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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationTue, 27 Nov 2007 13:55:42 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/27/t1196196458wcy367bfhya1mgs.htm/, Retrieved Tue, 10 Feb 2026 16:25:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6959, Retrieved Tue, 10 Feb 2026 16:25:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsgroep MENS
Estimated Impact420

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Variance Reduction Matrix] [Transport_Q2] [2007-11-27 20:55:42] [68ccea1ea79fa519d33f2664ba3973dd] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
99,9
99,9
99,9
99,9
99,9
99,7
99,6
99,5
100,6
100,2
100,1
100,2
99,1
99,5
99,5
99,6
99,5
99,6
99,8
99,9
100,5
100,5
100,5
100,5
99,5
99,9
100,4
99,6
99,5
99,6
98,4
99,9
100,3
100,3
101,3
101,0
99,7
99,4
99,9
100,7
99,8
98,8
99,6
99,1
100,3
100,5
100,8
100,6
99,1
98,8
99,0
99,9
99,5
99,2
99,6
100,1
99,8
101,6
101,7
101,9
100,0
102,0
102,0
102,9
102,7
102,7
102,7
102,7
102,6
102,6
102,5
102,5
102,1

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6959&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6959&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6959&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)1.31296803652968Range4.5Trim Var.0.877418154761904
V(Y[t],d=1,D=0)0.465532081377152Range3.90000000000001Trim Var.0.208888888888889
V(Y[t],d=2,D=0)1.16111066398390Range6.00000000000001Trim Var.0.592846902201742
V(Y[t],d=3,D=0)3.70634368530021Range11.9000000000000Trim Var.1.85292702273929
V(Y[t],d=0,D=1)1.41716393442623Range4.89999999999999Trim Var.0.870544267053703
V(Y[t],d=1,D=1)0.672370056497174Range4.3Trim Var.0.346642208245982
V(Y[t],d=2,D=1)1.93430157802454Range7.09999999999998Trim Var.1.08898403483309
V(Y[t],d=3,D=1)6.54480641258316Range13.9000000000000Trim Var.3.4566628959276
V(Y[t],d=0,D=2)2.37409863945579Range5.80000000000001Trim Var.1.60339977851606
V(Y[t],d=1,D=2)2.11787234042553Range6.79999999999997Trim Var.1.06945993031359
V(Y[t],d=2,D=2)6.56994449583717Range12.2000000000000Trim Var.3.31401219512195
V(Y[t],d=3,D=2)22.8045410628019Range22.4999999999999Trim Var.10.6789679487179

