Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_variability.wasp
Title produced by softwareVariability
Date of computationThu, 05 Dec 2013 16:46:49 -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/2013/Dec/05/t1386280031gyo4r2tz3hfada4.htm/, Retrieved Fri, 29 Mar 2024 06:47:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=231257, Retrieved Fri, 29 Mar 2024 06:47:53 +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] [] [2013-12-05 21:46:49] [ccf63754fa7d22a76bdef567828ba364] [Current]
Feedback Forum

Post a new message
Dataseries X:
9,27
9,30
9,35
9,33
9,37
9,42
9,45
9,38
9,40
9,43
9,45
9,49
9,47
9,48
9,52
9,53
9,53
9,54
9,57
9,61
9,61
9,63
9,64
9,60
9,64
9,66
9,67
9,70
9,72
9,73
9,77
9,72
9,68
9,62
9,79
9,77
9,79
9,77
9,78
9,81
9,74
9,70
9,78
9,85
9,83
9,90
9,93
9,85
9,95
9,97
10,02
9,97
9,95
9,95
9,98
10,00
10,04
10,05
10,06
10,09
10,14
10,13
10,12
10,10
10,12
10,06
10,21
10,18
10,26
10,39
10,41
10,46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231257&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231257&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231257&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'Gertrude Mary Cox' @ cox.wessa.net







Variability - Ungrouped Data
Absolute range1.19
Relative range (unbiased)4.17644555759494
Relative range (biased)4.20575430704963
Variance (unbiased)0.0811858372456964
Variance (biased)0.0800582561728396
Standard Deviation (unbiased)0.28493128512976
Standard Deviation (biased)0.282945677070422
Coefficient of Variation (unbiased)0.0291332507730164
Coefficient of Variation (biased)0.028930229130436
Mean Squared Error (MSE versus 0)95.7338916666667
Mean Squared Error (MSE versus Mean)0.0800582561728396
Mean Absolute Deviation from Mean (MAD Mean)0.233086419753087
Mean Absolute Deviation from Median (MAD Median)0.2325
Median Absolute Deviation from Mean0.215
Median Absolute Deviation from Median0.220000000000001
Mean Squared Deviation from Mean0.0800582561728396
Mean Squared Deviation from Median0.080163888888889
Interquartile Difference (Weighted Average at Xnp)0.440000000000001
Interquartile Difference (Weighted Average at X(n+1)p)0.447500000000002
Interquartile Difference (Empirical Distribution Function)0.440000000000001
Interquartile Difference (Empirical Distribution Function - Averaging)0.435
Interquartile Difference (Empirical Distribution Function - Interpolation)0.422499999999999
Interquartile Difference (Closest Observation)0.440000000000001
Interquartile Difference (True Basic - Statistics Graphics Toolkit)0.422499999999999
Interquartile Difference (MS Excel (old versions))0.460000000000001
Semi Interquartile Difference (Weighted Average at Xnp)0.220000000000001
Semi Interquartile Difference (Weighted Average at X(n+1)p)0.223750000000001
Semi Interquartile Difference (Empirical Distribution Function)0.220000000000001
Semi Interquartile Difference (Empirical Distribution Function - Averaging)0.2175
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)0.21125
Semi Interquartile Difference (Closest Observation)0.220000000000001
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)0.21125
Semi Interquartile Difference (MS Excel (old versions))0.23
Coefficient of Quartile Variation (Weighted Average at Xnp)0.0225409836065574
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.0228988102852758
Coefficient of Quartile Variation (Empirical Distribution Function)0.0225409836065574
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.022256331542594
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.0216140171377414
Coefficient of Quartile Variation (Closest Observation)0.0225409836065574
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.0216140171377414
Coefficient of Quartile Variation (MS Excel (old versions))0.0235414534288639
Number of all Pairs of Observations2556
Squared Differences between all Pairs of Observations0.162371674491393
Mean Absolute Differences between all Pairs of Observations0.327143974960875
Gini Mean Difference0.327143974960874
Leik Measure of Dispersion0.50728906941607
Index of Diversity0.986099486692256
Index of Qualitative Variation0.999988211856936
Coefficient of Dispersion0.0238573612848604
Observations72

