Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_variability.wasp
Title produced by softwareVariability
Date of computationWed, 19 Dec 2012 20:04:56 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/19/t1355966487x7f8demdxanl5eo.htm/, Retrieved Thu, 31 Oct 2024 23:53:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=202517, Retrieved Thu, 31 Oct 2024 23:53:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2012-12-19 22:05:59] [f34b53bee6b9c32e69f6aece59a7b011]
- RM D    [Variability] [Kengetallen van s...] [2012-12-20 01:04:56] [cae7db30b04823cf35f719a9709248c2] [Current]
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Dataseries X:
210907
120982
176508
179321
123185
52746
385534
33170
101645
149061
165446
237213
173326
133131
258873
180083
324799
230964
236785
135473
202925
215147
344297
153935
132943
174724
174415
225548
223632
124817
221698
210767
170266
260561
84853
294424
101011
215641
325107
7176
167542
106408
96560
265769
269651
149112
175824
152871
111665
116408
362301
78800
183167
277965
150629
168809
24188
329267
65029
101097
218946
244052
341570
103597
233328
256462
206161
311473
235800
177939
207176
196553
174184
143246
187559
187681
119016
182192
73566
194979
167488
143756
275541
243199
182999
135649
152299
120221
346485
145790
193339
80953
122774
130585
112611
286468
241066
148446
204713
182079
140344
220516
243060
162765
182613
232138
265318
85574
310839
225060
232317
144966
43287
155754
164709
201940
235454
220801
99466
92661
133328
61361
125930
100750
224549
82316
102010
101523
243511
22938
41566
152474
61857
99923
132487
317394
21054
209641
22648
31414
46698
131698
91735
244749
184510
79863
128423
97839
38214
151101
272458
172494
108043
328107
250579
351067
158015
98866
85439
229242
351619
84207
120445
324598
131069
204271
165543
141722
116048
250047
299775
195838
173260
254488
104389
136084
199476
92499
224330
135781
74408
81240
14688
181633
271856
7199
46660
17547
133368
95227
152601
98146
79619
59194
139942
118612
72880
65475
99643
71965
77272
49289
135131
108446
89746
44296
77648
181528
134019
124064
92630
121848
52915
81872
58981
53515
60812
56375
65490
80949
76302
104011
98104
67989
30989
135458
73504
63123
61254
74914
31774
81437
87186
50090
65745
56653
158399
46455
73624
38395
91899
139526
52164
51567
70551
84856
102538
86678
85709
34662
150580
99611
19349
99373
86230
30837
31706
89806
62088
40151
27634
76990
37460
54157
49862
84337
64175
59382
119308
76702
103425
70344
43410
104838
62215
69304
53117
19764
86680
84105
77945
89113
91005
40248
64187
50857
56613
62792
72535




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202517&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202517&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202517&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Variability - Ungrouped Data
Absolute range378358
Relative range (unbiased)4.59510239158893
Relative range (biased)4.60307308689699
Variance (unbiased)6779777729.09105
Variance (biased)6756318290.58208
Standard Deviation (unbiased)82339.4056882307
Standard Deviation (biased)82196.8265237903
Coefficient of Variation (unbiased)0.596281898060246
Coefficient of Variation (biased)0.59524937451838
Mean Squared Error (MSE versus 0)25824628368.9792
Mean Squared Error (MSE versus Mean)6756318290.58208
Mean Absolute Deviation from Mean (MAD Mean)67339.4994312808
Mean Absolute Deviation from Median (MAD Median)66168.2525951557
Median Absolute Deviation from Mean60440.0519031142
Median Absolute Deviation from Median55492
Mean Squared Deviation from Mean6756318290.58208
Mean Squared Deviation from Median7048935302.29412
Interquartile Difference (Weighted Average at Xnp)112262.25
Interquartile Difference (Weighted Average at X(n+1)p)112959
Interquartile Difference (Empirical Distribution Function)112645
