Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_variability.wasp
Title produced by softwareVariability
Date of computationWed, 30 Nov 2011 07:37:40 -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/2011/Nov/30/t132265701503mh34md4yktymo.htm/, Retrieved Thu, 28 Mar 2024 18:00:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148909, Retrieved Thu, 28 Mar 2024 18:00:26 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Variability] [] [2011-11-30 12:37:40] [d22ab4133447fd2cf74cbadcaeb9b5f8] [Current]
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Dataseries X:
20,89
21,04
21,07
21,12
21,25
21,24
21,24
21,22
21,29
21,25
21,15
21,16
21,16
21,52
21,59
21,6
21,68
21,67
21,67
21,65
21,74
21,72
21,84
21,94
21,94
21,95
21,96
22,1
22,13
22,18
22,18
22,27
22,3
22,04
22,05
22,06
22,06
22,06
21,97
22,03
22,08
22,13
22,13
22,4
22,4
22,12
22,22
22,14
22,14
22,19
22,29
22,24
22,26
22,29
22,29
22,29
22,29
22,35
22,39
22,43




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148909&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148909&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148909&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 time0 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Variability - Ungrouped Data
Absolute range1.54
Relative range (unbiased)3.53065272693757
Relative range (biased)3.56044779295208
Variance (unbiased)0.190252966101695
Variance (biased)0.187082083333333
Standard Deviation (unbiased)0.436179969853838
Standard Deviation (biased)0.432529864094184
Coefficient of Variation (unbiased)0.0199464945628827
Coefficient of Variation (biased)0.0197795753558561
Mean Squared Error (MSE versus 0)478.374638333333
Mean Squared Error (MSE versus Mean)0.187082083333333
Mean Absolute Deviation from Mean (MAD Mean)0.373083333333333
Mean Absolute Deviation from Median (MAD Median)0.347833333333333
Median Absolute Deviation from Mean0.317500000000001
Median Absolute Deviation from Median0.244999999999997
Mean Squared Deviation from Mean0.187082083333333
Mean Squared Deviation from Median0.218588333333334
Interquartile Difference (Weighted Average at Xnp)0.600000000000001
Interquartile Difference (Weighted Average at X(n+1)p)0.619999999999997
Interquartile Difference (Empirical Distribution Function)0.600000000000001
Interquartile Difference (Empirical Distribution Function - Averaging)0.609999999999999
Interquartile Difference (Empirical Distribution Function - Interpolation)0.600000000000001
Interquartile Difference (Closest Observation)0.600000000000001
Interquartile Difference (True Basic - Statistics Graphics Toolkit)0.599999999999998
Interquartile Difference (MS Excel (old versions))0.629999999999999
Semi Interquartile Difference (Weighted Average at Xnp)0.300000000000001
Semi Interquartile Difference (Weighted Average at X(n+1)p)0.309999999999999
Semi Interquartile Difference (Empirical Distribution Function)0.300000000000001
Semi Interquartile Difference (Empirical Distribution Function - Averaging)0.305
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)0.300000000000001
Semi Interquartile Difference (Closest Observation)0.300000000000001
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)0.299999999999999
Semi Interquartile Difference (MS Excel (old versions))0.315
Coefficient of Quartile Variation (Weighted Average at Xnp)0.0137048880767474
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.0141536354297454
Coefficient of Quartile Variation (Empirical Distribution Function)0.0137048880767474
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.0139269406392694
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.0137001940860829
Coefficient of Quartile Variation (Closest Observation)0.0137048880767474
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.0137001940860828
Coefficient of Quartile Variation (MS Excel (old versions))0.0143802784752339
Number of all Pairs of Observations1770
Squared Differences between all Pairs of Observations0.380505932203391
Mean Absolute Differences between all Pairs of Observations0.486344632768362
Gini Mean Difference0.486344632768359
Leik Measure of Dispersion0.506370739540078
Index of Diversity0.983326812806646
Index of Qualitative Variation0.999993368955911
Coefficient of Dispersion0.0169237166402056
Observations60

\begin{tabular}{lllllllll}
\hline
Variability - Ungrouped Data \tabularnewline
Absolute range & 1.54 \tabularnewline
Relative range (unbiased) & 3.53065272693757 \tabularnewline
Relative range (biased) & 3.56044779295208 \tabularnewline
Variance (unbiased) & 0.190252966101695 \tabularnewline
Variance (biased) & 0.187082083333333 \tabularnewline
Standard Deviation (unbiased) & 0.436179969853838 \tabularnewline
Standard Deviation (biased) & 0.432529864094184 \tabularnewline
Coefficient of Variation (unbiased) & 0.0199464945628827 \tabularnewline
Coefficient of Variation (biased) & 0.0197795753558561 \tabularnewline
Mean Squared Error (MSE versus 0) & 478.374638333333 \tabularnewline
Mean Squared Error (MSE versus Mean) & 0.187082083333333 \tabularnewline
