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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationSun, 19 Dec 2010 19:28:48 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/19/t12927867984m16f5mzmtmop90.htm/, Retrieved Wed, 11 Feb 2026 13:49:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112694, Retrieved Wed, 11 Feb 2026 13:49:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact339

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] [Unemployment] [2010-11-29 09:29:57] [b98453cac15ba1066b407e146608df68]
-   PD  [Variance Reduction Matrix] [] [2010-12-07 13:27:30] [1908ef7bb1a3d37a854f5aaad1a1c348]
-    D      [Variance Reduction Matrix] [] [2010-12-19 19:28:48] [23ca1b0f6f6de1e008a90be3f55e3db8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8,7000
8,9000
8,9000
8,1000
8,0000
8,3000
8,5000
8,7000
8,6000
8,3000
7,9000
7,9000
8,1000
8,3000
8,1000
7,4000
7,3000
7,7000
8,0000
8,0000
7,7000
6,9000
6,6000
6,9000
7,5000
7,9000
7,7000
6,5000
6,1000
6,4000
6,8000
7,1000
7,3000
7,2000
7,0000
7,0000
7,0000
7,3000
7,5000
7,2000
7,7000
8,0000
7,9000
8,0000
8,0000
7,9000
7,9000
8,0000
8,1000
8,1000
8,2000
8,0000
8,3000
8,5000
8,6000
8,7000
8,7000
8,5000
8,4000
8,5000
8,7000
8,7000
8,6000
7,9000
8,1000
8,2000
8,5000
8,6000
8,5000
8,3000
8,2000
8,7000
9,3000
9,3000
8,8000
7,4000
7,2000
7,5000
8,3000
8,8000
8,9000
8,6000
8,4000
8,4000
8,4000
8,4000
8,3000
7,6000
7,6000
7,9000
8,0000
8,2000
8,3000
8,2000
8,1000
8,0000
7,8000
7,6000
7,5000
6,8000
6,9000
7,1000
7,3000
7,4000
7,6000
7,6000
7,5000
7,5000
6,8000
6,4000
6,2000
6,0000
6,3000
6,3000
6,1000
6,1000
6,3000

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112694&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112694&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112694&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.582636310050103Range3.3Trim Var.0.355981362842166
V(Y[t],d=1,D=0)0.116089955022489Range2.2Trim Var.0.0503769274700171
V(Y[t],d=2,D=0)0.15Range2.2Trim Var.0.0776039603960396
V(Y[t],d=3,D=0)0.310784039745381Range3.1Trim Var.0.145992040380509
V(Y[t],d=0,D=1)0.506782051282051Range3Trim Var.0.344605828953655
V(Y[t],d=1,D=1)0.09364357729649Range1.6Trim Var.0.0451599511599512
V(Y[t],d=2,D=1)0.0927450980392158Range1.5Trim Var.0.0555360195360196
V(Y[t],d=3,D=1)0.159496214327315Range2Trim Var.0.08373595505618
V(Y[t],d=0,D=2)0.770857877512857Range4.4Trim Var.0.419523949456362
V(Y[t],d=1,D=2)0.258638318203536Range2.6Trim Var.0.131062932851551
V(Y[t],d=2,D=2)0.245211233211234Range2.2Trim Var.0.150278481012658
V(Y[t],d=3,D=2)0.419436953807741Range3.2Trim Var.0.24420253164557