Interquartile Difference (Empirical Distribution Function - Averaging)112645
Interquartile Difference (Empirical Distribution Function - Interpolation)112645
Interquartile Difference (Closest Observation)113151
Interquartile Difference (True Basic - Statistics Graphics Toolkit)112959
Interquartile Difference (MS Excel (old versions))112959
Semi Interquartile Difference (Weighted Average at Xnp)56131.125
Semi Interquartile Difference (Weighted Average at X(n+1)p)56479.5
Semi Interquartile Difference (Empirical Distribution Function)56322.5
Semi Interquartile Difference (Empirical Distribution Function - Averaging)56322.5
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)56322.5
Semi Interquartile Difference (Closest Observation)56575.5
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)56479.5
Semi Interquartile Difference (MS Excel (old versions))56479.5
Coefficient of Quartile Variation (Weighted Average at Xnp)0.429578360796881
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.430679309595434
Coefficient of Quartile Variation (Empirical Distribution Function)0.429167952513211
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.429167952513211
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.429167952513211
Coefficient of Quartile Variation (Closest Observation)0.431928449003119
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.430679309595434
Coefficient of Quartile Variation (MS Excel (old versions))0.430679309595434
Number of all Pairs of Observations41616
Squared Differences between all Pairs of Observations13559555458.1821
Mean Absolute Differences between all Pairs of Observations91881.0185986159
Gini Mean Difference91881.0185986159
Leik Measure of Dispersion0.444565995831973
Index of Diversity0.995313765336109
Index of Qualitative Variation0.998769715910193
Coefficient of Dispersion0.556607589817334
Observations289

\begin{tabular}{lllllllll}
\hline
Variability - Ungrouped Data \tabularnewline
Absolute range & 378358 \tabularnewline
Relative range (unbiased) & 4.59510239158893 \tabularnewline
Relative range (biased) & 4.60307308689699 \tabularnewline
Variance (unbiased) & 6779777729.09105 \tabularnewline
Variance (biased) & 6756318290.58208 \tabularnewline
Standard Deviation (unbiased) & 82339.4056882307 \tabularnewline
Standard Deviation (biased) & 82196.8265237903 \tabularnewline
Coefficient of Variation (unbiased) & 0.596281898060246 \tabularnewline
Coefficient of Variation (biased) & 0.59524937451838 \tabularnewline
Mean Squared Error (MSE versus 0) & 25824628368.9792 \tabularnewline
Mean Squared Error (MSE versus Mean) & 6756318290.58208 \tabularnewline
Mean Absolute Deviation from Mean (MAD Mean) & 67339.4994312808 \tabularnewline
Mean Absolute Deviation from Median (MAD Median) & 66168.2525951557 \tabularnewline
Median Absolute Deviation from Mean & 60440.0519031142 \tabularnewline
Median Absolute Deviation from Median & 55492 \tabularnewline
Mean Squared Deviation from Mean & 6756318290.58208 \tabularnewline
Mean Squared Deviation from Median & 7048935302.29412 \tabularnewline
Interquartile Difference (Weighted Average at Xnp) & 112262.25 \tabularnewline
Interquartile Difference (Weighted Average at X(n+1)p) & 112959 \tabularnewline
Interquartile Difference (Empirical Distribution Function) & 112645 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Averaging) & 112645 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Interpolation) & 112645 \tabularnewline
Interquartile Difference (Closest Observation) & 113151 \tabularnewline
Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 112959 \tabularnewline
Interquartile Difference (MS Excel (old versions)) & 112959 \tabularnewline
Semi Interquartile Difference (Weighted Average at Xnp) & 56131.125 \tabularnewline
