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 computationMon, 19 Oct 2009 13:37:50 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/19/t1255981124h5voc8y6oodid5z.htm/, Retrieved Thu, 31 Oct 2024 23:17:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48156, Retrieved Thu, 31 Oct 2024 23:17:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsShwWs3V2
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMP       [Mean versus Median] [Ws3 part 1 mean v...] [2009-10-18 14:09:14] [e0fc65a5811681d807296d590d5b45de]
-    D        [Mean versus Median] [WS3 Part 2 Yt mea...] [2009-10-18 16:50:27] [e0fc65a5811681d807296d590d5b45de]
- R  D          [Mean versus Median] [WS3Part2Yt/Xt] [2009-10-18 19:21:00] [e0fc65a5811681d807296d590d5b45de]
- RM D              [Variability] [WS3Part2Yt*Xt] [2009-10-19 19:37:50] [51108381f3361ca8af49c4f74052c840] [Current]
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Dataseries X:
6165561.60
4930198.00
5425516.80
4882416.00
5013277.20
4824106.60
4386552.80
3612685.50
3354824.00
4573662.50
3607962.50
2313181.20
6068078.55
5733506.24
5801696.32
5679979.04
4473715.68
4134416.13
3817990.84
2860636.20
3467462.88
4132339.80
3002307.36
2004734.61
5512120.68
4808915.54
5330777.00
4821427.17
4115383.80
4432005.74
3902015.55
3196453.24
3798522.75
4694299.60
3333356.94
2913313.14
5227244.40
5552024.24
6820771.05
5963048.74
4331811.21
4820109.95
3463539.62
3293941.28
3729726.82
4312980.00
3719352.72
2773137.94
5691542.88
5058654.30
5838951.24
5399831.16
4662499.05
5538644.50
3662097.01
3730770.83
3982615.85
4148178.34
3991276.66
2349702.88




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48156&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48156&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48156&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Variability - Ungrouped Data
Absolute range4816036.44
Relative range (unbiased)4.4907477117586
Relative range (biased)4.52864498879904
Variance (unbiased)1150117506365.87
Variance (biased)1130948881259.77
Standard Deviation (unbiased)1072435.31570247
Standard Deviation (biased)1063460.80381920
Coefficient of Variation (unbiased)0.244487419961107
Coefficient of Variation (biased)0.242441464159739
Mean Squared Error (MSE versus 0)20372017083998.0
Mean Squared Error (MSE versus Mean)1130948881259.77
Mean Absolute Deviation from Mean (MAD Mean)884573.616166667
Mean Absolute Deviation from Median (MAD Median)884573.616166667
Median Absolute Deviation from Mean776140.202833333
Median Absolute Deviation from Median748858.005
Mean Squared Deviation from Mean1130948881259.77
Mean Squared Deviation from Median1131693199578.39
Interquartile Difference (Weighted Average at Xnp)1614558.9
Interquartile Difference (Weighted Average at X(n+1)p)1679855.4725
Interquartile Difference (Empirical Distribution Function)1614558.9
Interquartile Difference (Empirical Distribution Function - Averaging)1641619.445
Interquartile Difference (Empirical Distribution Function - Interpolation)1603383.4175
Interquartile Difference (Closest Observation)1614558.9
Interquartile Difference (True Basic - Statistics Graphics Toolkit)1603383.4175
Interquartile Difference (MS Excel (old versions))1718091.5
Semi Interquartile Difference (Weighted Average at Xnp)807279.45
Semi Interquartile Difference (Weighted Average at X(n+1)p)839927.73625
Semi Interquartile Difference (Empirical Distribution Function)807279.45
Semi Interquartile Difference (Empirical Distribution Function - Averaging)820809.7225
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)801691.70875
Semi Interquartile Difference (Closest Observation)807279.45
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)801691.70875
Semi Interquartile Difference (MS Excel (old versions))859045.75
Coefficient of Quartile Variation (Weighted Average at Xnp)0.182643857843262
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.188115142388968
Coefficient of Quartile Variation (Empirical Distribution Function)0.182643857843262
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.184112319440628
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.180097329792106
Coefficient of Quartile Variation (Closest Observation)0.182643857843262
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.180097329792106
Coefficient of Quartile Variation (MS Excel (old versions))0.192105853856937
Number of all Pairs of Observations1770
Squared Differences between all Pairs of Observations2300235012731.73
Mean Absolute Differences between all Pairs of Observations1234470.77565537
Gini Mean Difference1234470.77565537
Leik Measure of Dispersion0.51497346142611
Index of Diversity0.982353702274268
Index of Qualitative Variation0.99900376502468
Coefficient of Dispersion0.202921927818581
Observations60

\begin{tabular}{lllllllll}
\hline
Variability - Ungrouped Data \tabularnewline
Absolute range & 4816036.44 \tabularnewline
Relative range (unbiased) & 4.4907477117586 \tabularnewline
Relative range (biased) & 4.52864498879904 \tabularnewline
Variance (unbiased) & 1150117506365.87 \tabularnewline
Variance (biased) & 1130948881259.77 \tabularnewline
Standard Deviation (unbiased) & 1072435.31570247 \tabularnewline