\begin{tabular}{lllllllll}
\hline
Variability - Ungrouped Data \tabularnewline
Absolute range & 1.19 \tabularnewline
Relative range (unbiased) & 4.17644555759494 \tabularnewline
Relative range (biased) & 4.20575430704963 \tabularnewline
Variance (unbiased) & 0.0811858372456964 \tabularnewline
Variance (biased) & 0.0800582561728396 \tabularnewline
Standard Deviation (unbiased) & 0.28493128512976 \tabularnewline
Standard Deviation (biased) & 0.282945677070422 \tabularnewline
Coefficient of Variation (unbiased) & 0.0291332507730164 \tabularnewline
Coefficient of Variation (biased) & 0.028930229130436 \tabularnewline
Mean Squared Error (MSE versus 0) & 95.7338916666667 \tabularnewline
Mean Squared Error (MSE versus Mean) & 0.0800582561728396 \tabularnewline
Mean Absolute Deviation from Mean (MAD Mean) & 0.233086419753087 \tabularnewline
Mean Absolute Deviation from Median (MAD Median) & 0.2325 \tabularnewline
Median Absolute Deviation from Mean & 0.215 \tabularnewline
Median Absolute Deviation from Median & 0.220000000000001 \tabularnewline
Mean Squared Deviation from Mean & 0.0800582561728396 \tabularnewline
Mean Squared Deviation from Median & 0.080163888888889 \tabularnewline
Interquartile Difference (Weighted Average at Xnp) & 0.440000000000001 \tabularnewline
Interquartile Difference (Weighted Average at X(n+1)p) & 0.447500000000002 \tabularnewline
Interquartile Difference (Empirical Distribution Function) & 0.440000000000001 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Averaging) & 0.435 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Interpolation) & 0.422499999999999 \tabularnewline
Interquartile Difference (Closest Observation) & 0.440000000000001 \tabularnewline
Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 0.422499999999999 \tabularnewline
Interquartile Difference (MS Excel (old versions)) & 0.460000000000001 \tabularnewline
Semi Interquartile Difference (Weighted Average at Xnp) & 0.220000000000001 \tabularnewline
Semi Interquartile Difference (Weighted Average at X(n+1)p) & 0.223750000000001 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function) & 0.220000000000001 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Averaging) & 0.2175 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Interpolation) & 0.21125 \tabularnewline
Semi Interquartile Difference (Closest Observation) & 0.220000000000001 \tabularnewline
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 0.21125 \tabularnewline
Semi Interquartile Difference (MS Excel (old versions)) & 0.23 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at Xnp) & 0.0225409836065574 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at X(n+1)p) & 0.0228988102852758 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function) & 0.0225409836065574 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging) & 0.022256331542594 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation) & 0.0216140171377414 \tabularnewline
Coefficient of Quartile Variation (Closest Observation) & 0.0225409836065574 \tabularnewline
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit) & 0.0216140171377414 \tabularnewline
Coefficient of Quartile Variation (MS Excel (old versions)) & 0.0235414534288639 \tabularnewline
Number of all Pairs of Observations & 2556 \tabularnewline
Squared Differences between all Pairs of Observations & 0.162371674491393 \tabularnewline
Mean Absolute Differences between all Pairs of Observations & 0.327143974960875 \tabularnewline
Gini Mean Difference & 0.327143974960874 \tabularnewline
Leik Measure of Dispersion & 0.50728906941607 \tabularnewline
Index of Diversity & 0.986099486692256 \tabularnewline
Index of Qualitative Variation & 0.999988211856936 \tabularnewline
Coefficient of Dispersion & 0.0238573612848604 \tabularnewline
Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231257&T=1

