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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 computationTue, 20 Dec 2011 06:09:37 -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/20/t1324379450vk5phrv6mfu2oe0.htm/, Retrieved Sun, 05 May 2024 21:15:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157920, Retrieved Sun, 05 May 2024 21:15:06 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Testing Mean with unknown Variance - Critical Value] [] [2010-10-25 13:12:27] [b98453cac15ba1066b407e146608df68]
- RMPD    [Variance Reduction Matrix] [Paper Variantie r...] [2011-12-20 11:09:37] [c98b04636162cea751932dfe577607eb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
276687
277915
277128
277103
275037
270150
267140
264993
287259
291186
292300
288186
281477
282656
280190
280408
276836
275216
274352
271311
289802
290726
292300
278506
269826
265861
269034
264176
255198
253353
246057
235372
258556
260993
254663
250643
243422
247105
248541
245039
237080
237085
225554
226839
247934
248333
246969
245098
246263
255765
264319
268347
273046
273963
267430
271993
292710
295881
293299
288576
286445
297584
300431
298522
292213
285383
277537
277891
302686
300653
296369
287224
279998
283495
285775
282329
277799
271980
266730
262433
285378
286692
282917
277686
274371

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=157920&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=157920&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157920&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)335614469.951821Range77132Trim Var.219600520.431712
V(Y[t],d=1,D=0)65046109.4767642Range38589Trim Var.29109287.6993706
V(Y[t],d=2,D=0)114788230.002057Range60697Trim Var.48241035.3238204
V(Y[t],d=3,D=0)304579366.378952Range91874Trim Var.129702372.894366
V(Y[t],d=0,D=1)495781483.479452Range85185Trim Var.353561127.410096
V(Y[t],d=1,D=1)24566070.2486307Range23666Trim Var.14833710.8244048
V(Y[t],d=2,D=1)37838940.8056338Range31737Trim Var.20184787.5104967
V(Y[t],d=3,D=1)122243761.403934Range57359Trim Var.69986002.0468006
V(Y[t],d=0,D=2)1146873537.88415Range118287Trim Var.864205207.664006
V(Y[t],d=1,D=2)72955293.2031073Range43280Trim Var.46609046.7732355
V(Y[t],d=2,D=2)121213645.758621Range54214Trim Var.79926919.2692308
V(Y[t],d=3,D=2)396722121.937387Range84540Trim Var.262193605.52451

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 335614469.951821 & Range & 77132 & Trim Var. & 219600520.431712 \tabularnewline
V(Y[t],d=1,D=0) & 65046109.4767642 & Range & 38589 & Trim Var. & 29109287.6993706 \tabularnewline
V(Y[t],d=2,D=0) & 114788230.002057 & Range & 60697 & Trim Var. & 48241035.3238204 \tabularnewline
V(Y[t],d=3,D=0) & 304579366.378952 & Range & 91874 & Trim Var. & 129702372.894366 \tabularnewline
V(Y[t],d=0,D=1) & 495781483.479452 & Range & 85185 & Trim Var. & 353561127.410096 \tabularnewline
V(Y[t],d=1,D=1) & 24566070.2486307 & Range & 23666 & Trim Var. & 14833710.8244048 \tabularnewline
V(Y[t],d=2,D=1) & 37838940.8056338 & Range & 31737 & Trim Var. & 20184787.5104967 \tabularnewline
V(Y[t],d=3,D=1) & 122243761.403934 & Range & 57359 & Trim Var. & 69986002.0468006 \tabularnewline
V(Y[t],d=0,D=2) & 1146873537.88415 & Range & 118287 & Trim Var. & 864205207.664006 \tabularnewline
V(Y[t],d=1,D=2) & 72955293.2031073 & Range & 43280 & Trim Var. & 46609046.7732355 \tabularnewline
V(Y[t],d=2,D=2) & 121213645.758621 & Range & 54214 & Trim Var. & 79926919.2692308 \tabularnewline
V(Y[t],d=3,D=2) & 396722121.937387 & Range & 84540 & Trim Var. & 262193605.52451 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157920&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]335614469.951821[/C][C]Range[/C][C]77132[/C][C]Trim Var.[/C][C]219600520.431712[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]65046109.4767642[/C][C]Range[/C][C]38589[/C][C]Trim Var.[/C][C]29109287.6993706[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]114788230.002057[/C][C]Range[/C][C]60697[/C][C]Trim Var.[/C][C]48241035.3238204[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]304579366.378952[/C][C]Range[/C][C]91874[/C][C]Trim Var.[/C][C]129702372.894366[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]495781483.479452[/C][C]Range[/C][C]85185[/C][C]Trim Var.[/C][C]353561127.410096[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]24566070.2486307[/C][C]Range[/C][C]23666[/C][C]Trim Var.[/C][C]14833710.8244048[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]37838940.8056338[/C][C]Range[/C][C]31737[/C][C]Trim Var.[/C][C]20184787.5104967[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]122243761.403934[/C][C]Range[/C][C]57359[/C][C]Trim Var.[/C][C]69986002.0468006[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1146873537.88415[/C][C]Range[/C][C]118287[/C][C]Trim Var.[/C][C]864205207.664006[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]72955293.2031073[/C][C]Range[/C][C]43280[/C][C]Trim Var.[/C][C]46609046.7732355[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]121213645.758621[/C][C]Range[/C][C]54214[/C][C]Trim Var.[/C][C]79926919.2692308[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]396722121.937387[/C][C]Range[/C][C]84540[/C][C]Trim Var.[/C][C]262193605.52451[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157920&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157920&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)335614469.951821Range77132Trim Var.219600520.431712
V(Y[t],d=1,D=0)65046109.4767642Range38589Trim Var.29109287.6993706
V(Y[t],d=2,D=0)114788230.002057Range60697Trim Var.48241035.3238204
V(Y[t],d=3,D=0)304579366.378952Range91874Trim Var.129702372.894366
V(Y[t],d=0,D=1)495781483.479452Range85185Trim Var.353561127.410096
V(Y[t],d=1,D=1)24566070.2486307Range23666Trim Var.14833710.8244048
V(Y[t],d=2,D=1)37838940.8056338Range31737Trim Var.20184787.5104967
V(Y[t],d=3,D=1)122243761.403934Range57359Trim Var.69986002.0468006
V(Y[t],d=0,D=2)1146873537.88415Range118287Trim Var.864205207.664006
V(Y[t],d=1,D=2)72955293.2031073Range43280Trim Var.46609046.7732355
V(Y[t],d=2,D=2)121213645.758621Range54214Trim Var.79926919.2692308
V(Y[t],d=3,D=2)396722121.937387Range84540Trim Var.262193605.52451


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()