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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 computationWed, 19 Dec 2007 05:00:25 -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/Dec/19/t11980646036anty6bx8j835et.htm/, Retrieved Tue, 08 Sep 2026 22:13:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4638, Retrieved Tue, 08 Sep 2026 22:13:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact541

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] [VRM EURO95] [2007-12-19 12:00:25] [5ac741e139b03fb8a6fb673aeace8af7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1
1,04
1,02
1,07
1,12
1,08
1,02
1,01
1,04
0,98
0,95
0,94
0,94
0,96
0,97
1,03
1,01
0,99
1
1
1,02
1,01
0,99
0,98
1,01
1,03
1,03
1
0,96
0,97
0,98
1,02
1,04
1,01
1,01
1
1,01
1,02
1,03
1,06
1,12
1,12
1,13
1,13
1,13
1,17
1,14
1,08
1,07
1,12
1,14
1,21
1,2
1,23
1,29
1,31
1,37
1,35
1,26
1,26
1,28
1,28
1,27
1,35
1,37
1,37
1,4
1,4
1,28
1,23
1,23
1,25
1,21
1,22
1,29
1,32
1,36
1,36
1,37
1,32

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=4638&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=4638&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4638&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)0.0199412025316456Range0.46Trim Var.0.0151542199488491
V(Y[t],d=1,D=0)0.00131671535215839Range0.2Trim Var.0.000644315188762072
V(Y[t],d=2,D=0)0.00208306693306694Range0.21Trim Var.0.00126046971027217
V(Y[t],d=3,D=0)0.00521052631578948Range0.34Trim Var.0.00320781387181739
V(Y[t],d=0,D=1)0.00793017998244074Range0.36Trim Var.0.0057969209039548
V(Y[t],d=1,D=1)0.00217869742198101Range0.28Trim Var.0.00103847549909256
V(Y[t],d=2,D=1)0.00414902097902098Range0.31Trim Var.0.00226942355889725
V(Y[t],d=3,D=1)0.0107297115384616Range0.51Trim Var.0.00599555137844612
V(Y[t],d=0,D=2)0.0163617857142857Range0.54Trim Var.0.0106166938775510
V(Y[t],d=1,D=2)0.00569932659932661Range0.39Trim Var.0.00304039115646259
V(Y[t],d=2,D=2)0.0112764849755416Range0.48Trim Var.0.00683422756706754
V(Y[t],d=3,D=2)0.0290537010159652Range0.78Trim Var.0.0178249768732655

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.0199412025316456 & Range & 0.46 & Trim Var. & 0.0151542199488491 \tabularnewline
V(Y[t],d=1,D=0) & 0.00131671535215839 & Range & 0.2 & Trim Var. & 0.000644315188762072 \tabularnewline
V(Y[t],d=2,D=0) & 0.00208306693306694 & Range & 0.21 & Trim Var. & 0.00126046971027217 \tabularnewline
V(Y[t],d=3,D=0) & 0.00521052631578948 & Range & 0.34 & Trim Var. & 0.00320781387181739 \tabularnewline
V(Y[t],d=0,D=1) & 0.00793017998244074 & Range & 0.36 & Trim Var. & 0.0057969209039548 \tabularnewline
V(Y[t],d=1,D=1) & 0.00217869742198101 & Range & 0.28 & Trim Var. & 0.00103847549909256 \tabularnewline
V(Y[t],d=2,D=1) & 0.00414902097902098 & Range & 0.31 & Trim Var. & 0.00226942355889725 \tabularnewline
V(Y[t],d=3,D=1) & 0.0107297115384616 & Range & 0.51 & Trim Var. & 0.00599555137844612 \tabularnewline
V(Y[t],d=0,D=2) & 0.0163617857142857 & Range & 0.54 & Trim Var. & 0.0106166938775510 \tabularnewline
V(Y[t],d=1,D=2) & 0.00569932659932661 & Range & 0.39 & Trim Var. & 0.00304039115646259 \tabularnewline
V(Y[t],d=2,D=2) & 0.0112764849755416 & Range & 0.48 & Trim Var. & 0.00683422756706754 \tabularnewline
V(Y[t],d=3,D=2) & 0.0290537010159652 & Range & 0.78 & Trim Var. & 0.0178249768732655 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4638&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.0199412025316456[/C][C]Range[/C][C]0.46[/C][C]Trim Var.[/C][C]0.0151542199488491[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.00131671535215839[/C][C]Range[/C][C]0.2[/C][C]Trim Var.[/C][C]0.000644315188762072[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.00208306693306694[/C][C]Range[/C][C]0.21[/C][C]Trim Var.[/C][C]0.00126046971027217[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.00521052631578948[/C][C]Range[/C][C]0.34[/C][C]Trim Var.[/C][C]0.00320781387181739[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.00793017998244074[/C][C]Range[/C][C]0.36[/C][C]Trim Var.[/C][C]0.0057969209039548[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.00217869742198101[/C][C]Range[/C][C]0.28[/C][C]Trim Var.[/C][C]0.00103847549909256[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.00414902097902098[/C][C]Range[/C][C]0.31[/C][C]Trim Var.[/C][C]0.00226942355889725[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.0107297115384616[/C][C]Range[/C][C]0.51[/C][C]Trim Var.[/C][C]0.00599555137844612[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.0163617857142857[/C][C]Range[/C][C]0.54[/C][C]Trim Var.[/C][C]0.0106166938775510[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.00569932659932661[/C][C]Range[/C][C]0.39[/C][C]Trim Var.[/C][C]0.00304039115646259[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.0112764849755416[/C][C]Range[/C][C]0.48[/C][C]Trim Var.[/C][C]0.00683422756706754[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.0290537010159652[/C][C]Range[/C][C]0.78[/C][C]Trim Var.[/C][C]0.0178249768732655[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4638&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4638&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)0.0199412025316456Range0.46Trim Var.0.0151542199488491
V(Y[t],d=1,D=0)0.00131671535215839Range0.2Trim Var.0.000644315188762072
V(Y[t],d=2,D=0)0.00208306693306694Range0.21Trim Var.0.00126046971027217
V(Y[t],d=3,D=0)0.00521052631578948Range0.34Trim Var.0.00320781387181739
V(Y[t],d=0,D=1)0.00793017998244074Range0.36Trim Var.0.0057969209039548
V(Y[t],d=1,D=1)0.00217869742198101Range0.28Trim Var.0.00103847549909256
V(Y[t],d=2,D=1)0.00414902097902098Range0.31Trim Var.0.00226942355889725
V(Y[t],d=3,D=1)0.0107297115384616Range0.51Trim Var.0.00599555137844612
V(Y[t],d=0,D=2)0.0163617857142857Range0.54Trim Var.0.0106166938775510
V(Y[t],d=1,D=2)0.00569932659932661Range0.39Trim Var.0.00304039115646259
V(Y[t],d=2,D=2)0.0112764849755416Range0.48Trim Var.0.00683422756706754
V(Y[t],d=3,D=2)0.0290537010159652Range0.78Trim Var.0.0178249768732655


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')