Semi Interquartile Difference (Weighted Average at X(n+1)p) & 56479.5 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function) & 56322.5 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Averaging) & 56322.5 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Interpolation) & 56322.5 \tabularnewline
Semi Interquartile Difference (Closest Observation) & 56575.5 \tabularnewline
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 56479.5 \tabularnewline
Semi Interquartile Difference (MS Excel (old versions)) & 56479.5 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at Xnp) & 0.429578360796881 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at X(n+1)p) & 0.430679309595434 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function) & 0.429167952513211 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging) & 0.429167952513211 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation) & 0.429167952513211 \tabularnewline
Coefficient of Quartile Variation (Closest Observation) & 0.431928449003119 \tabularnewline
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit) & 0.430679309595434 \tabularnewline
Coefficient of Quartile Variation (MS Excel (old versions)) & 0.430679309595434 \tabularnewline
Number of all Pairs of Observations & 41616 \tabularnewline
Squared Differences between all Pairs of Observations & 13559555458.1821 \tabularnewline
Mean Absolute Differences between all Pairs of Observations & 91881.0185986159 \tabularnewline
Gini Mean Difference & 91881.0185986159 \tabularnewline
Leik Measure of Dispersion & 0.444565995831973 \tabularnewline
Index of Diversity & 0.995313765336109 \tabularnewline
Index of Qualitative Variation & 0.998769715910193 \tabularnewline
Coefficient of Dispersion & 0.556607589817334 \tabularnewline
Observations & 289 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202517&T=1

[TABLE]
[ROW][C]Variability - Ungrouped Data[/C][/ROW]
[ROW][C]Absolute range[/C][C]378358[/C][/ROW]
[ROW][C]Relative range (unbiased)[/C][C]4.59510239158893[/C][/ROW]
[ROW][C]Relative range (biased)[/C][C]4.60307308689699[/C][/ROW]
[ROW][C]Variance (unbiased)[/C][C]6779777729.09105[/C][/ROW]
[ROW][C]Variance (biased)[/C][C]6756318290.58208[/C][/ROW]
[ROW][C]Standard Deviation (unbiased)[/C][C]82339.4056882307[/C][/ROW]
[ROW][C]Standard Deviation (biased)[/C][C]82196.8265237903[/C][/ROW]
[ROW][C]Coefficient of Variation (unbiased)[/C][C]0.596281898060246[/C][/ROW]
[ROW][C]Coefficient of Variation (biased)[/C][C]0.59524937451838[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus 0)[/C][C]25824628368.9792[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus Mean)[/C][C]6756318290.58208[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Mean (MAD Mean)[/C][C]67339.4994312808[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Median (MAD Median)[/C][C]66168.2525951557[/C][/ROW]
[ROW][C]Median Absolute Deviation from Mean[/C][C]60440.0519031142[/C][/ROW]
[ROW][C]Median Absolute Deviation from Median[/C][C]55492[/C][/ROW]
[ROW][C]Mean Squared Deviation from Mean[/C][C]6756318290.58208[/C][/ROW]
[ROW][C]Mean Squared Deviation from Median[/C][C]7048935302.29412[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at Xnp)[/C][C]112262.25[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]112959[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function)[/C][C]112645[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]112645[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]112645[/C][/ROW]
[ROW][C]Interquartile Difference (Closest Observation)[/C][C]113151[/C][/ROW]
[ROW][C]Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]112959[/C][/ROW]
