX OF DISPERSIONName:
where s^{2} is the sample variance and \( \bar{x} \) is the sample mean. That is, it shows the variability, as defined by the variance, relative to the mean. The index of dispersion is related to the coefficient of variation (the ratio of the standard deviation to the mean) and the coefficient of dispersion (the ratio of the median absolute deviation to the median). The index of dispersion is also referred to the coefficient of dispersion. However, Dataplot reserves this term for the ratio of the median absolute deviation to the mean. The index of dispersion should typically only be used for data measured on a ratio scale. That is, the data should be have a meaningful zero. The index of dispersion is sometimes used for count data. If the count data follows a Poisson distribution, then the mean and variance should be equal and the index of dispersion is 1. If the counts follow a geometric or negative binomial, then the index of dispersion should be greater than 1. If the counts follow a binomial distribution, the index of dispersion should be less than 1.
<SUBSET/EXCEPT/FOR qualification> where <y> is a response variable; <par> is a parameter where the index 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 index of dispersion values is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET D = INDEX OF DISPERSION Y1 SUBSET TAG > 2
LET D = DIFFERENCE OF INDEX OF DISPERSION Y1 Y2
2017/06: Added DIFFERENCE OF INDEX OF DISPERSION LET LAMBDA = 2.9 LET Y1 = POISSON RANDOM NUMBERS FOR I = 1 1 100 LET D = INDEX OF DISPERSION Y1Program 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 Index of Dispersion x1label Group title Index 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 y1tic mark label decimals 3 . character X line blank . set statistic plot reference line average index of dispersion plot y x . tabulate index of dispersion y x Cross Tabulate INDEX OF DISPERSION (Response Variables: Y )  X  INDEX OF DISPER  1.000000  0.000019 2.000000  0.000027 3.000000  0.000016 4.000000  0.000015 5.000000  0.000058 6.000000  0.000098 7.000000  0.000062 8.000000  0.000013 9.000000  0.000017 10.000000  0.000029Program 3: SKIP 25 READ IRIS.DAT Y1 TO Y4 X . LET A = DIFFERENCE OF INDEX OF DISPERSION Y1 Y2 SET WRITE DECIMALS 4 TABULATE DIFFERENCE OF INDEX OF DISPERSION Y1 Y2 XCross Tabulate DIFFERENCE OF INDEX OF DISPERSION (Response Variables: Y1 Y2 )  X  DIFFERENCE OF I  1.0000  0.0171 2.0000  0.0093 3.0000  0.0264. XTIC OFFSET 0.2 0.2 X1LABEL GROUP ID Y1LABEL DIFFERENCE OF INDEX OF DISPERSION CHAR X LINE BLANK DIFFERENCE OF INDEX OF DISPERSION PLOT Y1 Y2 X  
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Date created: 01/24/2017 