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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 computationWed, 21 Dec 2011 04:50:39 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/21/t1324461055h0et165kmagvh6z.htm/, Retrieved Sun, 17 May 2026 03:52:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158400, Retrieved Sun, 17 May 2026 03:52:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact399

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] [] [2011-12-21 09:50:39] [bbaf0bbad09b34135f8973992e5d67ea] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2,581
2,592
2,600
2,602
2,608
2,619
2,637
2,646
2,659
2,671
2,684
2,686
2,691
2,705
2,723
2,725
2,734
2,735
2,740
2,744
2,737
2,743
2,747
2,748
2,749
2,754
2,766
2,784
2,794
2,804
2,818
2,833
2,836
2,866
2,893
2,897
2,897
2,913
2,921
2,922
2,924
2,924
2,945
2,948
2,952
2,968
2,987
2,997
3,002
3,012
3,027
3,032
3,036
3,039
3,048
3,050
3,089
3,093
3,094
3,098
3,104
3,106
3,116
3,119
3,124
3,131
3,147
3,156

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158400&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158400&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158400&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.0297985689201054Range0.575Trim Var.0.0237265251412429
V(Y[t],d=1,D=0)5.98833107191319e-05Range0.0460000000000003Trim Var.2.67744360902257e-05
V(Y[t],d=2,D=0)0.000111968298368299Range0.0720000000000005Trim Var.3.76651542649735e-05
V(Y[t],d=3,D=0)0.000316933653846157Range0.116000000000001Trim Var.0.000125669799498746
V(Y[t],d=0,D=1)0.000712176623376621Range0.116Trim Var.0.000462575102040816
V(Y[t],d=1,D=1)0.000113327946127946Range0.0550000000000002Trim Var.5.74455782312921e-05
V(Y[t],d=2,D=1)0.000164862334032145Range0.0830000000000006Trim Var.7.86023936170208e-05
V(Y[t],d=3,D=1)0.000460039912917268Range0.124000000000001Trim Var.0.000234260869565215
V(Y[t],d=0,D=2)0.00256478224101479Range0.191999999999999Trim Var.0.00169256330014224
V(Y[t],d=1,D=2)0.000313549280177184Range0.0720000000000005Trim Var.0.000182336336336334
V(Y[t],d=2,D=2)0.0003455238095238Range0.0689999999999982Trim Var.0.000223094444444441
V(Y[t],d=3,D=2)0.000929545121951182Range0.116999999999999Trim Var.0.000583986554621824

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.0297985689201054 & Range & 0.575 & Trim Var. & 0.0237265251412429 \tabularnewline
V(Y[t],d=1,D=0) & 5.98833107191319e-05 & Range & 0.0460000000000003 & Trim Var. & 2.67744360902257e-05 \tabularnewline
V(Y[t],d=2,D=0) & 0.000111968298368299 & Range & 0.0720000000000005 & Trim Var. & 3.76651542649735e-05 \tabularnewline
V(Y[t],d=3,D=0) & 0.000316933653846157 & Range & 0.116000000000001 & Trim Var. & 0.000125669799498746 \tabularnewline
V(Y[t],d=0,D=1) & 0.000712176623376621 & Range & 0.116 & Trim Var. & 0.000462575102040816 \tabularnewline
V(Y[t],d=1,D=1) & 0.000113327946127946 & Range & 0.0550000000000002 & Trim Var. & 5.74455782312921e-05 \tabularnewline
V(Y[t],d=2,D=1) & 0.000164862334032145 & Range & 0.0830000000000006 & Trim Var. & 7.86023936170208e-05 \tabularnewline
V(Y[t],d=3,D=1) & 0.000460039912917268 & Range & 0.124000000000001 & Trim Var. & 0.000234260869565215 \tabularnewline
V(Y[t],d=0,D=2) & 0.00256478224101479 & Range & 0.191999999999999 & Trim Var. & 0.00169256330014224 \tabularnewline
V(Y[t],d=1,D=2) & 0.000313549280177184 & Range & 0.0720000000000005 & Trim Var. & 0.000182336336336334 \tabularnewline
V(Y[t],d=2,D=2) & 0.0003455238095238 & Range & 0.0689999999999982 & Trim Var. & 0.000223094444444441 \tabularnewline
V(Y[t],d=3,D=2) & 0.000929545121951182 & Range & 0.116999999999999 & Trim Var. & 0.000583986554621824 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158400&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.0297985689201054[/C][C]Range[/C][C]0.575[/C][C]Trim Var.[/C][C]0.0237265251412429[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]5.98833107191319e-05[/C][C]Range[/C][C]0.0460000000000003[/C][C]Trim Var.[/C][C]2.67744360902257e-05[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.000111968298368299[/C][C]Range[/C][C]0.0720000000000005[/C][C]Trim Var.[/C][C]3.76651542649735e-05[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.000316933653846157[/C][C]Range[/C][C]0.116000000000001[/C][C]Trim Var.[/C][C]0.000125669799498746[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.000712176623376621[/C][C]Range[/C][C]0.116[/C][C]Trim Var.[/C][C]0.000462575102040816[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.000113327946127946[/C][C]Range[/C][C]0.0550000000000002[/C][C]Trim Var.[/C][C]5.74455782312921e-05[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.000164862334032145[/C][C]Range[/C][C]0.0830000000000006[/C][C]Trim Var.[/C][C]7.86023936170208e-05[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.000460039912917268[/C][C]Range[/C][C]0.124000000000001[/C][C]Trim Var.[/C][C]0.000234260869565215[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.00256478224101479[/C][C]Range[/C][C]0.191999999999999[/C][C]Trim Var.[/C][C]0.00169256330014224[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.000313549280177184[/C][C]Range[/C][C]0.0720000000000005[/C][C]Trim Var.[/C][C]0.000182336336336334[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.0003455238095238[/C][C]Range[/C][C]0.0689999999999982[/C][C]Trim Var.[/C][C]0.000223094444444441[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.000929545121951182[/C][C]Range[/C][C]0.116999999999999[/C][C]Trim Var.[/C][C]0.000583986554621824[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158400&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158400&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)0.0297985689201054Range0.575Trim Var.0.0237265251412429
V(Y[t],d=1,D=0)5.98833107191319e-05Range0.0460000000000003Trim Var.2.67744360902257e-05
V(Y[t],d=2,D=0)0.000111968298368299Range0.0720000000000005Trim Var.3.76651542649735e-05
V(Y[t],d=3,D=0)0.000316933653846157Range0.116000000000001Trim Var.0.000125669799498746
V(Y[t],d=0,D=1)0.000712176623376621Range0.116Trim Var.0.000462575102040816
V(Y[t],d=1,D=1)0.000113327946127946Range0.0550000000000002Trim Var.5.74455782312921e-05
V(Y[t],d=2,D=1)0.000164862334032145Range0.0830000000000006Trim Var.7.86023936170208e-05
V(Y[t],d=3,D=1)0.000460039912917268Range0.124000000000001Trim Var.0.000234260869565215
V(Y[t],d=0,D=2)0.00256478224101479Range0.191999999999999Trim Var.0.00169256330014224
V(Y[t],d=1,D=2)0.000313549280177184Range0.0720000000000005Trim Var.0.000182336336336334
V(Y[t],d=2,D=2)0.0003455238095238Range0.0689999999999982Trim Var.0.000223094444444441
V(Y[t],d=3,D=2)0.000929545121951182Range0.116999999999999Trim Var.0.000583986554621824


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()