[ROW][C]Interquartile Difference (MS Excel (old versions))[/C][C]112959[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at Xnp)[/C][C]56131.125[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]56479.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function)[/C][C]56322.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]56322.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]56322.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Closest Observation)[/C][C]56575.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]56479.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (MS Excel (old versions))[/C][C]56479.5[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at Xnp)[/C][C]0.429578360796881[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at X(n+1)p)[/C][C]0.430679309595434[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function)[/C][C]0.429167952513211[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)[/C][C]0.429167952513211[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)[/C][C]0.429167952513211[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Closest Observation)[/C][C]0.431928449003119[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)[/C][C]0.430679309595434[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (MS Excel (old versions))[/C][C]0.430679309595434[/C][/ROW]
[ROW][C]Number of all Pairs of Observations[/C][C]41616[/C][/ROW]
[ROW][C]Squared Differences between all Pairs of Observations[/C][C]13559555458.1821[/C][/ROW]
[ROW][C]Mean Absolute Differences between all Pairs of Observations[/C][C]91881.0185986159[/C][/ROW]
[ROW][C]Gini Mean Difference[/C][C]91881.0185986159[/C][/ROW]
[ROW][C]Leik Measure of Dispersion[/C][C]0.444565995831973[/C][/ROW]
[ROW][C]Index of Diversity[/C][C]0.995313765336109[/C][/ROW]
[ROW][C]Index of Qualitative Variation[/C][C]0.998769715910193[/C][/ROW]
[ROW][C]Coefficient of Dispersion[/C][C]0.556607589817334[/C][/ROW]
[ROW][C]Observations[/C][C]289[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202517&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202517&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Variability - Ungrouped Data
Absolute range378358
Relative range (unbiased)4.59510239158893
Relative range (biased)4.60307308689699
Variance (unbiased)6779777729.09105
Variance (biased)6756318290.58208
Standard Deviation (unbiased)82339.4056882307
Standard Deviation (biased)82196.8265237903
Coefficient of Variation (unbiased)0.596281898060246
Coefficient of Variation (biased)0.59524937451838
Mean Squared Error (MSE versus 0)25824628368.9792
Mean Squared Error (MSE versus Mean)6756318290.58208
Mean Absolute Deviation from Mean (MAD Mean)67339.4994312808
Mean Absolute Deviation from Median (MAD Median)66168.2525951557
Median Absolute Deviation from Mean60440.0519031142
Median Absolute Deviation from Median55492
Mean Squared Deviation from Mean6756318290.58208
Mean Squared Deviation from Median7048935302.29412
Interquartile Difference (Weighted Average at Xnp)112262.25
Interquartile Difference (Weighted Average at X(n+1)p)112959
Interquartile Difference (Empirical Distribution Function)112645
Interquartile Difference (Empirical Distribution Function - Averaging)112645
Interquartile Difference (Empirical Distribution Function - Interpolation)112645
Interquartile Difference (Closest Observation)113151
Interquartile Difference (True Basic - Statistics Graphics Toolkit)112959
Interquartile Difference (MS Excel (old versions))112959
Semi Interquartile Difference (Weighted Average at Xnp)56131.125
Semi Interquartile Difference (Weighted Average at X(n+1)p)56479.5
Semi Interquartile Difference (Empirical Distribution Function)56322.5
Semi Interquartile Difference (Empirical Distribution Function - Averaging)56322.5
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)56322.5
Semi Interquartile Difference (Closest Observation)56575.5
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)56479.5
Semi Interquartile Difference (MS Excel (old versions))56479.5
Coefficient of Quartile Variation (Weighted Average at Xnp)0.429578360796881
