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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationFri, 24 Dec 2010 15:08:41 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/24/t1293203187ls7o9s2xgkivimg.htm/, Retrieved Tue, 30 Apr 2024 07:24:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115070, Retrieved Tue, 30 Apr 2024 07:24:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120

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] [paperVRL_werk] [2010-12-24 15:08:41] [13dfa60174f50d862e8699db2153bfc5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6.7
6.7
6.5
6.3
6.3
6.3
6.5
6.6
6.5
6.3
6.3
6.5
7
7.1
7.3
7.3
7.4
7.4
7.3
7.4
7.5
7.7
7.7
7.7
7.7
7.7
7.8
8
8.1
8.1
8.2
8.2
8.2
8.1
8.1
8.2
8.3
8.3
8.4
8.5
8.5
8.4
8
7.9
8.1
8.5
8.8
8.8
8.6
8.3
8.3
8.3
8.4
8.4
8.5
8.6
8.6
8.6
8.6
8.6
8.5
8.4
8.4
8.4
8.5
8.5
8.6
8.6
8.4
8.2
8
8
8
8
7.9
7.9
7.8
7.8
8
7.8
7.4
7.2
7
7
7.2
7.2
7.2
7
6.9
6.8
6.8
6.8
6.9
7.2
7.2
7.2
7.1
7.2
7.3
7.5
7.6
7.7
7.7
7.7
7.8
8
8.1
8.1
8
8.1
8.2
8.3
8.4
8.4
8.4
8.5
8.5
8.6
8.6
8.5
8.5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115070&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115070&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115070&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.46796694214876Range2.5Trim Var.0.300408080808081
V(Y[t],d=1,D=0)0.0189327731092437Range0.9Trim Var.0.00573796192609181
V(Y[t],d=2,D=0)0.0205084745762712Range0.700000000000001Trim Var.0.0124752920035939
V(Y[t],d=3,D=0)0.0443524554541504Range1.30000000000000Trim Var.0.0237490664675131
V(Y[t],d=0,D=1)0.407995242949371Range2.6Trim Var.0.295735745614035
V(Y[t],d=1,D=1)0.0375666320526134Range1Trim Var.0.0163257835735529
V(Y[t],d=2,D=1)0.0403773584905661Range0.800000000000002Trim Var.0.0251982799808887
V(Y[t],d=3,D=1)0.0844752920035941Range1.50000000000000Trim Var.0.0464890135577373
V(Y[t],d=0,D=2)0.506741838487972Range3.2Trim Var.0.289625170998632
V(Y[t],d=1,D=2)0.105614035087719Range1.9Trim Var.0.0549220246238031
V(Y[t],d=2,D=2)0.119458006718925Range1.50000000000000Trim Var.0.0774569707401035
V(Y[t],d=3,D=2)0.259648821779914Range2.80000000000000Trim Var.0.150411646586346

