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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 computationMon, 20 Dec 2010 21:28:00 +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/20/t1292880365yuudsomy6399acl.htm/, Retrieved Fri, 03 May 2024 22:38:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113139, Retrieved Fri, 03 May 2024 22:38:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103

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] [] [2010-12-14 19:53:56] [afd301b68d203992295e6972aed62880]
- R  D    [Variance Reduction Matrix] [] [2010-12-20 21:28:00] [5a59313293e5c9f616ad36f6edd018c5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9,1
5,9
7,2
6,8
8
14,3
14,6
17,5
17,2
17,2
14,1
10,4
6,8
4,1
6,5
6,1
6,3
9,3
16,4
16,1
18
17,6
14
10,5
6,9
2,8
0,7
3,6
6,7
12,5
14,4
16,5
18,7
19,4
15,8
11,3
9,7
2,9
0,1
2,5
6,7
10,3
11,2
17,4
20,5
17
14,2
10,6
6,1

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=113139&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=113139&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113139&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)30.2851615646258Range20.4Trim Var.22.3134772978959
V(Y[t],d=1,D=0)11.2164361702128Range13.9Trim Var.7.58485481997677
V(Y[t],d=2,D=0)10.7724791859389Range12.7Trim Var.6.51282051282051
V(Y[t],d=3,D=0)26.5499130434783Range21.1Trim Var.15.8594615384615
V(Y[t],d=0,D=1)3.98472972972973Range9Trim Var.2.21755681818182
V(Y[t],d=1,D=1)6.3920873015873Range12Trim Var.3.65273185483871
V(Y[t],d=2,D=1)17.6273445378151Range20.1Trim Var.9.0819569892473
V(Y[t],d=3,D=1)56.7148663101604Range35.7Trim Var.30.7756781609195
V(Y[t],d=0,D=2)11.3908333333333Range14.6Trim Var.5.42614285714285
V(Y[t],d=1,D=2)18.1744927536232Range18.1Trim Var.9.30997368421052
V(Y[t],d=2,D=2)51.7040316205533Range35.7Trim Var.19.8458479532164
V(Y[t],d=3,D=2)173.780627705628Range60.8Trim Var.68.9694117647058

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 30.2851615646258 & Range & 20.4 & Trim Var. & 22.3134772978959 \tabularnewline
V(Y[t],d=1,D=0) & 11.2164361702128 & Range & 13.9 & Trim Var. & 7.58485481997677 \tabularnewline
V(Y[t],d=2,D=0) & 10.7724791859389 & Range & 12.7 & Trim Var. & 6.51282051282051 \tabularnewline
V(Y[t],d=3,D=0) & 26.5499130434783 & Range & 21.1 & Trim Var. & 15.8594615384615 \tabularnewline
V(Y[t],d=0,D=1) & 3.98472972972973 & Range & 9 & Trim Var. & 2.21755681818182 \tabularnewline
V(Y[t],d=1,D=1) & 6.3920873015873 & Range & 12 & Trim Var. & 3.65273185483871 \tabularnewline
V(Y[t],d=2,D=1) & 17.6273445378151 & Range & 20.1 & Trim Var. & 9.0819569892473 \tabularnewline
V(Y[t],d=3,D=1) & 56.7148663101604 & Range & 35.7 & Trim Var. & 30.7756781609195 \tabularnewline
V(Y[t],d=0,D=2) & 11.3908333333333 & Range & 14.6 & Trim Var. & 5.42614285714285 \tabularnewline
V(Y[t],d=1,D=2) & 18.1744927536232 & Range & 18.1 & Trim Var. & 9.30997368421052 \tabularnewline
V(Y[t],d=2,D=2) & 51.7040316205533 & Range & 35.7 & Trim Var. & 19.8458479532164 \tabularnewline
V(Y[t],d=3,D=2) & 173.780627705628 & Range & 60.8 & Trim Var. & 68.9694117647058 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113139&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]30.2851615646258[/C][C]Range[/C][C]20.4[/C][C]Trim Var.[/C][C]22.3134772978959[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]11.2164361702128[/C][C]Range[/C][C]13.9[/C][C]Trim Var.[/C][C]7.58485481997677[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]10.7724791859389[/C][C]Range[/C][C]12.7[/C][C]Trim Var.[/C][C]6.51282051282051[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]26.5499130434783[/C][C]Range[/C][C]21.1[/C][C]Trim Var.[/C][C]15.8594615384615[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]3.98472972972973[/C][C]Range[/C][C]9[/C][C]Trim Var.[/C][C]2.21755681818182[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]6.3920873015873[/C][C]Range[/C][C]12[/C][C]Trim Var.[/C][C]3.65273185483871[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]17.6273445378151[/C][C]Range[/C][C]20.1[/C][C]Trim Var.[/C][C]9.0819569892473[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]56.7148663101604[/C][C]Range[/C][C]35.7[/C][C]Trim Var.[/C][C]30.7756781609195[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]11.3908333333333[/C][C]Range[/C][C]14.6[/C][C]Trim Var.[/C][C]5.42614285714285[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]18.1744927536232[/C][C]Range[/C][C]18.1[/C][C]Trim Var.[/C][C]9.30997368421052[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]51.7040316205533[/C][C]Range[/C][C]35.7[/C][C]Trim Var.[/C][C]19.8458479532164[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]173.780627705628[/C][C]Range[/C][C]60.8[/C][C]Trim Var.[/C][C]68.9694117647058[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113139&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113139&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)30.2851615646258Range20.4Trim Var.22.3134772978959
V(Y[t],d=1,D=0)11.2164361702128Range13.9Trim Var.7.58485481997677
V(Y[t],d=2,D=0)10.7724791859389Range12.7Trim Var.6.51282051282051
V(Y[t],d=3,D=0)26.5499130434783Range21.1Trim Var.15.8594615384615
V(Y[t],d=0,D=1)3.98472972972973Range9Trim Var.2.21755681818182
V(Y[t],d=1,D=1)6.3920873015873Range12Trim Var.3.65273185483871
V(Y[t],d=2,D=1)17.6273445378151Range20.1Trim Var.9.0819569892473
V(Y[t],d=3,D=1)56.7148663101604Range35.7Trim Var.30.7756781609195
V(Y[t],d=0,D=2)11.3908333333333Range14.6Trim Var.5.42614285714285
V(Y[t],d=1,D=2)18.1744927536232Range18.1Trim Var.9.30997368421052
V(Y[t],d=2,D=2)51.7040316205533Range35.7Trim Var.19.8458479532164
V(Y[t],d=3,D=2)173.780627705628Range60.8Trim Var.68.9694117647058


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()