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 computationFri, 21 Dec 2012 08:26:04 -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/21/t1356096378m12cx26az1ijsjw.htm/, Retrieved Thu, 28 Mar 2024 18:08:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203625, Retrieved Thu, 28 Mar 2024 18:08:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variability] [one sample chi-sq...] [2012-12-20 17:30:36] [73586a5ad7cb70bd9d8f219d68ef24b6]
-         [Variability] [One sample chi sq...] [2012-12-21 13:26:04] [fc11b595ce1e8c0e30ce0084e7aafbef] [Current]
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Dataseries X:
26
20
19

20
25

22
26
22


19
24
26

13


22

21
7

17
25
25
19

23

22
21



18


22
18
23
20


15


21

18
19
22
16

18
20
24


24
18
21

17



22
16
21


24
24
16
16




18

20


24
17
19
20
15

22
23
16
19

19


21

24
22

18

24
24
22
23
22
20
18
25

16
20

15
19
19
16
17
28

25
20


16




23
21


23
18
20
9

25
20




21
22
27



18
16
22
20

20




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
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=203625&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]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=203625&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203625&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
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Variability - Ungrouped Data
Absolute range21
Relative range (unbiased)5.81743614413938
Relative range (biased)5.84734603869162
Variance (unbiased)13.0309278350515
Variance (biased)12.8979591836735
Standard Deviation (unbiased)3.60983764663337
Standard Deviation (biased)3.59137288285044
Coefficient of Variation (unbiased)0.177949743143899
Coefficient of Variation (biased)0.177039508309529
Mean Squared Error (MSE versus 0)424.408163265306
Mean Squared Error (MSE versus Mean)12.8979591836735
Mean Absolute Deviation from Mean (MAD Mean)2.80758017492711
Mean Absolute Deviation from Median (MAD Median)2.79591836734694
Median Absolute Deviation from Mean2.28571428571428
Median Absolute Deviation from Median2
Mean Squared Deviation from Mean12.8979591836735
Mean Squared Deviation from Median12.9795918367347
Interquartile Difference (Weighted Average at Xnp)5
Interquartile Difference (Weighted Average at X(n+1)p)5
Interquartile Difference (Empirical Distribution Function)5
Interquartile Difference (Empirical Distribution Function - Averaging)5
Interquartile Difference (Empirical Distribution Function - Interpolation)5
Interquartile Difference (Closest Observation)5
Interquartile Difference (True Basic - Statistics Graphics Toolkit)5
Interquartile Difference (MS Excel (old versions))5
Semi Interquartile Difference (Weighted Average at Xnp)2.5
Semi Interquartile Difference (Weighted Average at X(n+1)p)2.5
Semi Interquartile Difference (Empirical Distribution Function)2.5
Semi Interquartile Difference (Empirical Distribution Function - Averaging)2.5
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)2.5
Semi Interquartile Difference (Closest Observation)2.5
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)2.5
Semi Interquartile Difference (MS Excel (old versions))2.5
Coefficient of Quartile Variation (Weighted Average at Xnp)0.121951219512195
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.121951219512195
Coefficient of Quartile Variation (Empirical Distribution Function)0.121951219512195
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.121951219512195
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.121951219512195
Coefficient of Quartile Variation (Closest Observation)0.121951219512195
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.121951219512195
Coefficient of Quartile Variation (MS Excel (old versions))0.121951219512195
Number of all Pairs of Observations4753
Squared Differences between all Pairs of Observations26.0618556701031
Mean Absolute Differences between all Pairs of Observations3.98737639385651
Gini Mean Difference3.98737639385651
Leik Measure of Dispersion0.510423364931859
Index of Diversity0.98947609196426
Index of Qualitative Variation0.9996768764175
Coefficient of Dispersion0.140379008746356
Observations98