Standard Deviation (biased) & 1063460.80381920 \tabularnewline
Coefficient of Variation (unbiased) & 0.244487419961107 \tabularnewline
Coefficient of Variation (biased) & 0.242441464159739 \tabularnewline
Mean Squared Error (MSE versus 0) & 20372017083998.0 \tabularnewline
Mean Squared Error (MSE versus Mean) & 1130948881259.77 \tabularnewline
Mean Absolute Deviation from Mean (MAD Mean) & 884573.616166667 \tabularnewline
Mean Absolute Deviation from Median (MAD Median) & 884573.616166667 \tabularnewline
Median Absolute Deviation from Mean & 776140.202833333 \tabularnewline
Median Absolute Deviation from Median & 748858.005 \tabularnewline
Mean Squared Deviation from Mean & 1130948881259.77 \tabularnewline
Mean Squared Deviation from Median & 1131693199578.39 \tabularnewline
Interquartile Difference (Weighted Average at Xnp) & 1614558.9 \tabularnewline
Interquartile Difference (Weighted Average at X(n+1)p) & 1679855.4725 \tabularnewline
Interquartile Difference (Empirical Distribution Function) & 1614558.9 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Averaging) & 1641619.445 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Interpolation) & 1603383.4175 \tabularnewline
Interquartile Difference (Closest Observation) & 1614558.9 \tabularnewline
Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 1603383.4175 \tabularnewline
Interquartile Difference (MS Excel (old versions)) & 1718091.5 \tabularnewline
Semi Interquartile Difference (Weighted Average at Xnp) & 807279.45 \tabularnewline
Semi Interquartile Difference (Weighted Average at X(n+1)p) & 839927.73625 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function) & 807279.45 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Averaging) & 820809.7225 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Interpolation) & 801691.70875 \tabularnewline
Semi Interquartile Difference (Closest Observation) & 807279.45 \tabularnewline
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 801691.70875 \tabularnewline
Semi Interquartile Difference (MS Excel (old versions)) & 859045.75 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at Xnp) & 0.182643857843262 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at X(n+1)p) & 0.188115142388968 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function) & 0.182643857843262 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging) & 0.184112319440628 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation) & 0.180097329792106 \tabularnewline
Coefficient of Quartile Variation (Closest Observation) & 0.182643857843262 \tabularnewline
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit) & 0.180097329792106 \tabularnewline
Coefficient of Quartile Variation (MS Excel (old versions)) & 0.192105853856937 \tabularnewline
Number of all Pairs of Observations & 1770 \tabularnewline
Squared Differences between all Pairs of Observations & 2300235012731.73 \tabularnewline
Mean Absolute Differences between all Pairs of Observations & 1234470.77565537 \tabularnewline
Gini Mean Difference & 1234470.77565537 \tabularnewline
Leik Measure of Dispersion & 0.51497346142611 \tabularnewline
Index of Diversity & 0.982353702274268 \tabularnewline
Index of Qualitative Variation & 0.99900376502468 \tabularnewline
Coefficient of Dispersion & 0.202921927818581 \tabularnewline
Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48156&T=1

[TABLE]
[ROW][C]Variability - Ungrouped Data[/C][/ROW]
[ROW][C]Absolute range[/C][C]4816036.44[/C][/ROW]
[ROW][C]Relative range (unbiased)[/C][C]4.4907477117586[/C][/ROW]
[ROW][C]Relative range (biased)[/C][C]4.52864498879904[/C][/ROW]
[ROW][C]Variance (unbiased)[/C][C]1150117506365.87[/C][/ROW]
[ROW][C]Variance (biased)[/C][C]1130948881259.77[/C][/ROW]
[ROW][C]Standard Deviation (unbiased)[/C][C]1072435.31570247[/C][/ROW]
[ROW][C]Standard Deviation (biased)[/C][C]1063460.80381920[/C][/ROW]
[ROW][C]Coefficient of Variation (unbiased)[/C][C]0.244487419961107[/C][/ROW]
[ROW][C]Coefficient of Variation (biased)[/C][C]0.242441464159739[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus 0)[/C][C]20372017083998.0[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus Mean)[/C][C]1130948881259.77[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Mean (MAD Mean)[/C][C]884573.616166667[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Median (MAD Median)[/C][C]884573.616166667[/C][/ROW]
[ROW][C]Median Absolute Deviation from Mean[/C][C]776140.202833333[/C][/ROW]
[ROW][C]Median Absolute Deviation from Median[/C][C]748858.005[/C][/ROW]
[ROW][C]Mean Squared Deviation from Mean[/C][C]1130948881259.77[/C][/ROW]
[ROW][C]Mean Squared Deviation from Median[/C][C]1131693199578.39[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at Xnp)[/C][C]1614558.9[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]1679855.4725[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function)[/C][C]1614558.9[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]1641619.445[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]1603383.4175[/C][/ROW]
[ROW][C]Interquartile Difference (Closest Observation)[/C][C]1614558.9[/C][/ROW]