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.46796694214876 & Range & 2.5 & Trim Var. & 0.300408080808081 \tabularnewline
V(Y[t],d=1,D=0) & 0.0189327731092437 & Range & 0.9 & Trim Var. & 0.00573796192609181 \tabularnewline
V(Y[t],d=2,D=0) & 0.0205084745762712 & Range & 0.700000000000001 & Trim Var. & 0.0124752920035939 \tabularnewline
V(Y[t],d=3,D=0) & 0.0443524554541504 & Range & 1.30000000000000 & Trim Var. & 0.0237490664675131 \tabularnewline
V(Y[t],d=0,D=1) & 0.407995242949371 & Range & 2.6 & Trim Var. & 0.295735745614035 \tabularnewline
V(Y[t],d=1,D=1) & 0.0375666320526134 & Range & 1 & Trim Var. & 0.0163257835735529 \tabularnewline
V(Y[t],d=2,D=1) & 0.0403773584905661 & Range & 0.800000000000002 & Trim Var. & 0.0251982799808887 \tabularnewline
V(Y[t],d=3,D=1) & 0.0844752920035941 & Range & 1.50000000000000 & Trim Var. & 0.0464890135577373 \tabularnewline
V(Y[t],d=0,D=2) & 0.506741838487972 & Range & 3.2 & Trim Var. & 0.289625170998632 \tabularnewline
V(Y[t],d=1,D=2) & 0.105614035087719 & Range & 1.9 & Trim Var. & 0.0549220246238031 \tabularnewline
V(Y[t],d=2,D=2) & 0.119458006718925 & Range & 1.50000000000000 & Trim Var. & 0.0774569707401035 \tabularnewline
V(Y[t],d=3,D=2) & 0.259648821779914 & Range & 2.80000000000000 & Trim Var. & 0.150411646586346 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115070&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.46796694214876[/C][C]Range[/C][C]2.5[/C][C]Trim Var.[/C][C]0.300408080808081[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.0189327731092437[/C][C]Range[/C][C]0.9[/C][C]Trim Var.[/C][C]0.00573796192609181[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.0205084745762712[/C][C]Range[/C][C]0.700000000000001[/C][C]Trim Var.[/C][C]0.0124752920035939[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.0443524554541504[/C][C]Range[/C][C]1.30000000000000[/C][C]Trim Var.[/C][C]0.0237490664675131[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.407995242949371[/C][C]Range[/C][C]2.6[/C][C]Trim Var.[/C][C]0.295735745614035[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.0375666320526134[/C][C]Range[/C][C]1[/C][C]Trim Var.[/C][C]0.0163257835735529[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.0403773584905661[/C][C]Range[/C][C]0.800000000000002[/C][C]Trim Var.[/C][C]0.0251982799808887[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.0844752920035941[/C][C]Range[/C][C]1.50000000000000[/C][C]Trim Var.[/C][C]0.0464890135577373[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.506741838487972[/C][C]Range[/C][C]3.2[/C][C]Trim Var.[/C][C]0.289625170998632[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.105614035087719[/C][C]Range[/C][C]1.9[/C][C]Trim Var.[/C][C]0.0549220246238031[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.119458006718925[/C][C]Range[/C][C]1.50000000000000[/C][C]Trim Var.[/C][C]0.0774569707401035[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.259648821779914[/C][C]Range[/C][C]2.80000000000000[/C][C]Trim Var.[/C][C]0.150411646586346[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115070&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115070&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)0.46796694214876Range2.5Trim Var.0.300408080808081
V(Y[t],d=1,D=0)0.0189327731092437Range0.9Trim Var.0.00573796192609181
V(Y[t],d=2,D=0)0.0205084745762712Range0.700000000000001Trim Var.0.0124752920035939
V(Y[t],d=3,D=0)0.0443524554541504Range1.30000000000000Trim Var.0.0237490664675131
V(Y[t],d=0,D=1)0.407995242949371Range2.6Trim Var.0.295735745614035
V(Y[t],d=1,D=1)0.0375666320526134Range1Trim Var.0.0163257835735529
V(Y[t],d=2,D=1)0.0403773584905661Range0.800000000000002Trim Var.0.0251982799808887
V(Y[t],d=3,D=1)0.0844752920035941Range1.50000000000000Trim Var.0.0464890135577373
V(Y[t],d=0,D=2)0.506741838487972Range3.2Trim Var.0.289625170998632
V(Y[t],d=1,D=2)0.105614035087719Range1.9Trim Var.0.0549220246238031
V(Y[t],d=2,D=2)0.119458006718925Range1.50000000000000Trim Var.0.0774569707401035
V(Y[t],d=3,D=2)0.259648821779914Range2.80000000000000Trim Var.0.150411646586346


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(myx,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')
bitmap(file='pic0.png')
op <- par(mfrow=c(2,2))
plot(x,type='l',xlab='time',ylab='value',main='d=0, D=0')
plot(diff(x,lag=1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=0')
plot(diff(x,lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=0, D=1')
plot(diff(diff(x,lag=1,differences=1),lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=1')
par(op)
dev.off()