\begin{tabular}{lllllllll}
\hline
Variability - Ungrouped Data \tabularnewline
Absolute range & 21 \tabularnewline
Relative range (unbiased) & 5.81743614413938 \tabularnewline
Relative range (biased) & 5.84734603869162 \tabularnewline
Variance (unbiased) & 13.0309278350515 \tabularnewline
Variance (biased) & 12.8979591836735 \tabularnewline
Standard Deviation (unbiased) & 3.60983764663337 \tabularnewline
Standard Deviation (biased) & 3.59137288285044 \tabularnewline
Coefficient of Variation (unbiased) & 0.177949743143899 \tabularnewline
Coefficient of Variation (biased) & 0.177039508309529 \tabularnewline
Mean Squared Error (MSE versus 0) & 424.408163265306 \tabularnewline
Mean Squared Error (MSE versus Mean) & 12.8979591836735 \tabularnewline
Mean Absolute Deviation from Mean (MAD Mean) & 2.80758017492711 \tabularnewline
Mean Absolute Deviation from Median (MAD Median) & 2.79591836734694 \tabularnewline
Median Absolute Deviation from Mean & 2.28571428571428 \tabularnewline
Median Absolute Deviation from Median & 2 \tabularnewline
Mean Squared Deviation from Mean & 12.8979591836735 \tabularnewline
Mean Squared Deviation from Median & 12.9795918367347 \tabularnewline
Interquartile Difference (Weighted Average at Xnp) & 5 \tabularnewline
Interquartile Difference (Weighted Average at X(n+1)p) & 5 \tabularnewline
Interquartile Difference (Empirical Distribution Function) & 5 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Averaging) & 5 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Interpolation) & 5 \tabularnewline
Interquartile Difference (Closest Observation) & 5 \tabularnewline
Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 5 \tabularnewline
Interquartile Difference (MS Excel (old versions)) & 5 \tabularnewline
Semi Interquartile Difference (Weighted Average at Xnp) & 2.5 \tabularnewline
Semi Interquartile Difference (Weighted Average at X(n+1)p) & 2.5 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function) & 2.5 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Averaging) & 2.5 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Interpolation) & 2.5 \tabularnewline
Semi Interquartile Difference (Closest Observation) & 2.5 \tabularnewline
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 2.5 \tabularnewline
Semi Interquartile Difference (MS Excel (old versions)) & 2.5 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at Xnp) & 0.121951219512195 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at X(n+1)p) & 0.121951219512195 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function) & 0.121951219512195 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging) & 0.121951219512195 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation) & 0.121951219512195 \tabularnewline
Coefficient of Quartile Variation (Closest Observation) & 0.121951219512195 \tabularnewline
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit) & 0.121951219512195 \tabularnewline
Coefficient of Quartile Variation (MS Excel (old versions)) & 0.121951219512195 \tabularnewline
Number of all Pairs of Observations & 4753 \tabularnewline
Squared Differences between all Pairs of Observations & 26.0618556701031 \tabularnewline
Mean Absolute Differences between all Pairs of Observations & 3.98737639385651 \tabularnewline
Gini Mean Difference & 3.98737639385651 \tabularnewline
Leik Measure of Dispersion & 0.510423364931859 \tabularnewline
Index of Diversity & 0.98947609196426 \tabularnewline
Index of Qualitative Variation & 0.9996768764175 \tabularnewline
Coefficient of Dispersion & 0.140379008746356 \tabularnewline
Observations & 98 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203625&T=1