[ROW][C]Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]1603383.4175[/C][/ROW]
[ROW][C]Interquartile Difference (MS Excel (old versions))[/C][C]1718091.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at Xnp)[/C][C]807279.45[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]839927.73625[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function)[/C][C]807279.45[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]820809.7225[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]801691.70875[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Closest Observation)[/C][C]807279.45[/C][/ROW]
[ROW][C]Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]801691.70875[/C][/ROW]
[ROW][C]Semi Interquartile Difference (MS Excel (old versions))[/C][C]859045.75[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at Xnp)[/C][C]0.182643857843262[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at X(n+1)p)[/C][C]0.188115142388968[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function)[/C][C]0.182643857843262[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)[/C][C]0.184112319440628[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)[/C][C]0.180097329792106[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Closest Observation)[/C][C]0.182643857843262[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)[/C][C]0.180097329792106[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (MS Excel (old versions))[/C][C]0.192105853856937[/C][/ROW]
[ROW][C]Number of all Pairs of Observations[/C][C]1770[/C][/ROW]
[ROW][C]Squared Differences between all Pairs of Observations[/C][C]2300235012731.73[/C][/ROW]
[ROW][C]Mean Absolute Differences between all Pairs of Observations[/C][C]1234470.77565537[/C][/ROW]
[ROW][C]Gini Mean Difference[/C][C]1234470.77565537[/C][/ROW]
[ROW][C]Leik Measure of Dispersion[/C][C]0.51497346142611[/C][/ROW]
[ROW][C]Index of Diversity[/C][C]0.982353702274268[/C][/ROW]
[ROW][C]Index of Qualitative Variation[/C][C]0.99900376502468[/C][/ROW]
[ROW][C]Coefficient of Dispersion[/C][C]0.202921927818581[/C][/ROW]
[ROW][C]Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48156&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48156&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 range4816036.44
Relative range (unbiased)4.4907477117586
Relative range (biased)4.52864498879904
Variance (unbiased)1150117506365.87
Variance (biased)1130948881259.77
Standard Deviation (unbiased)1072435.31570247
Standard Deviation (biased)1063460.80381920
Coefficient of Variation (unbiased)0.244487419961107
Coefficient of Variation (biased)0.242441464159739
Mean Squared Error (MSE versus 0)20372017083998.0
Mean Squared Error (MSE versus Mean)1130948881259.77
Mean Absolute Deviation from Mean (MAD Mean)884573.616166667
Mean Absolute Deviation from Median (MAD Median)884573.616166667
Median Absolute Deviation from Mean776140.202833333
Median Absolute Deviation from Median748858.005
Mean Squared Deviation from Mean1130948881259.77
Mean Squared Deviation from Median1131693199578.39
Interquartile Difference (Weighted Average at Xnp)1614558.9
Interquartile Difference (Weighted Average at X(n+1)p)1679855.4725
Interquartile Difference (Empirical Distribution Function)1614558.9
Interquartile Difference (Empirical Distribution Function - Averaging)1641619.445
Interquartile Difference (Empirical Distribution Function - Interpolation)1603383.4175
Interquartile Difference (Closest Observation)1614558.9
Interquartile Difference (True Basic - Statistics Graphics Toolkit)1603383.4175
Interquartile Difference (MS Excel (old versions))1718091.5
Semi Interquartile Difference (Weighted Average at Xnp)807279.45
Semi Interquartile Difference (Weighted Average at X(n+1)p)839927.73625
Semi Interquartile Difference (Empirical Distribution Function)807279.45
Semi Interquartile Difference (Empirical Distribution Function - Averaging)820809.7225
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)801691.70875
Semi Interquartile Difference (Closest Observation)807279.45
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)801691.70875
Semi Interquartile Difference (MS Excel (old versions))859045.75
Coefficient of Quartile Variation (Weighted Average at Xnp)0.182643857843262
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.188115142388968
Coefficient of Quartile Variation (Empirical Distribution Function)0.182643857843262
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.184112319440628
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.180097329792106
Coefficient of Quartile Variation (Closest Observation)0.182643857843262
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.180097329792106
Coefficient of Quartile Variation (MS Excel (old versions))0.192105853856937
Number of all Pairs of Observations1770
Squared Differences between all Pairs of Observations2300235012731.73
Mean Absolute Differences between all Pairs of Observations1234470.77565537
Gini Mean Difference1234470.77565537
Leik Measure of Dispersion0.51497346142611
Index of Diversity0.982353702274268
Index of Qualitative Variation0.99900376502468
Coefficient of Dispersion0.202921927818581
Observations60



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')