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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, 29 Nov 2007 02:55:54 -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/29/t11963295548dfft8vlujhl76n.htm/, Retrieved Wed, 22 Apr 2026 21:52:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7333, Retrieved Wed, 22 Apr 2026 21:52:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact409

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] [Q2_T3] [2007-11-29 09:55:54] [031886dbad66702fa31ca1c4d15fdd0f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5,74
5,72
5,24
5,16
5,1
4,89
5,14
5,39
5,29
5,24
4,97
4,73
4,57
4,65
5,09
5,04
4,91
5,28
5,21
5,16
4,93
4,65
4,26
3,87
3,94
4,05
4,03
4,05
3,9
3,81
3,96
3,57
3,33
3,97
4,44
4,27
4,29
4,3
4,27
4,15
4,08
3,83
4,35
4,72
4,73
4,5
4,28
4,13
4,1
4,19
4,23
4,22
4,17
4,5
4,34
4,14
4
4,18
4,26
4,2
4,46
4,53
4,47
4,42
4,57
4,72
4,99
5,11
5,11
5,09
4,88
4,72
4,73
4,6
4,56
4,76
4,72
4,56
4,7
4,75
5,1
5
4,67
4,52
4,53

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=7333&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=7333&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7333&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)0.230729775910364Range2.41Trim Var.0.146486486486486
V(Y[t],d=1,D=0)0.0459912076878944Range1.12Trim Var.0.0224137747336378
V(Y[t],d=2,D=0)0.0729181604466647Range1.52Trim Var.0.0353247716894977
V(Y[t],d=3,D=0)0.177910027100271Range2Trim Var.0.094983548513302
V(Y[t],d=0,D=1)0.390399543378996Range3Trim Var.0.218669086538462
V(Y[t],d=1,D=1)0.117620168231612Range1.79Trim Var.0.0528920634920635
V(Y[t],d=2,D=1)0.181220845070422Range2.19Trim Var.0.0923221198156682
V(Y[t],d=3,D=1)0.443658819875776Range3.19Trim Var.0.238959703860391
V(Y[t],d=0,D=2)1.13423551912568Range5.13Trim Var.0.631473657474601
V(Y[t],d=1,D=2)0.411391497175141Range3.07Trim Var.0.237444619147449
V(Y[t],d=2,D=2)0.598308007013442Range3.92Trim Var.0.322365747460087
V(Y[t],d=3,D=2)1.41923245614035Range5.4Trim Var.0.837503469079939

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.230729775910364 & Range & 2.41 & Trim Var. & 0.146486486486486 \tabularnewline
V(Y[t],d=1,D=0) & 0.0459912076878944 & Range & 1.12 & Trim Var. & 0.0224137747336378 \tabularnewline
V(Y[t],d=2,D=0) & 0.0729181604466647 & Range & 1.52 & Trim Var. & 0.0353247716894977 \tabularnewline
V(Y[t],d=3,D=0) & 0.177910027100271 & Range & 2 & Trim Var. & 0.094983548513302 \tabularnewline
V(Y[t],d=0,D=1) & 0.390399543378996 & Range & 3 & Trim Var. & 0.218669086538462 \tabularnewline
V(Y[t],d=1,D=1) & 0.117620168231612 & Range & 1.79 & Trim Var. & 0.0528920634920635 \tabularnewline
V(Y[t],d=2,D=1) & 0.181220845070422 & Range & 2.19 & Trim Var. & 0.0923221198156682 \tabularnewline
V(Y[t],d=3,D=1) & 0.443658819875776 & Range & 3.19 & Trim Var. & 0.238959703860391 \tabularnewline
V(Y[t],d=0,D=2) & 1.13423551912568 & Range & 5.13 & Trim Var. & 0.631473657474601 \tabularnewline
V(Y[t],d=1,D=2) & 0.411391497175141 & Range & 3.07 & Trim Var. & 0.237444619147449 \tabularnewline
V(Y[t],d=2,D=2) & 0.598308007013442 & Range & 3.92 & Trim Var. & 0.322365747460087 \tabularnewline
V(Y[t],d=3,D=2) & 1.41923245614035 & Range & 5.4 & Trim Var. & 0.837503469079939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7333&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.230729775910364[/C][C]Range[/C][C]2.41[/C][C]Trim Var.[/C][C]0.146486486486486[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.0459912076878944[/C][C]Range[/C][C]1.12[/C][C]Trim Var.[/C][C]0.0224137747336378[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.0729181604466647[/C][C]Range[/C][C]1.52[/C][C]Trim Var.[/C][C]0.0353247716894977[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.177910027100271[/C][C]Range[/C][C]2[/C][C]Trim Var.[/C][C]0.094983548513302[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.390399543378996[/C][C]Range[/C][C]3[/C][C]Trim Var.[/C][C]0.218669086538462[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.117620168231612[/C][C]Range[/C][C]1.79[/C][C]Trim Var.[/C][C]0.0528920634920635[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.181220845070422[/C][C]Range[/C][C]2.19[/C][C]Trim Var.[/C][C]0.0923221198156682[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.443658819875776[/C][C]Range[/C][C]3.19[/C][C]Trim Var.[/C][C]0.238959703860391[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1.13423551912568[/C][C]Range[/C][C]5.13[/C][C]Trim Var.[/C][C]0.631473657474601[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.411391497175141[/C][C]Range[/C][C]3.07[/C][C]Trim Var.[/C][C]0.237444619147449[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.598308007013442[/C][C]Range[/C][C]3.92[/C][C]Trim Var.[/C][C]0.322365747460087[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1.41923245614035[/C][C]Range[/C][C]5.4[/C][C]Trim Var.[/C][C]0.837503469079939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7333&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7333&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)0.230729775910364Range2.41Trim Var.0.146486486486486
V(Y[t],d=1,D=0)0.0459912076878944Range1.12Trim Var.0.0224137747336378
V(Y[t],d=2,D=0)0.0729181604466647Range1.52Trim Var.0.0353247716894977
V(Y[t],d=3,D=0)0.177910027100271Range2Trim Var.0.094983548513302
V(Y[t],d=0,D=1)0.390399543378996Range3Trim Var.0.218669086538462
V(Y[t],d=1,D=1)0.117620168231612Range1.79Trim Var.0.0528920634920635
V(Y[t],d=2,D=1)0.181220845070422Range2.19Trim Var.0.0923221198156682
V(Y[t],d=3,D=1)0.443658819875776Range3.19Trim Var.0.238959703860391
V(Y[t],d=0,D=2)1.13423551912568Range5.13Trim Var.0.631473657474601
V(Y[t],d=1,D=2)0.411391497175141Range3.07Trim Var.0.237444619147449
V(Y[t],d=2,D=2)0.598308007013442Range3.92Trim Var.0.322365747460087
V(Y[t],d=3,D=2)1.41923245614035Range5.4Trim Var.0.837503469079939


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')