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.430679309595434
Coefficient of Quartile Variation (Empirical Distribution Function)0.429167952513211
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.429167952513211
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.429167952513211
Coefficient of Quartile Variation (Closest Observation)0.431928449003119
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.430679309595434
Coefficient of Quartile Variation (MS Excel (old versions))0.430679309595434
Number of all Pairs of Observations41616
Squared Differences between all Pairs of Observations13559555458.1821
Mean Absolute Differences between all Pairs of Observations91881.0185986159
Gini Mean Difference91881.0185986159
Leik Measure of Dispersion0.444565995831973
Index of Diversity0.995313765336109
Index of Qualitative Variation0.998769715910193
Coefficient of Dispersion0.556607589817334
Observations289



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
num <- 50
res <- array(NA,dim=c(num,3))
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
iqd <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
iqdiff <- qvalue3 - qvalue1
return(c(iqdiff,iqdiff/2,iqdiff/(qvalue3 + qvalue1)))
}
range <- max(x) - min(x)
lx <- length(x)
biasf <- (lx-1)/lx
varx <- var(x)
bvarx <- varx*biasf
sdx <- sqrt(varx)
mx <- mean(x)
bsdx <- sqrt(bvarx)
x2 <- x*x
mse0 <- sum(x2)/lx
xmm <- x-mx
xmm2 <- xmm*xmm
msem <- sum(xmm2)/lx
axmm <- abs(x - mx)
medx <- median(x)
axmmed <- abs(x - medx)
xmmed <- x - medx
xmmed2 <- xmmed*xmmed
msemed <- sum(xmmed2)/lx
qarr <- array(NA,dim=c(8,3))
for (j in 1:8) {
qarr[j,] <- iqd(x,j)
}
sdpo <- 0
adpo <- 0
for (i in 1:(lx-1)) {
for (j in (i+1):lx) {
ldi <- x[i]-x[j]
aldi <- abs(ldi)
sdpo = sdpo + ldi * ldi
adpo = adpo + aldi
}
}
denom <- (lx*(lx-1)/2)
sdpo = sdpo / denom
adpo = adpo / denom
gmd <- 0
for (i in 1:lx) {
for (j in 1:lx) {
ldi <- abs(x[i]-x[j])
gmd = gmd + ldi
}
}
gmd <- gmd / (lx*(lx-1))
sumx <- sum(x)
pk <- x / sumx
ck <- cumsum(pk)
dk <- array(NA,dim=lx)
for (i in 1:lx) {
if (ck[i] <= 0.5) dk[i] <- ck[i] else dk[i] <- 1 - ck[i]
}
bigd <- sum(dk) * 2 / (lx-1)
iod <- 1 - sum(pk*pk)
res[1,] <- c('Absolute range','absolute.htm', range)
res[2,] <- c('Relative range (unbiased)','relative.htm', range/sd(x))
res[3,] <- c('Relative range (biased)','relative.htm', range/sqrt(varx*biasf))
res[4,] <- c('Variance (unbiased)','unbiased.htm', varx)
res[5,] <- c('Variance (biased)','biased.htm', bvarx)
res[6,] <- c('Standard Deviation (unbiased)','unbiased1.htm', sdx)
res[7,] <- c('Standard Deviation (biased)','biased1.htm', bsdx)
res[8,] <- c('Coefficient of Variation (unbiased)','variation.htm', sdx/mx)
res[9,] <- c('Coefficient of Variation (biased)','variation.htm', bsdx/mx)
res[10,] <- c('Mean Squared Error (MSE versus 0)','mse.htm', mse0)
res[11,] <- c('Mean Squared Error (MSE versus Mean)','mse.htm', msem)
res[12,] <- c('Mean Absolute Deviation from Mean (MAD Mean)', 'mean2.htm', sum(axmm)/lx)
res[13,] <- c('Mean Absolute Deviation from Median (MAD Median)', 'median1.htm', sum(axmmed)/lx)
res[14,] <- c('Median Absolute Deviation from Mean', 'mean3.htm', median(axmm))
res[15,] <- c('Median Absolute Deviation from Median', 'median2.htm', median(axmmed))
res[16,] <- c('Mean Squared Deviation from Mean', 'mean1.htm', msem)
res[17,] <- c('Mean Squared Deviation from Median', 'median.htm', msemed)
load(file='createtable')
mylink1 <- hyperlink('difference.htm','Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[18,] <- c('', mylink2, qarr[1,1])
mylink2 <- paste(mylink1,hyperlink('method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[19,] <- c('', mylink2, qarr[2,1])
mylink2 <- paste(mylink1,hyperlink('method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[20,] <- c('', mylink2, qarr[3,1])
