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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, 09 Dec 2008 12:31:29 -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/2008/Dec/09/t122885118210oqmyydf2r81m5.htm/, Retrieved Thu, 12 Feb 2026 13:33:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31734, Retrieved Thu, 12 Feb 2026 13:33:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact381

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] [Laura_Reussens_VRM5] [2008-12-09 13:33:45] [66eaf6cf5556820c444aae1569718ff9]
-   PD    [Variance Reduction Matrix] [Laura_Reussens_VRM5] [2008-12-09 19:31:29] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5,5
5,3
5,2
5,3
5,3
5
4,8
4,9
5,3
6
6,2
6,4
6,4
6,4
6,2
6,1
6
5,9
6,2
6,2
6,4
6,8
6,9
7
7
6,9
6,7
6,6
6,5
6,4
6,5
6,5
6,6
6,7
6,8
7,2
7,6
7,6
7,3
6,4
6,1
6,3
7,1
7,5
7,4
7,1
6,8
6,9
7,2
7,4
7,3
6,9
6,9
6,8
7,1
7,2
7,1
7
6,9
7
7,4
7,5
7,5
7,4
7,3
7
6,7
6,5
6,5
6,5
6,6
6,8
6,9
6,9
6,8
6,8
6,5
6,1
6
5,9
5,8
5,9
5,9
6,2
6,3
6,2
6
5,8
5,5
5,5
5,7
5,8

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31734&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31734&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31734&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 computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.44673674151935Range2.8Trim Var.0.253667640376501
V(Y[t],d=1,D=0)0.0592112332112332Range1.7Trim Var.0.0301234567901234
V(Y[t],d=2,D=0)0.0580786516853932Range1.2Trim Var.0.0341708860759494
V(Y[t],d=3,D=0)0.109767620020429Range2.20000000000000Trim Var.0.0529470950989938
V(Y[t],d=0,D=1)0.372094936708861Range2.4Trim Var.0.274969818913481
V(Y[t],d=1,D=1)0.0649659201557936Range1.5Trim Var.0.0339047619047619
V(Y[t],d=2,D=1)0.0701298701298702Range1.30000000000000Trim Var.0.0402855924978687
V(Y[t],d=3,D=1)0.127098427887902Range2.20000000000000Trim Var.0.0729326513213983
V(Y[t],d=0,D=2)0.298375768217735Range2.5Trim Var.0.184455535390200
V(Y[t],d=1,D=2)0.164400723654455Range2.5Trim Var.0.0740327293980129
V(Y[t],d=2,D=2)0.179039627039627Range2.10000000000000Trim Var.0.105251058681186
V(Y[t],d=3,D=2)0.328711538461539Range3.1Trim Var.0.166773182957394

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.44673674151935 & Range & 2.8 & Trim Var. & 0.253667640376501 \tabularnewline
V(Y[t],d=1,D=0) & 0.0592112332112332 & Range & 1.7 & Trim Var. & 0.0301234567901234 \tabularnewline
V(Y[t],d=2,D=0) & 0.0580786516853932 & Range & 1.2 & Trim Var. & 0.0341708860759494 \tabularnewline
V(Y[t],d=3,D=0) & 0.109767620020429 & Range & 2.20000000000000 & Trim Var. & 0.0529470950989938 \tabularnewline
V(Y[t],d=0,D=1) & 0.372094936708861 & Range & 2.4 & Trim Var. & 0.274969818913481 \tabularnewline
V(Y[t],d=1,D=1) & 0.0649659201557936 & Range & 1.5 & Trim Var. & 0.0339047619047619 \tabularnewline
V(Y[t],d=2,D=1) & 0.0701298701298702 & Range & 1.30000000000000 & Trim Var. & 0.0402855924978687 \tabularnewline
V(Y[t],d=3,D=1) & 0.127098427887902 & Range & 2.20000000000000 & Trim Var. & 0.0729326513213983 \tabularnewline
V(Y[t],d=0,D=2) & 0.298375768217735 & Range & 2.5 & Trim Var. & 0.184455535390200 \tabularnewline
V(Y[t],d=1,D=2) & 0.164400723654455 & Range & 2.5 & Trim Var. & 0.0740327293980129 \tabularnewline
V(Y[t],d=2,D=2) & 0.179039627039627 & Range & 2.10000000000000 & Trim Var. & 0.105251058681186 \tabularnewline
V(Y[t],d=3,D=2) & 0.328711538461539 & Range & 3.1 & Trim Var. & 0.166773182957394 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31734&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.44673674151935[/C][C]Range[/C][C]2.8[/C][C]Trim Var.[/C][C]0.253667640376501[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.0592112332112332[/C][C]Range[/C][C]1.7[/C][C]Trim Var.[/C][C]0.0301234567901234[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.0580786516853932[/C][C]Range[/C][C]1.2[/C][C]Trim Var.[/C][C]0.0341708860759494[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.109767620020429[/C][C]Range[/C][C]2.20000000000000[/C][C]Trim Var.[/C][C]0.0529470950989938[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.372094936708861[/C][C]Range[/C][C]2.4[/C][C]Trim Var.[/C][C]0.274969818913481[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.0649659201557936[/C][C]Range[/C][C]1.5[/C][C]Trim Var.[/C][C]0.0339047619047619[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.0701298701298702[/C][C]Range[/C][C]1.30000000000000[/C][C]Trim Var.[/C][C]0.0402855924978687[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.127098427887902[/C][C]Range[/C][C]2.20000000000000[/C][C]Trim Var.[/C][C]0.0729326513213983[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.298375768217735[/C][C]Range[/C][C]2.5[/C][C]Trim Var.[/C][C]0.184455535390200[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.164400723654455[/C][C]Range[/C][C]2.5[/C][C]Trim Var.[/C][C]0.0740327293980129[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.179039627039627[/C][C]Range[/C][C]2.10000000000000[/C][C]Trim Var.[/C][C]0.105251058681186[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.328711538461539[/C][C]Range[/C][C]3.1[/C][C]Trim Var.[/C][C]0.166773182957394[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31734&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31734&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)0.44673674151935Range2.8Trim Var.0.253667640376501
V(Y[t],d=1,D=0)0.0592112332112332Range1.7Trim Var.0.0301234567901234
V(Y[t],d=2,D=0)0.0580786516853932Range1.2Trim Var.0.0341708860759494
V(Y[t],d=3,D=0)0.109767620020429Range2.20000000000000Trim Var.0.0529470950989938
V(Y[t],d=0,D=1)0.372094936708861Range2.4Trim Var.0.274969818913481
V(Y[t],d=1,D=1)0.0649659201557936Range1.5Trim Var.0.0339047619047619
V(Y[t],d=2,D=1)0.0701298701298702Range1.30000000000000Trim Var.0.0402855924978687
V(Y[t],d=3,D=1)0.127098427887902Range2.20000000000000Trim Var.0.0729326513213983
V(Y[t],d=0,D=2)0.298375768217735Range2.5Trim Var.0.184455535390200
V(Y[t],d=1,D=2)0.164400723654455Range2.5Trim Var.0.0740327293980129
V(Y[t],d=2,D=2)0.179039627039627Range2.10000000000000Trim Var.0.105251058681186
V(Y[t],d=3,D=2)0.328711538461539Range3.1Trim Var.0.166773182957394


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')