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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 computationThu, 22 Nov 2007 08:08:33 -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/Nov/22/t1195745819siep23mawjmbwzt.htm/, Retrieved Wed, 11 Feb 2026 04:08:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6058, Retrieved Wed, 11 Feb 2026 04:08:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact474

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] [] [2007-11-22 15:08:33] [80e26e27d8b229550cb490fed3b7813c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
102,7
103,2
105,6
103,9
107,2
100,7
92,1
90,3
93,4
98,5
100,8
102,3
104,7
101,1
101,4
99,5
98,4
96,3
100,7
101,2
100,3
97,8
97,4
98,6
99,7
99
98,1
97
98,5
103,8
114,4
124,5
134,2
131,8
125,6
119,9
114,9
115,5
112,5
111,4
115,3
110,8
103,7
111,1
113
111,2
117,6
121,7
127,3
129,8
137,1
141,4
137,4
130,7
117,2
110,8
111,4
108,2
108,8
110,2
109,5
109,5
116
111,2
112,1
114
119,1
114,1
115,1
115,4
110,8
116
119,2
126,5
127,8
131,3
140,3
137,3
143
134,5
139,9
159,3
170,4
175
175,8
180,9
180,3
169,6
172,3
184,8
177,7
184,6
211,4

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6058&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6058&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6058&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Variance Reduction Matrix
V(Y[t],d=0,D=0)663.217470780739Range121.1Trim Var.408.938084043491
V(Y[t],d=1,D=0)36.1606438127090Range40.3Trim Var.16.8830548027702
V(Y[t],d=2,D=0)47.1687667887668Range39.5Trim Var.25.6608611111111
V(Y[t],d=3,D=0)114.405168539326Range63Trim Var.55.5741202531645
V(Y[t],d=0,D=1)474.165Range101.7Trim Var.279.821227364185
V(Y[t],d=1,D=1)62.1606566455696Range39.1Trim Var.37.2863536776213
V(Y[t],d=2,D=1)80.8897306069458Range56.5Trim Var.43.7228249496982
V(Y[t],d=3,D=1)215.121232101232Range106.6Trim Var.109.096374741201
V(Y[t],d=0,D=2)773.641628303495Range117.8Trim Var.473.896010928962
V(Y[t],d=1,D=2)143.735564091308Range48.9Trim Var.102.34545480226
V(Y[t],d=2,D=2)183.449507010403Range68.6Trim Var.98.0060257159555
V(Y[t],d=3,D=2)493.280503496504Range134.7Trim Var.262.929461584997

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 663.217470780739 & Range & 121.1 & Trim Var. & 408.938084043491 \tabularnewline
V(Y[t],d=1,D=0) & 36.1606438127090 & Range & 40.3 & Trim Var. & 16.8830548027702 \tabularnewline
V(Y[t],d=2,D=0) & 47.1687667887668 & Range & 39.5 & Trim Var. & 25.6608611111111 \tabularnewline
V(Y[t],d=3,D=0) & 114.405168539326 & Range & 63 & Trim Var. & 55.5741202531645 \tabularnewline
V(Y[t],d=0,D=1) & 474.165 & Range & 101.7 & Trim Var. & 279.821227364185 \tabularnewline
V(Y[t],d=1,D=1) & 62.1606566455696 & Range & 39.1 & Trim Var. & 37.2863536776213 \tabularnewline
V(Y[t],d=2,D=1) & 80.8897306069458 & Range & 56.5 & Trim Var. & 43.7228249496982 \tabularnewline
V(Y[t],d=3,D=1) & 215.121232101232 & Range & 106.6 & Trim Var. & 109.096374741201 \tabularnewline
V(Y[t],d=0,D=2) & 773.641628303495 & Range & 117.8 & Trim Var. & 473.896010928962 \tabularnewline
V(Y[t],d=1,D=2) & 143.735564091308 & Range & 48.9 & Trim Var. & 102.34545480226 \tabularnewline
V(Y[t],d=2,D=2) & 183.449507010403 & Range & 68.6 & Trim Var. & 98.0060257159555 \tabularnewline
V(Y[t],d=3,D=2) & 493.280503496504 & Range & 134.7 & Trim Var. & 262.929461584997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6058&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]663.217470780739[/C][C]Range[/C][C]121.1[/C][C]Trim Var.[/C][C]408.938084043491[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]36.1606438127090[/C][C]Range[/C][C]40.3[/C][C]Trim Var.[/C][C]16.8830548027702[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]47.1687667887668[/C][C]Range[/C][C]39.5[/C][C]Trim Var.[/C][C]25.6608611111111[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]114.405168539326[/C][C]Range[/C][C]63[/C][C]Trim Var.[/C][C]55.5741202531645[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]474.165[/C][C]Range[/C][C]101.7[/C][C]Trim Var.[/C][C]279.821227364185[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]62.1606566455696[/C][C]Range[/C][C]39.1[/C][C]Trim Var.[/C][C]37.2863536776213[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]80.8897306069458[/C][C]Range[/C][C]56.5[/C][C]Trim Var.[/C][C]43.7228249496982[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]215.121232101232[/C][C]Range[/C][C]106.6[/C][C]Trim Var.[/C][C]109.096374741201[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]773.641628303495[/C][C]Range[/C][C]117.8[/C][C]Trim Var.[/C][C]473.896010928962[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]143.735564091308[/C][C]Range[/C][C]48.9[/C][C]Trim Var.[/C][C]102.34545480226[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]183.449507010403[/C][C]Range[/C][C]68.6[/C][C]Trim Var.[/C][C]98.0060257159555[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]493.280503496504[/C][C]Range[/C][C]134.7[/C][C]Trim Var.[/C][C]262.929461584997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6058&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6058&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)663.217470780739Range121.1Trim Var.408.938084043491
V(Y[t],d=1,D=0)36.1606438127090Range40.3Trim Var.16.8830548027702
V(Y[t],d=2,D=0)47.1687667887668Range39.5Trim Var.25.6608611111111
V(Y[t],d=3,D=0)114.405168539326Range63Trim Var.55.5741202531645
V(Y[t],d=0,D=1)474.165Range101.7Trim Var.279.821227364185
V(Y[t],d=1,D=1)62.1606566455696Range39.1Trim Var.37.2863536776213
V(Y[t],d=2,D=1)80.8897306069458Range56.5Trim Var.43.7228249496982
V(Y[t],d=3,D=1)215.121232101232Range106.6Trim Var.109.096374741201
V(Y[t],d=0,D=2)773.641628303495Range117.8Trim Var.473.896010928962
V(Y[t],d=1,D=2)143.735564091308Range48.9Trim Var.102.34545480226
V(Y[t],d=2,D=2)183.449507010403Range68.6Trim Var.98.0060257159555
V(Y[t],d=3,D=2)493.280503496504Range134.7Trim Var.262.929461584997


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')