Mean Absolute Deviation from Mean (MAD Mean) & 0.373083333333333 \tabularnewline
Mean Absolute Deviation from Median (MAD Median) & 0.347833333333333 \tabularnewline
Median Absolute Deviation from Mean & 0.317500000000001 \tabularnewline
Median Absolute Deviation from Median & 0.244999999999997 \tabularnewline
Mean Squared Deviation from Mean & 0.187082083333333 \tabularnewline
Mean Squared Deviation from Median & 0.218588333333334 \tabularnewline
Interquartile Difference (Weighted Average at Xnp) & 0.600000000000001 \tabularnewline
Interquartile Difference (Weighted Average at X(n+1)p) & 0.619999999999997 \tabularnewline
Interquartile Difference (Empirical Distribution Function) & 0.600000000000001 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Averaging) & 0.609999999999999 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Interpolation) & 0.600000000000001 \tabularnewline
Interquartile Difference (Closest Observation) & 0.600000000000001 \tabularnewline
Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 0.599999999999998 \tabularnewline
Interquartile Difference (MS Excel (old versions)) & 0.629999999999999 \tabularnewline
Semi Interquartile Difference (Weighted Average at Xnp) & 0.300000000000001 \tabularnewline
Semi Interquartile Difference (Weighted Average at X(n+1)p) & 0.309999999999999 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function) & 0.300000000000001 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Averaging) & 0.305 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Interpolation) & 0.300000000000001 \tabularnewline
Semi Interquartile Difference (Closest Observation) & 0.300000000000001 \tabularnewline
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 0.299999999999999 \tabularnewline
Semi Interquartile Difference (MS Excel (old versions)) & 0.315 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at Xnp) & 0.0137048880767474 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at X(n+1)p) & 0.0141536354297454 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function) & 0.0137048880767474 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging) & 0.0139269406392694 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation) & 0.0137001940860829 \tabularnewline
Coefficient of Quartile Variation (Closest Observation) & 0.0137048880767474 \tabularnewline
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit) & 0.0137001940860828 \tabularnewline
Coefficient of Quartile Variation (MS Excel (old versions)) & 0.0143802784752339 \tabularnewline
Number of all Pairs of Observations & 1770 \tabularnewline
Squared Differences between all Pairs of Observations & 0.380505932203391 \tabularnewline
Mean Absolute Differences between all Pairs of Observations & 0.486344632768362 \tabularnewline
Gini Mean Difference & 0.486344632768359 \tabularnewline
Leik Measure of Dispersion & 0.506370739540078 \tabularnewline
Index of Diversity & 0.983326812806646 \tabularnewline
Index of Qualitative Variation & 0.999993368955911 \tabularnewline
Coefficient of Dispersion & 0.0169237166402056 \tabularnewline
Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148909&T=1

[TABLE]
[ROW][C]Variability - Ungrouped Data[/C][/ROW]
[ROW][C]Absolute range[/C][C]1.54[/C][/ROW]
[ROW][C]Relative range (unbiased)[/C][C]3.53065272693757[/C][/ROW]
[ROW][C]Relative range (biased)[/C][C]3.56044779295208[/C][/ROW]
[ROW][C]Variance (unbiased)[/C][C]0.190252966101695[/C][/ROW]
[ROW][C]Variance (biased)[/C][C]0.187082083333333[/C][/ROW]
[ROW][C]Standard Deviation (unbiased)[/C][C]0.436179969853838[/C][/ROW]
[ROW][C]Standard Deviation (biased)[/C][C]0.432529864094184[/C][/ROW]
[ROW][C]Coefficient of Variation (unbiased)[/C][C]0.0199464945628827[/C][/ROW]
[ROW][C]Coefficient of Variation (biased)[/C][C]0.0197795753558561[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus 0)[/C][C]478.374638333333[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus Mean)[/C][C]0.187082083333333[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Mean (MAD Mean)[/C][C]0.373083333333333[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Median (MAD Median)[/C][C]0.347833333333333[/C][/ROW]
[ROW][C]Median Absolute Deviation from Mean[/C][C]0.317500000000001[/C][/ROW]
[ROW][C]Median Absolute Deviation from Median[/C][C]0.244999999999997[/C][/ROW]
[ROW][C]Mean Squared Deviation from Mean[/C][C]0.187082083333333[/C][/ROW]
[ROW][C]Mean Squared Deviation from Median[/C][C]0.218588333333334[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at Xnp)[/C][C]0.600000000000001[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]0.619999999999997[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function)[/C][C]0.600000000000001[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]0.609999999999999[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]0.600000000000001[/C][/ROW]
[ROW][C]Interquartile Difference (Closest Observation)[/C][C]0.600000000000001[/C][/ROW]
[ROW][C]Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]0.599999999999998[/C][/ROW]
