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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, 25 Dec 2007 05:16:10 -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/25/t1198583819kbzstptf3o06tn0.htm/, Retrieved Sun, 24 May 2026 07:02:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4870, Retrieved Sun, 24 May 2026 07:02:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKlaas Van Pelt
Estimated Impact511

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 3] [2007-12-25 12:16:10] [6abd901c2e17b7d5559c695bbff3d863] [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
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
99,9
99,5
99,2
99,6
100,1
99,8
101,6
101,7
101,9
100
102
102
102,9
102,7
102,7
102,7
102,7
102,6
102,6
102,5
102,5
102,1
103,5
103,2
102,1
103,8
104
103,9
104,1

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=4870&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=4870&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4870&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)2.03288607594937Range5.69999999999999Trim Var.1.43464788732394
V(Y[t],d=1,D=0)0.501752677702046Range3.90000000000001Trim Var.0.255066398390343
V(Y[t],d=2,D=0)1.27687645687646Range6.00000000000001Trim Var.0.712662525879918
V(Y[t],d=3,D=0)4.03801093643199Range11.9000000000000Trim Var.2.21643222506394
V(Y[t],d=0,D=1)1.34820676031607Range4.89999999999999Trim Var.0.853939216832263
V(Y[t],d=1,D=1)0.725572139303483Range4.30000000000001Trim Var.0.326914085330216
V(Y[t],d=2,D=1)2.12122144522144Range7.9Trim Var.1.07544162129461
V(Y[t],d=3,D=1)7.22441346153845Range13.9000000000000Trim Var.3.62357769423559
V(Y[t],d=0,D=2)2.96142532467533Range7.70000000000002Trim Var.1.96800408163266
V(Y[t],d=1,D=2)2.13583838383838Range6.79999999999997Trim Var.1.18849489795918
V(Y[t],d=2,D=2)6.680143256464Range12.2000000000000Trim Var.3.92822695035461
V(Y[t],d=3,D=2)23.5739477503628Range22.4999999999999Trim Var.13.3952173913043

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 2.03288607594937 & Range & 5.69999999999999 & Trim Var. & 1.43464788732394 \tabularnewline
V(Y[t],d=1,D=0) & 0.501752677702046 & Range & 3.90000000000001 & Trim Var. & 0.255066398390343 \tabularnewline
V(Y[t],d=2,D=0) & 1.27687645687646 & Range & 6.00000000000001 & Trim Var. & 0.712662525879918 \tabularnewline
V(Y[t],d=3,D=0) & 4.03801093643199 & Range & 11.9000000000000 & Trim Var. & 2.21643222506394 \tabularnewline
V(Y[t],d=0,D=1) & 1.34820676031607 & Range & 4.89999999999999 & Trim Var. & 0.853939216832263 \tabularnewline
V(Y[t],d=1,D=1) & 0.725572139303483 & Range & 4.30000000000001 & Trim Var. & 0.326914085330216 \tabularnewline
V(Y[t],d=2,D=1) & 2.12122144522144 & Range & 7.9 & Trim Var. & 1.07544162129461 \tabularnewline
V(Y[t],d=3,D=1) & 7.22441346153845 & Range & 13.9000000000000 & Trim Var. & 3.62357769423559 \tabularnewline
V(Y[t],d=0,D=2) & 2.96142532467533 & Range & 7.70000000000002 & Trim Var. & 1.96800408163266 \tabularnewline
V(Y[t],d=1,D=2) & 2.13583838383838 & Range & 6.79999999999997 & Trim Var. & 1.18849489795918 \tabularnewline
V(Y[t],d=2,D=2) & 6.680143256464 & Range & 12.2000000000000 & Trim Var. & 3.92822695035461 \tabularnewline
V(Y[t],d=3,D=2) & 23.5739477503628 & Range & 22.4999999999999 & Trim Var. & 13.3952173913043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4870&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]2.03288607594937[/C][C]Range[/C][C]5.69999999999999[/C][C]Trim Var.[/C][C]1.43464788732394[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.501752677702046[/C][C]Range[/C][C]3.90000000000001[/C][C]Trim Var.[/C][C]0.255066398390343[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1.27687645687646[/C][C]Range[/C][C]6.00000000000001[/C][C]Trim Var.[/C][C]0.712662525879918[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]4.03801093643199[/C][C]Range[/C][C]11.9000000000000[/C][C]Trim Var.[/C][C]2.21643222506394[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1.34820676031607[/C][C]Range[/C][C]4.89999999999999[/C][C]Trim Var.[/C][C]0.853939216832263[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.725572139303483[/C][C]Range[/C][C]4.30000000000001[/C][C]Trim Var.[/C][C]0.326914085330216[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]2.12122144522144[/C][C]Range[/C][C]7.9[/C][C]Trim Var.[/C][C]1.07544162129461[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]7.22441346153845[/C][C]Range[/C][C]13.9000000000000[/C][C]Trim Var.[/C][C]3.62357769423559[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]2.96142532467533[/C][C]Range[/C][C]7.70000000000002[/C][C]Trim Var.[/C][C]1.96800408163266[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]2.13583838383838[/C][C]Range[/C][C]6.79999999999997[/C][C]Trim Var.[/C][C]1.18849489795918[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]6.680143256464[/C][C]Range[/C][C]12.2000000000000[/C][C]Trim Var.[/C][C]3.92822695035461[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]23.5739477503628[/C][C]Range[/C][C]22.4999999999999[/C][C]Trim Var.[/C][C]13.3952173913043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4870&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4870&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)2.03288607594937Range5.69999999999999Trim Var.1.43464788732394
V(Y[t],d=1,D=0)0.501752677702046Range3.90000000000001Trim Var.0.255066398390343
V(Y[t],d=2,D=0)1.27687645687646Range6.00000000000001Trim Var.0.712662525879918
V(Y[t],d=3,D=0)4.03801093643199Range11.9000000000000Trim Var.2.21643222506394
V(Y[t],d=0,D=1)1.34820676031607Range4.89999999999999Trim Var.0.853939216832263
V(Y[t],d=1,D=1)0.725572139303483Range4.30000000000001Trim Var.0.326914085330216
V(Y[t],d=2,D=1)2.12122144522144Range7.9Trim Var.1.07544162129461
V(Y[t],d=3,D=1)7.22441346153845Range13.9000000000000Trim Var.3.62357769423559
V(Y[t],d=0,D=2)2.96142532467533Range7.70000000000002Trim Var.1.96800408163266
V(Y[t],d=1,D=2)2.13583838383838Range6.79999999999997Trim Var.1.18849489795918
V(Y[t],d=2,D=2)6.680143256464Range12.2000000000000Trim Var.3.92822695035461
V(Y[t],d=3,D=2)23.5739477503628Range22.4999999999999Trim Var.13.3952173913043


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')