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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, 18 Dec 2007 14:19:01 -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/18/t1198011689d0d30rhbav9zxj2.htm/, Retrieved Tue, 10 Feb 2026 14:08:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4620, Retrieved Tue, 10 Feb 2026 14:08:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact419

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] [] [2007-12-18 21:19:01] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
99,5
101,6
103,9
106,6
108,3
102
93,8
91,6
97,7
94,8
98
103,8
97,8
91,2
89,3
87,5
90,4
94,2
102,2
101,3
96
90,8
93,2
90,9
91,1
90,2
94,3
96
99
103,3
113,1
112,8
112,1
107,4
111
110,5
110,8
112,4
111,5
116,2
122,5
121,3
113,9
110,7
120,8
106,8
109,05
109,5
108,65
110,35
118,55
120,1
124,85
129,1
124,85
120,1
112,5
106,2
107,1
108,5
106,5
108,3
125,6
124
127,2
136,9
135,8
124,3
115,4
113,6
114,4
118,4
117
116,5
115,4
113,6
117,4
116,9
116,4
111,1
110,2
118,9
131,8
130,6
138,3
148,4
148,7
144,3
152,5
162,9
167,2
166,5
166,5

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=4620&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=4620&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4620&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)320.089320359981Range79.7Trim Var.171.003584337349
V(Y[t],d=1,D=0)28.5427090301003Range31.3Trim Var.16.0129358626920
V(Y[t],d=2,D=0)46.9244615384615Range40.35Trim Var.23.7136875
V(Y[t],d=3,D=0)125.490193508115Range77.75Trim Var.55.4416060126582
V(Y[t],d=0,D=1)253.03674845679Range76.3Trim Var.113.850106639839
V(Y[t],d=1,D=1)42.1218987341772Range34.6Trim Var.22.1735661189358
V(Y[t],d=2,D=1)71.5283771502759Range45.5Trim Var.40.0931392339545
V(Y[t],d=3,D=1)191.619843489843Range76Trim Var.98.832716873706
V(Y[t],d=0,D=2)509.866502557545Range100.55Trim Var.263.247259562841
V(Y[t],d=1,D=2)98.788759877085Range49.6Trim Var.48.5649406779661
V(Y[t],d=2,D=2)182.694253731343Range75.35Trim Var.100.892567212157
V(Y[t],d=3,D=2)505.968067599068Range137.85Trim Var.240.659141712039

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 320.089320359981 & Range & 79.7 & Trim Var. & 171.003584337349 \tabularnewline
V(Y[t],d=1,D=0) & 28.5427090301003 & Range & 31.3 & Trim Var. & 16.0129358626920 \tabularnewline
V(Y[t],d=2,D=0) & 46.9244615384615 & Range & 40.35 & Trim Var. & 23.7136875 \tabularnewline
V(Y[t],d=3,D=0) & 125.490193508115 & Range & 77.75 & Trim Var. & 55.4416060126582 \tabularnewline
V(Y[t],d=0,D=1) & 253.03674845679 & Range & 76.3 & Trim Var. & 113.850106639839 \tabularnewline
V(Y[t],d=1,D=1) & 42.1218987341772 & Range & 34.6 & Trim Var. & 22.1735661189358 \tabularnewline
V(Y[t],d=2,D=1) & 71.5283771502759 & Range & 45.5 & Trim Var. & 40.0931392339545 \tabularnewline
V(Y[t],d=3,D=1) & 191.619843489843 & Range & 76 & Trim Var. & 98.832716873706 \tabularnewline
V(Y[t],d=0,D=2) & 509.866502557545 & Range & 100.55 & Trim Var. & 263.247259562841 \tabularnewline
V(Y[t],d=1,D=2) & 98.788759877085 & Range & 49.6 & Trim Var. & 48.5649406779661 \tabularnewline
V(Y[t],d=2,D=2) & 182.694253731343 & Range & 75.35 & Trim Var. & 100.892567212157 \tabularnewline
V(Y[t],d=3,D=2) & 505.968067599068 & Range & 137.85 & Trim Var. & 240.659141712039 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4620&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]320.089320359981[/C][C]Range[/C][C]79.7[/C][C]Trim Var.[/C][C]171.003584337349[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]28.5427090301003[/C][C]Range[/C][C]31.3[/C][C]Trim Var.[/C][C]16.0129358626920[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]46.9244615384615[/C][C]Range[/C][C]40.35[/C][C]Trim Var.[/C][C]23.7136875[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]125.490193508115[/C][C]Range[/C][C]77.75[/C][C]Trim Var.[/C][C]55.4416060126582[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]253.03674845679[/C][C]Range[/C][C]76.3[/C][C]Trim Var.[/C][C]113.850106639839[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]42.1218987341772[/C][C]Range[/C][C]34.6[/C][C]Trim Var.[/C][C]22.1735661189358[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]71.5283771502759[/C][C]Range[/C][C]45.5[/C][C]Trim Var.[/C][C]40.0931392339545[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]191.619843489843[/C][C]Range[/C][C]76[/C][C]Trim Var.[/C][C]98.832716873706[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]509.866502557545[/C][C]Range[/C][C]100.55[/C][C]Trim Var.[/C][C]263.247259562841[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]98.788759877085[/C][C]Range[/C][C]49.6[/C][C]Trim Var.[/C][C]48.5649406779661[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]182.694253731343[/C][C]Range[/C][C]75.35[/C][C]Trim Var.[/C][C]100.892567212157[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]505.968067599068[/C][C]Range[/C][C]137.85[/C][C]Trim Var.[/C][C]240.659141712039[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4620&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4620&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)320.089320359981Range79.7Trim Var.171.003584337349
V(Y[t],d=1,D=0)28.5427090301003Range31.3Trim Var.16.0129358626920
V(Y[t],d=2,D=0)46.9244615384615Range40.35Trim Var.23.7136875
V(Y[t],d=3,D=0)125.490193508115Range77.75Trim Var.55.4416060126582
V(Y[t],d=0,D=1)253.03674845679Range76.3Trim Var.113.850106639839
V(Y[t],d=1,D=1)42.1218987341772Range34.6Trim Var.22.1735661189358
V(Y[t],d=2,D=1)71.5283771502759Range45.5Trim Var.40.0931392339545
V(Y[t],d=3,D=1)191.619843489843Range76Trim Var.98.832716873706
V(Y[t],d=0,D=2)509.866502557545Range100.55Trim Var.263.247259562841
V(Y[t],d=1,D=2)98.788759877085Range49.6Trim Var.48.5649406779661
V(Y[t],d=2,D=2)182.694253731343Range75.35Trim Var.100.892567212157
V(Y[t],d=3,D=2)505.968067599068Range137.85Trim Var.240.659141712039


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')