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.582636310050103 & Range & 3.3 & Trim Var. & 0.355981362842166 \tabularnewline
V(Y[t],d=1,D=0) & 0.116089955022489 & Range & 2.2 & Trim Var. & 0.0503769274700171 \tabularnewline
V(Y[t],d=2,D=0) & 0.15 & Range & 2.2 & Trim Var. & 0.0776039603960396 \tabularnewline
V(Y[t],d=3,D=0) & 0.310784039745381 & Range & 3.1 & Trim Var. & 0.145992040380509 \tabularnewline
V(Y[t],d=0,D=1) & 0.506782051282051 & Range & 3 & Trim Var. & 0.344605828953655 \tabularnewline
V(Y[t],d=1,D=1) & 0.09364357729649 & Range & 1.6 & Trim Var. & 0.0451599511599512 \tabularnewline
V(Y[t],d=2,D=1) & 0.0927450980392158 & Range & 1.5 & Trim Var. & 0.0555360195360196 \tabularnewline
V(Y[t],d=3,D=1) & 0.159496214327315 & Range & 2 & Trim Var. & 0.08373595505618 \tabularnewline
V(Y[t],d=0,D=2) & 0.770857877512857 & Range & 4.4 & Trim Var. & 0.419523949456362 \tabularnewline
V(Y[t],d=1,D=2) & 0.258638318203536 & Range & 2.6 & Trim Var. & 0.131062932851551 \tabularnewline
V(Y[t],d=2,D=2) & 0.245211233211234 & Range & 2.2 & Trim Var. & 0.150278481012658 \tabularnewline
V(Y[t],d=3,D=2) & 0.419436953807741 & Range & 3.2 & Trim Var. & 0.24420253164557 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112694&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.582636310050103[/C][C]Range[/C][C]3.3[/C][C]Trim Var.[/C][C]0.355981362842166[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.116089955022489[/C][C]Range[/C][C]2.2[/C][C]Trim Var.[/C][C]0.0503769274700171[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.15[/C][C]Range[/C][C]2.2[/C][C]Trim Var.[/C][C]0.0776039603960396[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.310784039745381[/C][C]Range[/C][C]3.1[/C][C]Trim Var.[/C][C]0.145992040380509[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.506782051282051[/C][C]Range[/C][C]3[/C][C]Trim Var.[/C][C]0.344605828953655[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.09364357729649[/C][C]Range[/C][C]1.6[/C][C]Trim Var.[/C][C]0.0451599511599512[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.0927450980392158[/C][C]Range[/C][C]1.5[/C][C]Trim Var.[/C][C]0.0555360195360196[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.159496214327315[/C][C]Range[/C][C]2[/C][C]Trim Var.[/C][C]0.08373595505618[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.770857877512857[/C][C]Range[/C][C]4.4[/C][C]Trim Var.[/C][C]0.419523949456362[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.258638318203536[/C][C]Range[/C][C]2.6[/C][C]Trim Var.[/C][C]0.131062932851551[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.245211233211234[/C][C]Range[/C][C]2.2[/C][C]Trim Var.[/C][C]0.150278481012658[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.419436953807741[/C][C]Range[/C][C]3.2[/C][C]Trim Var.[/C][C]0.24420253164557[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112694&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112694&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)0.582636310050103Range3.3Trim Var.0.355981362842166
V(Y[t],d=1,D=0)0.116089955022489Range2.2Trim Var.0.0503769274700171
V(Y[t],d=2,D=0)0.15Range2.2Trim Var.0.0776039603960396
V(Y[t],d=3,D=0)0.310784039745381Range3.1Trim Var.0.145992040380509
V(Y[t],d=0,D=1)0.506782051282051Range3Trim Var.0.344605828953655
V(Y[t],d=1,D=1)0.09364357729649Range1.6Trim Var.0.0451599511599512
V(Y[t],d=2,D=1)0.0927450980392158Range1.5Trim Var.0.0555360195360196
V(Y[t],d=3,D=1)0.159496214327315Range2Trim Var.0.08373595505618
V(Y[t],d=0,D=2)0.770857877512857Range4.4Trim Var.0.419523949456362
V(Y[t],d=1,D=2)0.258638318203536Range2.6Trim Var.0.131062932851551
V(Y[t],d=2,D=2)0.245211233211234Range2.2Trim Var.0.150278481012658
V(Y[t],d=3,D=2)0.419436953807741Range3.2Trim Var.0.24420253164557


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')