[ROW][C]Interquartile Difference (MS Excel (old versions))[/C][C]0.629999999999999[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at Xnp)[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]0.309999999999999[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function)[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]0.305[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Closest Observation)[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]0.299999999999999[/C][/ROW]
[ROW][C]Semi Interquartile Difference (MS Excel (old versions))[/C][C]0.315[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at Xnp)[/C][C]0.0137048880767474[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at X(n+1)p)[/C][C]0.0141536354297454[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function)[/C][C]0.0137048880767474[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)[/C][C]0.0139269406392694[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)[/C][C]0.0137001940860829[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Closest Observation)[/C][C]0.0137048880767474[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)[/C][C]0.0137001940860828[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (MS Excel (old versions))[/C][C]0.0143802784752339[/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]0.380505932203391[/C][/ROW]
[ROW][C]Mean Absolute Differences between all Pairs of Observations[/C][C]0.486344632768362[/C][/ROW]
[ROW][C]Gini Mean Difference[/C][C]0.486344632768359[/C][/ROW]
[ROW][C]Leik Measure of Dispersion[/C][C]0.506370739540078[/C][/ROW]
[ROW][C]Index of Diversity[/C][C]0.983326812806646[/C][/ROW]
[ROW][C]Index of Qualitative Variation[/C][C]0.999993368955911[/C][/ROW]
[ROW][C]Coefficient of Dispersion[/C][C]0.0169237166402056[/C][/ROW]
[ROW][C]Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148909&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148909&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 range1.54
Relative range (unbiased)3.53065272693757
Relative range (biased)3.56044779295208
Variance (unbiased)0.190252966101695
Variance (biased)0.187082083333333
Standard Deviation (unbiased)0.436179969853838
Standard Deviation (biased)0.432529864094184
Coefficient of Variation (unbiased)0.0199464945628827
Coefficient of Variation (biased)0.0197795753558561
Mean Squared Error (MSE versus 0)478.374638333333
Mean Squared Error (MSE versus Mean)0.187082083333333
Mean Absolute Deviation from Mean (MAD Mean)0.373083333333333
Mean Absolute Deviation from Median (MAD Median)0.347833333333333
Median Absolute Deviation from Mean0.317500000000001
Median Absolute Deviation from Median0.244999999999997
Mean Squared Deviation from Mean0.187082083333333
Mean Squared Deviation from Median0.218588333333334
Interquartile Difference (Weighted Average at Xnp)0.600000000000001
Interquartile Difference (Weighted Average at X(n+1)p)0.619999999999997
Interquartile Difference (Empirical Distribution Function)0.600000000000001
Interquartile Difference (Empirical Distribution Function - Averaging)0.609999999999999
Interquartile Difference (Empirical Distribution Function - Interpolation)0.600000000000001
Interquartile Difference (Closest Observation)0.600000000000001
Interquartile Difference (True Basic - Statistics Graphics Toolkit)0.599999999999998
Interquartile Difference (MS Excel (old versions))0.629999999999999
Semi Interquartile Difference (Weighted Average at Xnp)0.300000000000001
Semi Interquartile Difference (Weighted Average at X(n+1)p)0.309999999999999
Semi Interquartile Difference (Empirical Distribution Function)0.300000000000001
Semi Interquartile Difference (Empirical Distribution Function - Averaging)0.305
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)0.300000000000001
Semi Interquartile Difference (Closest Observation)0.300000000000001
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)0.299999999999999
Semi Interquartile Difference (MS Excel (old versions))0.315
Coefficient of Quartile Variation (Weighted Average at Xnp)0.0137048880767474
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.0141536354297454
Coefficient of Quartile Variation (Empirical Distribution Function)0.0137048880767474
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.0139269406392694
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.0137001940860829
Coefficient of Quartile Variation (Closest Observation)0.0137048880767474
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.0137001940860828
Coefficient of Quartile Variation (MS Excel (old versions))0.0143802784752339
Number of all Pairs of Observations1770
Squared Differences between all Pairs of Observations0.380505932203391
Mean Absolute Differences between all Pairs of Observations0.486344632768362
Gini Mean Difference0.486344632768359
Leik Measure of Dispersion0.506370739540078
Index of Diversity0.983326812806646
Index of Qualitative Variation0.999993368955911
Coefficient of Dispersion0.0169237166402056
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')