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1.31296803652968 & Range & 4.5 & Trim Var. & 0.877418154761904 \tabularnewline
V(Y[t],d=1,D=0) & 0.465532081377152 & Range & 3.90000000000001 & Trim Var. & 0.208888888888889 \tabularnewline
V(Y[t],d=2,D=0) & 1.16111066398390 & Range & 6.00000000000001 & Trim Var. & 0.592846902201742 \tabularnewline
V(Y[t],d=3,D=0) & 3.70634368530021 & Range & 11.9000000000000 & Trim Var. & 1.85292702273929 \tabularnewline
V(Y[t],d=0,D=1) & 1.41716393442623 & Range & 4.89999999999999 & Trim Var. & 0.870544267053703 \tabularnewline
V(Y[t],d=1,D=1) & 0.672370056497174 & Range & 4.3 & Trim Var. & 0.346642208245982 \tabularnewline
V(Y[t],d=2,D=1) & 1.93430157802454 & Range & 7.09999999999998 & Trim Var. & 1.08898403483309 \tabularnewline
V(Y[t],d=3,D=1) & 6.54480641258316 & Range & 13.9000000000000 & Trim Var. & 3.4566628959276 \tabularnewline
V(Y[t],d=0,D=2) & 2.37409863945579 & Range & 5.80000000000001 & Trim Var. & 1.60339977851606 \tabularnewline
V(Y[t],d=1,D=2) & 2.11787234042553 & Range & 6.79999999999997 & Trim Var. & 1.06945993031359 \tabularnewline
V(Y[t],d=2,D=2) & 6.56994449583717 & Range & 12.2000000000000 & Trim Var. & 3.31401219512195 \tabularnewline
V(Y[t],d=3,D=2) & 22.8045410628019 & Range & 22.4999999999999 & Trim Var. & 10.6789679487179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6959&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1.31296803652968[/C][C]Range[/C][C]4.5[/C][C]Trim Var.[/C][C]0.877418154761904[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.465532081377152[/C][C]Range[/C][C]3.90000000000001[/C][C]Trim Var.[/C][C]0.208888888888889[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1.16111066398390[/C][C]Range[/C][C]6.00000000000001[/C][C]Trim Var.[/C][C]0.592846902201742[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]3.70634368530021[/C][C]Range[/C][C]11.9000000000000[/C][C]Trim Var.[/C][C]1.85292702273929[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1.41716393442623[/C][C]Range[/C][C]4.89999999999999[/C][C]Trim Var.[/C][C]0.870544267053703[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.672370056497174[/C][C]Range[/C][C]4.3[/C][C]Trim Var.[/C][C]0.346642208245982[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1.93430157802454[/C][C]Range[/C][C]7.09999999999998[/C][C]Trim Var.[/C][C]1.08898403483309[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]6.54480641258316[/C][C]Range[/C][C]13.9000000000000[/C][C]Trim Var.[/C][C]3.4566628959276[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]2.37409863945579[/C][C]Range[/C][C]5.80000000000001[/C][C]Trim Var.[/C][C]1.60339977851606[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]2.11787234042553[/C][C]Range[/C][C]6.79999999999997[/C][C]Trim Var.[/C][C]1.06945993031359[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]6.56994449583717[/C][C]Range[/C][C]12.2000000000000[/C][C]Trim Var.[/C][C]3.31401219512195[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]22.8045410628019[/C][C]Range[/C][C]22.4999999999999[/C][C]Trim Var.[/C][C]10.6789679487179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6959&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6959&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Variance Reduction Matrix
V(Y[t],d=0,D=0)1.31296803652968Range4.5Trim Var.0.877418154761904
V(Y[t],d=1,D=0)0.465532081377152Range3.90000000000001Trim Var.0.208888888888889
V(Y[t],d=2,D=0)1.16111066398390Range6.00000000000001Trim Var.0.592846902201742
V(Y[t],d=3,D=0)3.70634368530021Range11.9000000000000Trim Var.1.85292702273929
V(Y[t],d=0,D=1)1.41716393442623Range4.89999999999999Trim Var.0.870544267053703
V(Y[t],d=1,D=1)0.672370056497174Range4.3Trim Var.0.346642208245982
V(Y[t],d=2,D=1)1.93430157802454Range7.09999999999998Trim Var.1.08898403483309
V(Y[t],d=3,D=1)6.54480641258316Range13.9000000000000Trim Var.3.4566628959276
V(Y[t],d=0,D=2)2.37409863945579Range5.80000000000001Trim Var.1.60339977851606
V(Y[t],d=1,D=2)2.11787234042553Range6.79999999999997Trim Var.1.06945993031359
V(Y[t],d=2,D=2)6.56994449583717Range12.2000000000000Trim Var.3.31401219512195
V(Y[t],d=3,D=2)22.8045410628019Range22.4999999999999Trim Var.10.6789679487179


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
n <- length(x)
sx <- sort(x)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Reduction Matrix',6,TRUE)
a<-table.row.end(a)
for (bigd in 0:2) {
for (smalld in 0:3) {
mylabel <- 'V(Y[t],d='
mylabel <- paste(mylabel,as.character(smalld),sep='')
mylabel <- paste(mylabel,',D=',sep='')
mylabel <- paste(mylabel,as.character(bigd),sep='')
mylabel <- paste(mylabel,')',sep='')
a<-table.row.start(a)
a<-table.element(a,mylabel,header=TRUE)
myx <- x
if (smalld > 0) myx <- diff(x,lag=1,differences=smalld)
if (bigd > 0) myx <- diff(myx,lag=par1,differences=bigd)
a<-table.element(a,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,var(smyx[smyx>quantile(smyx,0.05) & smyxa<-table.row.end(a)
}
}
a<-table.end(a)
table.save(a,file='mytable.tab')