[TABLE]
[ROW][C]Variability - Ungrouped Data[/C][/ROW]
[ROW][C]Absolute range[/C][C]1.19[/C][/ROW]
[ROW][C]Relative range (unbiased)[/C][C]4.17644555759494[/C][/ROW]
[ROW][C]Relative range (biased)[/C][C]4.20575430704963[/C][/ROW]
[ROW][C]Variance (unbiased)[/C][C]0.0811858372456964[/C][/ROW]
[ROW][C]Variance (biased)[/C][C]0.0800582561728396[/C][/ROW]
[ROW][C]Standard Deviation (unbiased)[/C][C]0.28493128512976[/C][/ROW]
[ROW][C]Standard Deviation (biased)[/C][C]0.282945677070422[/C][/ROW]
[ROW][C]Coefficient of Variation (unbiased)[/C][C]0.0291332507730164[/C][/ROW]
[ROW][C]Coefficient of Variation (biased)[/C][C]0.028930229130436[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus 0)[/C][C]95.7338916666667[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus Mean)[/C][C]0.0800582561728396[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Mean (MAD Mean)[/C][C]0.233086419753087[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Median (MAD Median)[/C][C]0.2325[/C][/ROW]
[ROW][C]Median Absolute Deviation from Mean[/C][C]0.215[/C][/ROW]
[ROW][C]Median Absolute Deviation from Median[/C][C]0.220000000000001[/C][/ROW]
[ROW][C]Mean Squared Deviation from Mean[/C][C]0.0800582561728396[/C][/ROW]
[ROW][C]Mean Squared Deviation from Median[/C][C]0.080163888888889[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at Xnp)[/C][C]0.440000000000001[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]0.447500000000002[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function)[/C][C]0.440000000000001[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]0.435[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]0.422499999999999[/C][/ROW]
[ROW][C]Interquartile Difference (Closest Observation)[/C][C]0.440000000000001[/C][/ROW]
[ROW][C]Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]0.422499999999999[/C][/ROW]
[ROW][C]Interquartile Difference (MS Excel (old versions))[/C][C]0.460000000000001[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at Xnp)[/C][C]0.220000000000001[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]0.223750000000001[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function)[/C][C]0.220000000000001[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]0.2175[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]0.21125[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Closest Observation)[/C][C]0.220000000000001[/C][/ROW]
[ROW][C]Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]0.21125[/C][/ROW]
[ROW][C]Semi Interquartile Difference (MS Excel (old versions))[/C][C]0.23[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at Xnp)[/C][C]0.0225409836065574[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at X(n+1)p)[/C][C]0.0228988102852758[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function)[/C][C]0.0225409836065574[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)[/C][C]0.022256331542594[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)[/C][C]0.0216140171377414[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Closest Observation)[/C][C]0.0225409836065574[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)[/C][C]0.0216140171377414[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (MS Excel (old versions))[/C][C]0.0235414534288639[/C][/ROW]
[ROW][C]Number of all Pairs of Observations[/C][C]2556[/C][/ROW]
[ROW][C]Squared Differences between all Pairs of Observations[/C][C]0.162371674491393[/C][/ROW]
[ROW][C]Mean Absolute Differences between all Pairs of Observations[/C][C]0.327143974960875[/C][/ROW]
[ROW][C]Gini Mean Difference[/C][C]0.327143974960874[/C][/ROW]
[ROW][C]Leik Measure of Dispersion[/C][C]0.50728906941607[/C][/ROW]
[ROW][C]Index of Diversity[/C][C]0.986099486692256[/C][/ROW]
[ROW][C]Index of Qualitative Variation[/C][C]0.999988211856936[/C][/ROW]
[ROW][C]Coefficient of Dispersion[/C][C]0.0238573612848604[/C][/ROW]
[ROW][C]Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231257&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231257&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 range1.19
Relative range (unbiased)4.17644555759494
Relative range (biased)4.20575430704963
Variance (unbiased)0.0811858372456964
Variance (biased)0.0800582561728396
Standard Deviation (unbiased)0.28493128512976
Standard Deviation (biased)0.282945677070422
Coefficient of Variation (unbiased)0.0291332507730164
Coefficient of Variation (biased)0.028930229130436
Mean Squared Error (MSE versus 0)95.7338916666667
Mean Squared Error (MSE versus Mean)0.0800582561728396
Mean Absolute Deviation from Mean (MAD Mean)0.233086419753087
Mean Absolute Deviation from Median (MAD Median)0.2325
Median Absolute Deviation from Mean0.215
Median Absolute Deviation from Median0.220000000000001
Mean Squared Deviation from Mean0.0800582561728396
Mean Squared Deviation from Median0.080163888888889
Interquartile Difference (Weighted Average at Xnp)0.440000000000001
Interquartile Difference (Weighted Average at X(n+1)p)0.447500000000002
Interquartile Difference (Empirical Distribution Function)0.440000000000001
Interquartile Difference (Empirical Distribution Function - Averaging)0.435
Interquartile Difference (Empirical Distribution Function - Interpolation)0.422499999999999
Interquartile Difference (Closest Observation)0.440000000000001
Interquartile Difference (True Basic - Statistics Graphics Toolkit)0.422499999999999
Interquartile Difference (MS Excel (old versions))0.460000000000001
Semi Interquartile Difference (Weighted Average at Xnp)0.220000000000001
Semi Interquartile Difference (Weighted Average at X(n+1)p)0.223750000000001
Semi Interquartile Difference (Empirical Distribution Function)0.220000000000001
Semi Interquartile Difference (Empirical Distribution Function - Averaging)0.2175
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)0.21125
Semi Interquartile Difference (Closest Observation)0.220000000000001
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)0.21125
Semi Interquartile Difference (MS Excel (old versions))0.23
Coefficient of Quartile Variation (Weighted Average at Xnp)0.0225409836065574
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.0228988102852758
Coefficient of Quartile Variation (Empirical Distribution Function)0.0225409836065574
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.022256331542594
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.0216140171377414
Coefficient of Quartile Variation (Closest Observation)0.0225409836065574
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.0216140171377414
Coefficient of Quartile Variation (MS Excel (old versions))0.0235414534288639
Number of all Pairs of Observations2556
Squared Differences between all Pairs of Observations0.162371674491393
Mean Absolute Differences between all Pairs of Observations0.327143974960875
Gini Mean Difference0.327143974960874
Leik Measure of Dispersion0.50728906941607
Index of Diversity0.986099486692256
Index of Qualitative Variation0.999988211856936
Coefficient of Dispersion0.0238573612848604
Observations72



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')