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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, 09 Dec 2011 06:51:49 -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/09/t1323431531dqkgp3loh7kascb.htm/, Retrieved Thu, 02 May 2024 17:51:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=153276, Retrieved Thu, 02 May 2024 17:51:57 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Tukey lambda PPCC Plot] [Intrinsic Motivat...] [2010-10-12 12:09:04] [b98453cac15ba1066b407e146608df68]
- R PD  [Tukey lambda PPCC Plot] [D1- Tukey] [2011-12-02 12:05:09] [7e261c986c934df955dd3ac53e9d45c6]
- RMP       [Variance Reduction Matrix] [paper VRM (0,0)] [2011-12-09 11:51:49] [13dfa60174f50d862e8699db2153bfc5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
617
614
647
580
614
636
388
356
639
753
611
639
630
586
695
552
619
681
421
307
754
690
644
643
608
651
691
627
634
731
475
337
803
722
590
724
627
696
825
677
656
785
412
352
839
729
696
641
695
638
762
635
721
854
418
367
824
687
601
676
740
691
683
594
729
731
386
331
706
715
657
653
642
643
718
654
632
731
392
344
792
852
649
629
685
617
715
715
629
916
531
357
917
828
708
858
775
785
1006
789
734
906
532
387
991
841
892
782
811
792
978
773
796
946
594
438
1023
868
791
760
779
852
1001
734
996
869
599
426
1138

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153276&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153276&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153276&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 time0 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)26765.3855377907Range831Trim Var.15749.6768878719
V(Y[t],d=1,D=0)41538.8847810039Range1148Trim Var.18643.7369973607
V(Y[t],d=2,D=0)101569.377827772Range1639Trim Var.56849.1468078382
V(Y[t],d=3,D=0)278489.250857143Range2458Trim Var.161211.495415058
V(Y[t],d=0,D=1)5086.09740642499Range414Trim Var.2602.84285714286
V(Y[t],d=1,D=1)8955.7940029985Range516Trim Var.5294.97899551904
V(Y[t],d=2,D=1)27872.7418764302Range888Trim Var.16659.850180849
V(Y[t],d=3,D=1)95104.9434094085Range1692Trim Var.55381.7390797903
V(Y[t],d=0,D=2)12404.015018315Range613Trim Var.6594.33941093969
V(Y[t],d=1,D=2)22033.8651979089Range769Trim Var.13368.9775441949
V(Y[t],d=2,D=2)66549.6750428327Range1199Trim Var.41674.3416361416
V(Y[t],d=3,D=2)224434.179867987Range2298Trim Var.138455.014856429

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 26765.3855377907 & Range & 831 & Trim Var. & 15749.6768878719 \tabularnewline
V(Y[t],d=1,D=0) & 41538.8847810039 & Range & 1148 & Trim Var. & 18643.7369973607 \tabularnewline
V(Y[t],d=2,D=0) & 101569.377827772 & Range & 1639 & Trim Var. & 56849.1468078382 \tabularnewline
V(Y[t],d=3,D=0) & 278489.250857143 & Range & 2458 & Trim Var. & 161211.495415058 \tabularnewline
V(Y[t],d=0,D=1) & 5086.09740642499 & Range & 414 & Trim Var. & 2602.84285714286 \tabularnewline
V(Y[t],d=1,D=1) & 8955.7940029985 & Range & 516 & Trim Var. & 5294.97899551904 \tabularnewline
V(Y[t],d=2,D=1) & 27872.7418764302 & Range & 888 & Trim Var. & 16659.850180849 \tabularnewline
V(Y[t],d=3,D=1) & 95104.9434094085 & Range & 1692 & Trim Var. & 55381.7390797903 \tabularnewline
V(Y[t],d=0,D=2) & 12404.015018315 & Range & 613 & Trim Var. & 6594.33941093969 \tabularnewline
V(Y[t],d=1,D=2) & 22033.8651979089 & Range & 769 & Trim Var. & 13368.9775441949 \tabularnewline
V(Y[t],d=2,D=2) & 66549.6750428327 & Range & 1199 & Trim Var. & 41674.3416361416 \tabularnewline
V(Y[t],d=3,D=2) & 224434.179867987 & Range & 2298 & Trim Var. & 138455.014856429 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153276&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]26765.3855377907[/C][C]Range[/C][C]831[/C][C]Trim Var.[/C][C]15749.6768878719[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]41538.8847810039[/C][C]Range[/C][C]1148[/C][C]Trim Var.[/C][C]18643.7369973607[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]101569.377827772[/C][C]Range[/C][C]1639[/C][C]Trim Var.[/C][C]56849.1468078382[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]278489.250857143[/C][C]Range[/C][C]2458[/C][C]Trim Var.[/C][C]161211.495415058[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]5086.09740642499[/C][C]Range[/C][C]414[/C][C]Trim Var.[/C][C]2602.84285714286[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]8955.7940029985[/C][C]Range[/C][C]516[/C][C]Trim Var.[/C][C]5294.97899551904[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]27872.7418764302[/C][C]Range[/C][C]888[/C][C]Trim Var.[/C][C]16659.850180849[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]95104.9434094085[/C][C]Range[/C][C]1692[/C][C]Trim Var.[/C][C]55381.7390797903[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]12404.015018315[/C][C]Range[/C][C]613[/C][C]Trim Var.[/C][C]6594.33941093969[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]22033.8651979089[/C][C]Range[/C][C]769[/C][C]Trim Var.[/C][C]13368.9775441949[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]66549.6750428327[/C][C]Range[/C][C]1199[/C][C]Trim Var.[/C][C]41674.3416361416[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]224434.179867987[/C][C]Range[/C][C]2298[/C][C]Trim Var.[/C][C]138455.014856429[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153276&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153276&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)26765.3855377907Range831Trim Var.15749.6768878719
V(Y[t],d=1,D=0)41538.8847810039Range1148Trim Var.18643.7369973607
V(Y[t],d=2,D=0)101569.377827772Range1639Trim Var.56849.1468078382
V(Y[t],d=3,D=0)278489.250857143Range2458Trim Var.161211.495415058
V(Y[t],d=0,D=1)5086.09740642499Range414Trim Var.2602.84285714286
V(Y[t],d=1,D=1)8955.7940029985Range516Trim Var.5294.97899551904
V(Y[t],d=2,D=1)27872.7418764302Range888Trim Var.16659.850180849
V(Y[t],d=3,D=1)95104.9434094085Range1692Trim Var.55381.7390797903
V(Y[t],d=0,D=2)12404.015018315Range613Trim Var.6594.33941093969
V(Y[t],d=1,D=2)22033.8651979089Range769Trim Var.13368.9775441949
V(Y[t],d=2,D=2)66549.6750428327Range1199Trim Var.41674.3416361416
V(Y[t],d=3,D=2)224434.179867987Range2298Trim Var.138455.014856429


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()