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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 05:17:32 -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/t1198583880xb38l6v1yd5f6ev.htm/, Retrieved Sat, 02 May 2026 11:23:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4871, Retrieved Sat, 02 May 2026 11:23:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKlaas Van Pelt
Estimated Impact487

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 4] [2007-12-25 12:17:32] [6abd901c2e17b7d5559c695bbff3d863] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
92,1
91,4
90,7
92,5
94,4
94,3
87,3
85,9
89
83,3
78,6
75,7
79,6
78,5
82,6
88,7
88,5
84,6
83,4
84,4
94,1
100,4
93,1
93,1
82,1
88,1
87,7
80,2
73,8
75,3
77,3
80,1
81,3
81,5
83,2
80,8
81,3
78,8
82,8
84,9
93,2
94,7
94,8
103,9
107
118,6
112,2
112,2
93,8
96,7
108,7
112,1
107,2
113,1
120
124,4
139,5
145,8
135,6
135,5
141,6
141,2
141,6
147,1
146,5
144,1
148,5
146,9
135,7
128,5
128,7
127,6
122,5
123,4
129,4
135,3
138,5
140,6
144,2
144,3

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4871&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]0 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=4871&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4871&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 time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)587.899943037975Range74.7Trim Var.504.593425273865
V(Y[t],d=1,D=0)30.9790814670562Range33.5Trim Var.15.9881690140845
V(Y[t],d=2,D=0)54.2949583749584Range39.7Trim Var.30.2366149068323
V(Y[t],d=3,D=0)149.523564593301Range66.2Trim Var.80.0658482523444
V(Y[t],d=0,D=1)331.932333187006Range66.9Trim Var.249.419601694915
V(Y[t],d=1,D=1)72.677684305744Range50.8Trim Var.38.4642489772063
V(Y[t],d=2,D=1)148.772664335664Range52.4Trim Var.94.3968814277072
V(Y[t],d=3,D=1)432.403403846154Range98Trim Var.277.418045112782
V(Y[t],d=0,D=2)807.321493506493Range122.9Trim Var.558.423220408163
V(Y[t],d=1,D=2)242.906175084175Range81.7Trim Var.132.18875
V(Y[t],d=2,D=2)540.162627533194Range98Trim Var.363.570354609929
V(Y[t],d=3,D=2)1601.37868650218Range177.5Trim Var.1054.42844588344

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 587.899943037975 & Range & 74.7 & Trim Var. & 504.593425273865 \tabularnewline
V(Y[t],d=1,D=0) & 30.9790814670562 & Range & 33.5 & Trim Var. & 15.9881690140845 \tabularnewline
V(Y[t],d=2,D=0) & 54.2949583749584 & Range & 39.7 & Trim Var. & 30.2366149068323 \tabularnewline
V(Y[t],d=3,D=0) & 149.523564593301 & Range & 66.2 & Trim Var. & 80.0658482523444 \tabularnewline
V(Y[t],d=0,D=1) & 331.932333187006 & Range & 66.9 & Trim Var. & 249.419601694915 \tabularnewline
V(Y[t],d=1,D=1) & 72.677684305744 & Range & 50.8 & Trim Var. & 38.4642489772063 \tabularnewline
V(Y[t],d=2,D=1) & 148.772664335664 & Range & 52.4 & Trim Var. & 94.3968814277072 \tabularnewline
V(Y[t],d=3,D=1) & 432.403403846154 & Range & 98 & Trim Var. & 277.418045112782 \tabularnewline
V(Y[t],d=0,D=2) & 807.321493506493 & Range & 122.9 & Trim Var. & 558.423220408163 \tabularnewline
V(Y[t],d=1,D=2) & 242.906175084175 & Range & 81.7 & Trim Var. & 132.18875 \tabularnewline
V(Y[t],d=2,D=2) & 540.162627533194 & Range & 98 & Trim Var. & 363.570354609929 \tabularnewline
V(Y[t],d=3,D=2) & 1601.37868650218 & Range & 177.5 & Trim Var. & 1054.42844588344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4871&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]587.899943037975[/C][C]Range[/C][C]74.7[/C][C]Trim Var.[/C][C]504.593425273865[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]30.9790814670562[/C][C]Range[/C][C]33.5[/C][C]Trim Var.[/C][C]15.9881690140845[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]54.2949583749584[/C][C]Range[/C][C]39.7[/C][C]Trim Var.[/C][C]30.2366149068323[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]149.523564593301[/C][C]Range[/C][C]66.2[/C][C]Trim Var.[/C][C]80.0658482523444[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]331.932333187006[/C][C]Range[/C][C]66.9[/C][C]Trim Var.[/C][C]249.419601694915[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]72.677684305744[/C][C]Range[/C][C]50.8[/C][C]Trim Var.[/C][C]38.4642489772063[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]148.772664335664[/C][C]Range[/C][C]52.4[/C][C]Trim Var.[/C][C]94.3968814277072[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]432.403403846154[/C][C]Range[/C][C]98[/C][C]Trim Var.[/C][C]277.418045112782[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]807.321493506493[/C][C]Range[/C][C]122.9[/C][C]Trim Var.[/C][C]558.423220408163[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]242.906175084175[/C][C]Range[/C][C]81.7[/C][C]Trim Var.[/C][C]132.18875[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]540.162627533194[/C][C]Range[/C][C]98[/C][C]Trim Var.[/C][C]363.570354609929[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1601.37868650218[/C][C]Range[/C][C]177.5[/C][C]Trim Var.[/C][C]1054.42844588344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4871&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4871&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)587.899943037975Range74.7Trim Var.504.593425273865
V(Y[t],d=1,D=0)30.9790814670562Range33.5Trim Var.15.9881690140845
V(Y[t],d=2,D=0)54.2949583749584Range39.7Trim Var.30.2366149068323
V(Y[t],d=3,D=0)149.523564593301Range66.2Trim Var.80.0658482523444
V(Y[t],d=0,D=1)331.932333187006Range66.9Trim Var.249.419601694915
V(Y[t],d=1,D=1)72.677684305744Range50.8Trim Var.38.4642489772063
V(Y[t],d=2,D=1)148.772664335664Range52.4Trim Var.94.3968814277072
V(Y[t],d=3,D=1)432.403403846154Range98Trim Var.277.418045112782
V(Y[t],d=0,D=2)807.321493506493Range122.9Trim Var.558.423220408163
V(Y[t],d=1,D=2)242.906175084175Range81.7Trim Var.132.18875
V(Y[t],d=2,D=2)540.162627533194Range98Trim Var.363.570354609929
V(Y[t],d=3,D=2)1601.37868650218Range177.5Trim Var.1054.42844588344


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')