mylink2 <- paste(mylink1,hyperlink('method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[21,] <- c('', mylink2, qarr[4,1])
mylink2 <- paste(mylink1,hyperlink('method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[22,] <- c('', mylink2, qarr[5,1])
mylink2 <- paste(mylink1,hyperlink('method_6.htm','(Closest Observation)',''),sep=' ')
res[23,] <- c('', mylink2, qarr[6,1])
mylink2 <- paste(mylink1,hyperlink('method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[24,] <- c('', mylink2, qarr[7,1])
mylink2 <- paste(mylink1,hyperlink('method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[25,] <- c('', mylink2, qarr[8,1])
mylink1 <- hyperlink('deviation.htm','Semi Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[26,] <- c('', mylink2, qarr[1,2])
mylink2 <- paste(mylink1,hyperlink('method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[27,] <- c('', mylink2, qarr[2,2])
mylink2 <- paste(mylink1,hyperlink('method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[28,] <- c('', mylink2, qarr[3,2])
mylink2 <- paste(mylink1,hyperlink('method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[29,] <- c('', mylink2, qarr[4,2])
mylink2 <- paste(mylink1,hyperlink('method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[30,] <- c('', mylink2, qarr[5,2])
mylink2 <- paste(mylink1,hyperlink('method_6.htm','(Closest Observation)',''),sep=' ')
res[31,] <- c('', mylink2, qarr[6,2])
mylink2 <- paste(mylink1,hyperlink('method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[32,] <- c('', mylink2, qarr[7,2])
mylink2 <- paste(mylink1,hyperlink('method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[33,] <- c('', mylink2, qarr[8,2])
mylink1 <- hyperlink('variation1.htm','Coefficient of Quartile Variation','')
mylink2 <- paste(mylink1,hyperlink('method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[34,] <- c('', mylink2, qarr[1,3])
mylink2 <- paste(mylink1,hyperlink('method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[35,] <- c('', mylink2, qarr[2,3])
mylink2 <- paste(mylink1,hyperlink('method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[36,] <- c('', mylink2, qarr[3,3])
mylink2 <- paste(mylink1,hyperlink('method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[37,] <- c('', mylink2, qarr[4,3])
mylink2 <- paste(mylink1,hyperlink('method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[38,] <- c('', mylink2, qarr[5,3])
mylink2 <- paste(mylink1,hyperlink('method_6.htm','(Closest Observation)',''),sep=' ')
res[39,] <- c('', mylink2, qarr[6,3])
mylink2 <- paste(mylink1,hyperlink('method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[40,] <- c('', mylink2, qarr[7,3])
mylink2 <- paste(mylink1,hyperlink('method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[41,] <- c('', mylink2, qarr[8,3])
res[42,] <- c('Number of all Pairs of Observations', 'pair_numbers.htm', lx*(lx-1)/2)
res[43,] <- c('Squared Differences between all Pairs of Observations', 'squared_differences.htm', sdpo)
res[44,] <- c('Mean Absolute Differences between all Pairs of Observations', 'mean_abs_differences.htm', adpo)
res[45,] <- c('Gini Mean Difference', 'gini_mean_difference.htm', gmd)
res[46,] <- c('Leik Measure of Dispersion', 'leiks_d.htm', bigd)
res[47,] <- c('Index of Diversity', 'diversity.htm', iod)
res[48,] <- c('Index of Qualitative Variation', 'qualitative_variation.htm', iod*lx/(lx-1))
res[49,] <- c('Coefficient of Dispersion', 'dispersion.htm', sum(axmm)/lx/medx)
res[50,] <- c('Observations', '', lx)
res
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variability - Ungrouped Data',2,TRUE)
a<-table.row.end(a)
for (i in 1:num) {
a<-table.row.start(a)
if (res[i,1] != '') {
a<-table.element(a,hyperlink(res[i,2],res[i,1],''),header=TRUE)
} else {
a<-table.element(a,res[i,2],header=TRUE)
}
a<-table.element(a,res[i,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')