FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationFri, 28 Nov 2008 04:55:17 -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/Nov/28/t1227873348krbm6fo9wjfwrem.htm/, Retrieved Tue, 25 Aug 2026 08:25:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26007, Retrieved Tue, 25 Aug 2026 08:25:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact458

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [tijdreeks verkoop...] [2008-10-13 20:55:30] [d2d412c7f4d35ffbf5ee5ee89db327d4]
-   PD  [Univariate Data Series] [totale werkloosheid] [2008-10-19 15:02:07] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP       [Variance Reduction Matrix] [] [2008-11-28 11:55:17] [f6a332ba2d530c028d935c5a5bbb53af] [Current]
F   PD        [Variance Reduction Matrix] [Q8 1] [2008-11-28 13:45:14] [87cabf13a90315c7085b765dcebb7412]
-    D        [Variance Reduction Matrix] [Non Stationary Ti...] [2008-11-30 13:11:49] [063e4b67ad7d3a8a83eccec794cd5aa7]
Feedback Forum

Post a new message

Dataset

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

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 0 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26007&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26007&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26007&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 time0 seconds
R Server'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.539534071054164Range2.4Trim Var.0.394398084815322
V(Y[t],d=1,D=0)0.0137366336633663Range0.700000000000001Trim Var.0.00518767507002801
V(Y[t],d=2,D=0)0.0153494949494949Range0.7Trim Var.0.00894382022471906
V(Y[t],d=3,D=0)0.0379591836734693Range1.1Trim Var.0.0192977528089887
V(Y[t],d=0,D=1)0.427395755305868Range2.4Trim Var.0.307641831852358
V(Y[t],d=1,D=1)0.0321578140960163Range1Trim Var.0.0170496592015579
V(Y[t],d=2,D=1)0.0399999999999999Range0.800000000000002Trim Var.0.0235603603603602
V(Y[t],d=3,D=1)0.0940577385725739Range1.30000000000000Trim Var.0.0626247436773749
V(Y[t],d=0,D=2)0.47525308025308Range3.1Trim Var.0.256853002070393
V(Y[t],d=1,D=2)0.0981749829118248Range1.6Trim Var.0.0525197541703247
V(Y[t],d=2,D=2)0.133305263157894Range1.5Trim Var.0.0976031606672516
V(Y[t],d=3,D=2)0.314587387387386Range2.40000000000001Trim Var.0.214070556309361

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.539534071054164 & Range & 2.4 & Trim Var. & 0.394398084815322 \tabularnewline
V(Y[t],d=1,D=0) & 0.0137366336633663 & Range & 0.700000000000001 & Trim Var. & 0.00518767507002801 \tabularnewline
V(Y[t],d=2,D=0) & 0.0153494949494949 & Range & 0.7 & Trim Var. & 0.00894382022471906 \tabularnewline
V(Y[t],d=3,D=0) & 0.0379591836734693 & Range & 1.1 & Trim Var. & 0.0192977528089887 \tabularnewline
V(Y[t],d=0,D=1) & 0.427395755305868 & Range & 2.4 & Trim Var. & 0.307641831852358 \tabularnewline
V(Y[t],d=1,D=1) & 0.0321578140960163 & Range & 1 & Trim Var. & 0.0170496592015579 \tabularnewline
V(Y[t],d=2,D=1) & 0.0399999999999999 & Range & 0.800000000000002 & Trim Var. & 0.0235603603603602 \tabularnewline
V(Y[t],d=3,D=1) & 0.0940577385725739 & Range & 1.30000000000000 & Trim Var. & 0.0626247436773749 \tabularnewline
V(Y[t],d=0,D=2) & 0.47525308025308 & Range & 3.1 & Trim Var. & 0.256853002070393 \tabularnewline
V(Y[t],d=1,D=2) & 0.0981749829118248 & Range & 1.6 & Trim Var. & 0.0525197541703247 \tabularnewline
V(Y[t],d=2,D=2) & 0.133305263157894 & Range & 1.5 & Trim Var. & 0.0976031606672516 \tabularnewline
V(Y[t],d=3,D=2) & 0.314587387387386 & Range & 2.40000000000001 & Trim Var. & 0.214070556309361 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26007&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.539534071054164[/C][C]Range[/C][C]2.4[/C][C]Trim Var.[/C][C]0.394398084815322[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.0137366336633663[/C][C]Range[/C][C]0.700000000000001[/C][C]Trim Var.[/C][C]0.00518767507002801[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.0153494949494949[/C][C]Range[/C][C]0.7[/C][C]Trim Var.[/C][C]0.00894382022471906[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.0379591836734693[/C][C]Range[/C][C]1.1[/C][C]Trim Var.[/C][C]0.0192977528089887[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.427395755305868[/C][C]Range[/C][C]2.4[/C][C]Trim Var.[/C][C]0.307641831852358[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.0321578140960163[/C][C]Range[/C][C]1[/C][C]Trim Var.[/C][C]0.0170496592015579[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.0399999999999999[/C][C]Range[/C][C]0.800000000000002[/C][C]Trim Var.[/C][C]0.0235603603603602[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.0940577385725739[/C][C]Range[/C][C]1.30000000000000[/C][C]Trim Var.[/C][C]0.0626247436773749[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.47525308025308[/C][C]Range[/C][C]3.1[/C][C]Trim Var.[/C][C]0.256853002070393[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.0981749829118248[/C][C]Range[/C][C]1.6[/C][C]Trim Var.[/C][C]0.0525197541703247[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.133305263157894[/C][C]Range[/C][C]1.5[/C][C]Trim Var.[/C][C]0.0976031606672516[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.314587387387386[/C][C]Range[/C][C]2.40000000000001[/C][C]Trim Var.[/C][C]0.214070556309361[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26007&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26007&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)0.539534071054164Range2.4Trim Var.0.394398084815322
V(Y[t],d=1,D=0)0.0137366336633663Range0.700000000000001Trim Var.0.00518767507002801
V(Y[t],d=2,D=0)0.0153494949494949Range0.7Trim Var.0.00894382022471906
V(Y[t],d=3,D=0)0.0379591836734693Range1.1Trim Var.0.0192977528089887
V(Y[t],d=0,D=1)0.427395755305868Range2.4Trim Var.0.307641831852358
V(Y[t],d=1,D=1)0.0321578140960163Range1Trim Var.0.0170496592015579
V(Y[t],d=2,D=1)0.0399999999999999Range0.800000000000002Trim Var.0.0235603603603602
V(Y[t],d=3,D=1)0.0940577385725739Range1.30000000000000Trim Var.0.0626247436773749
V(Y[t],d=0,D=2)0.47525308025308Range3.1Trim Var.0.256853002070393
V(Y[t],d=1,D=2)0.0981749829118248Range1.6Trim Var.0.0525197541703247
V(Y[t],d=2,D=2)0.133305263157894Range1.5Trim Var.0.0976031606672516
V(Y[t],d=3,D=2)0.314587387387386Range2.40000000000001Trim Var.0.214070556309361


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')