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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, 02 Dec 2008 12:38:51 -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/02/t12282467572vxhl579rdl5vrl.htm/, Retrieved Tue, 10 Feb 2026 20:04:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28256, Retrieved Tue, 10 Feb 2026 20:04:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact400

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] [Toon Wouters] [2008-12-02 19:38:51] [14e94996a4178d938cb12bed20a4a373] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
103,1
100,6
103,1
95,5
90,5
90,9
88,8
90,7
94,3
104,6
111,1
110,8
107,2
99
99
91
96,2
96,9
96,2
100,1
99
115,4
106,9
107,1
99,3
99,2
108,3
105,6
99,5
107,4
93,1
88,1
110,7
113,1
99,6
93,6
98,6
99,6
114,3
107,8
101,2
112,5
100,5
93,9
116,2
112
106,4
95,7
96
95,8
103
102,2
98,4
111,4
86,6
91,3
107,9
101,8
104,4
93,4
100,1
98,5
112,9
101,4
107,1
110,8
90,3
95,5
111,4
113
107,5
95,9
106,3
105,2
117,2
106,9
108,2
113
97,2
99,9
108,1
118,1
109,1
93,3

Tables (Output of Computation)





Summary of computational 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 computational 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=28256&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]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=28256&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28256&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)59.6071069994263Range31.5Trim Var.41.8249611255091
V(Y[t],d=1,D=0)86.167596238613Range47.4Trim Var.48.893801369863
V(Y[t],d=2,D=0)212.259664257754Range67.3Trim Var.134.860655320814
V(Y[t],d=3,D=0)639.486762345679Range122.7Trim Var.395.958189134809
V(Y[t],d=0,D=1)38.9478384194053Range28.5Trim Var.23.8364260912698
V(Y[t],d=1,D=1)50.4111106639839Range38.7Trim Var.29.0480184331797
V(Y[t],d=2,D=1)143.610113871636Range70.3Trim Var.79.4046218931782
V(Y[t],d=3,D=1)483.583375959079Range117Trim Var.278.569464480874
V(Y[t],d=0,D=2)102.986042372881Range42.8Trim Var.67.7992732354997
V(Y[t],d=1,D=2)129.185569842198Range52.4Trim Var.89.6433309143687
V(Y[t],d=2,D=2)375.051929824562Range87.8Trim Var.267.579317496229
V(Y[t],d=3,D=2)1296.53765037594Range166.4Trim Var.920.593631372549

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 59.6071069994263 & Range & 31.5 & Trim Var. & 41.8249611255091 \tabularnewline
V(Y[t],d=1,D=0) & 86.167596238613 & Range & 47.4 & Trim Var. & 48.893801369863 \tabularnewline
V(Y[t],d=2,D=0) & 212.259664257754 & Range & 67.3 & Trim Var. & 134.860655320814 \tabularnewline
V(Y[t],d=3,D=0) & 639.486762345679 & Range & 122.7 & Trim Var. & 395.958189134809 \tabularnewline
V(Y[t],d=0,D=1) & 38.9478384194053 & Range & 28.5 & Trim Var. & 23.8364260912698 \tabularnewline
V(Y[t],d=1,D=1) & 50.4111106639839 & Range & 38.7 & Trim Var. & 29.0480184331797 \tabularnewline
V(Y[t],d=2,D=1) & 143.610113871636 & Range & 70.3 & Trim Var. & 79.4046218931782 \tabularnewline
V(Y[t],d=3,D=1) & 483.583375959079 & Range & 117 & Trim Var. & 278.569464480874 \tabularnewline
V(Y[t],d=0,D=2) & 102.986042372881 & Range & 42.8 & Trim Var. & 67.7992732354997 \tabularnewline
V(Y[t],d=1,D=2) & 129.185569842198 & Range & 52.4 & Trim Var. & 89.6433309143687 \tabularnewline
V(Y[t],d=2,D=2) & 375.051929824562 & Range & 87.8 & Trim Var. & 267.579317496229 \tabularnewline
V(Y[t],d=3,D=2) & 1296.53765037594 & Range & 166.4 & Trim Var. & 920.593631372549 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28256&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]59.6071069994263[/C][C]Range[/C][C]31.5[/C][C]Trim Var.[/C][C]41.8249611255091[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]86.167596238613[/C][C]Range[/C][C]47.4[/C][C]Trim Var.[/C][C]48.893801369863[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]212.259664257754[/C][C]Range[/C][C]67.3[/C][C]Trim Var.[/C][C]134.860655320814[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]639.486762345679[/C][C]Range[/C][C]122.7[/C][C]Trim Var.[/C][C]395.958189134809[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]38.9478384194053[/C][C]Range[/C][C]28.5[/C][C]Trim Var.[/C][C]23.8364260912698[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]50.4111106639839[/C][C]Range[/C][C]38.7[/C][C]Trim Var.[/C][C]29.0480184331797[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]143.610113871636[/C][C]Range[/C][C]70.3[/C][C]Trim Var.[/C][C]79.4046218931782[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]483.583375959079[/C][C]Range[/C][C]117[/C][C]Trim Var.[/C][C]278.569464480874[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]102.986042372881[/C][C]Range[/C][C]42.8[/C][C]Trim Var.[/C][C]67.7992732354997[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]129.185569842198[/C][C]Range[/C][C]52.4[/C][C]Trim Var.[/C][C]89.6433309143687[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]375.051929824562[/C][C]Range[/C][C]87.8[/C][C]Trim Var.[/C][C]267.579317496229[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1296.53765037594[/C][C]Range[/C][C]166.4[/C][C]Trim Var.[/C][C]920.593631372549[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28256&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28256&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)59.6071069994263Range31.5Trim Var.41.8249611255091
V(Y[t],d=1,D=0)86.167596238613Range47.4Trim Var.48.893801369863
V(Y[t],d=2,D=0)212.259664257754Range67.3Trim Var.134.860655320814
V(Y[t],d=3,D=0)639.486762345679Range122.7Trim Var.395.958189134809
V(Y[t],d=0,D=1)38.9478384194053Range28.5Trim Var.23.8364260912698
V(Y[t],d=1,D=1)50.4111106639839Range38.7Trim Var.29.0480184331797
V(Y[t],d=2,D=1)143.610113871636Range70.3Trim Var.79.4046218931782
V(Y[t],d=3,D=1)483.583375959079Range117Trim Var.278.569464480874
V(Y[t],d=0,D=2)102.986042372881Range42.8Trim Var.67.7992732354997
V(Y[t],d=1,D=2)129.185569842198Range52.4Trim Var.89.6433309143687
V(Y[t],d=2,D=2)375.051929824562Range87.8Trim Var.267.579317496229
V(Y[t],d=3,D=2)1296.53765037594Range166.4Trim Var.920.593631372549


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')