[TABLE]
[ROW][C]Variability - Ungrouped Data[/C][/ROW]
[ROW][C]Absolute range[/C][C]21[/C][/ROW]
[ROW][C]Relative range (unbiased)[/C][C]5.81743614413938[/C][/ROW]
[ROW][C]Relative range (biased)[/C][C]5.84734603869162[/C][/ROW]
[ROW][C]Variance (unbiased)[/C][C]13.0309278350515[/C][/ROW]
[ROW][C]Variance (biased)[/C][C]12.8979591836735[/C][/ROW]
[ROW][C]Standard Deviation (unbiased)[/C][C]3.60983764663337[/C][/ROW]
[ROW][C]Standard Deviation (biased)[/C][C]3.59137288285044[/C][/ROW]
[ROW][C]Coefficient of Variation (unbiased)[/C][C]0.177949743143899[/C][/ROW]
[ROW][C]Coefficient of Variation (biased)[/C][C]0.177039508309529[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus 0)[/C][C]424.408163265306[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus Mean)[/C][C]12.8979591836735[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Mean (MAD Mean)[/C][C]2.80758017492711[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Median (MAD Median)[/C][C]2.79591836734694[/C][/ROW]
[ROW][C]Median Absolute Deviation from Mean[/C][C]2.28571428571428[/C][/ROW]
[ROW][C]Median Absolute Deviation from Median[/C][C]2[/C][/ROW]
[ROW][C]Mean Squared Deviation from Mean[/C][C]12.8979591836735[/C][/ROW]
[ROW][C]Mean Squared Deviation from Median[/C][C]12.9795918367347[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at Xnp)[/C][C]5[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]5[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function)[/C][C]5[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]5[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]5[/C][/ROW]
[ROW][C]Interquartile Difference (Closest Observation)[/C][C]5[/C][/ROW]
[ROW][C]Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]5[/C][/ROW]
[ROW][C]Interquartile Difference (MS Excel (old versions))[/C][C]5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at Xnp)[/C][C]2.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]2.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function)[/C][C]2.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]2.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]2.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Closest Observation)[/C][C]2.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]2.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (MS Excel (old versions))[/C][C]2.5[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at Xnp)[/C][C]0.121951219512195[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at X(n+1)p)[/C][C]0.121951219512195[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function)[/C][C]0.121951219512195[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)[/C][C]0.121951219512195[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)[/C][C]0.121951219512195[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Closest Observation)[/C][C]0.121951219512195[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)[/C][C]0.121951219512195[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (MS Excel (old versions))[/C][C]0.121951219512195[/C][/ROW]
[ROW][C]Number of all Pairs of Observations[/C][C]4753[/C][/ROW]
[ROW][C]Squared Differences between all Pairs of Observations[/C][C]26.0618556701031[/C][/ROW]
[ROW][C]Mean Absolute Differences between all Pairs of Observations[/C][C]3.98737639385651[/C][/ROW]
[ROW][C]Gini Mean Difference[/C][C]3.98737639385651[/C][/ROW]
[ROW][C]Leik Measure of Dispersion[/C][C]0.510423364931859[/C][/ROW]
[ROW][C]Index of Diversity[/C][C]0.98947609196426[/C][/ROW]
[ROW][C]Index of Qualitative Variation[/C][C]0.9996768764175[/C][/ROW]
[ROW][C]Coefficient of Dispersion[/C][C]0.140379008746356[/C][/ROW]
[ROW][C]Observations[/C][C]98[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203625&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203625&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 range21
Relative range (unbiased)5.81743614413938
Relative range (biased)5.84734603869162
Variance (unbiased)13.0309278350515
Variance (biased)12.8979591836735
Standard Deviation (unbiased)3.60983764663337
Standard Deviation (biased)3.59137288285044
Coefficient of Variation (unbiased)0.177949743143899
Coefficient of Variation (biased)0.177039508309529
Mean Squared Error (MSE versus 0)424.408163265306
Mean Squared Error (MSE versus Mean)12.8979591836735
Mean Absolute Deviation from Mean (MAD Mean)2.80758017492711
Mean Absolute Deviation from Median (MAD Median)2.79591836734694
Median Absolute Deviation from Mean2.28571428571428
Median Absolute Deviation from Median2
Mean Squared Deviation from Mean12.8979591836735
Mean Squared Deviation from Median12.9795918367347
Interquartile Difference (Weighted Average at Xnp)5
Interquartile Difference (Weighted Average at X(n+1)p)5
Interquartile Difference (Empirical Distribution Function)5
Interquartile Difference (Empirical Distribution Function - Averaging)5
Interquartile Difference (Empirical Distribution Function - Interpolation)5
Interquartile Difference (Closest Observation)5
Interquartile Difference (True Basic - Statistics Graphics Toolkit)5
Interquartile Difference (MS Excel (old versions))5
Semi Interquartile Difference (Weighted Average at Xnp)2.5
Semi Interquartile Difference (Weighted Average at X(n+1)p)2.5
Semi Interquartile Difference (Empirical Distribution Function)2.5
Semi Interquartile Difference (Empirical Distribution Function - Averaging)2.5
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)2.5
Semi Interquartile Difference (Closest Observation)2.5
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)2.5
Semi Interquartile Difference (MS Excel (old versions))2.5
Coefficient of Quartile Variation (Weighted Average at Xnp)0.121951219512195
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.121951219512195
Coefficient of Quartile Variation (Empirical Distribution Function)0.121951219512195
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.121951219512195
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.121951219512195
Coefficient of Quartile Variation (Closest Observation)0.121951219512195
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.121951219512195
Coefficient of Quartile Variation (MS Excel (old versions))0.121951219512195
Number of all Pairs of Observations4753
Squared Differences between all Pairs of Observations26.0618556701031
Mean Absolute Differences between all Pairs of Observations3.98737639385651
Gini Mean Difference3.98737639385651
Leik Measure of Dispersion0.510423364931859
Index of Diversity0.98947609196426
Index of Qualitative Variation0.9996768764175
Coefficient of Dispersion0.140379008746356
Observations98



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')