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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_variancereduction.wasp

Title produced by software

Variance Reduction Matrix

Date of computation

Tue, 24 Nov 2009 13:46:29 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/24/t125909564004s2fbgt2bt7mn3.htm/, Retrieved Sat, 26 Apr 2025 04:29:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59274, Retrieved Sat, 26 Apr 2025 04:29:14 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

311

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Variance Reduction Matrix] [Identifying Integ...] [2009-11-22 12:29:54] [b98453cac15ba1066b407e146608df68]
F    D          [Variance Reduction Matrix] [ws 8] [2009-11-24 20:46:29] [f7d3e79b917995ba1c8c80042fc22ef9] [Current]
-    D            [Variance Reduction Matrix] [WS8 VRM] [2009-11-27 15:39:14] [37a8d600db9abe09a2528d150ccff095] 
- RMPD            [Spectral Analysis] [spectrum d=1 en D=1] [2009-12-08 18:53:31] [cd6314e7e707a6546bd4604c9d1f2b69] 
- RMPD            [Spectral Analysis] [spectrum d=2 en D=1] [2009-12-08 18:55:13] [cd6314e7e707a6546bd4604c9d1f2b69] 
- RM D            [Mean Plot] [verbetering] [2009-12-09 21:09:27] [f5d341d4bbba73282fc6e80153a6d315] 
-    D              [Mean Plot] [verbetering] [2009-12-10 16:01:19] [f5d341d4bbba73282fc6e80153a6d315] 
-    D                [Mean Plot] [verbetering] [2009-12-10 17:38:18] [f5d341d4bbba73282fc6e80153a6d315] 
-    D                [Mean Plot] [verbetering] [2009-12-11 09:16:10] [f5d341d4bbba73282fc6e80153a6d315] 

Feedback Forum

2009-12-08 19:55:18 [Joris Van Mol] [reply] 
Bij deze methode zou het echter nuttig geweest zijn om ook de spectraalanalyse er eventjes bij te nemen om eventueel uitsluitsel te geven over deze differentiatie. Ik heb dit even voor jouw gedaan en heb de uitkomsten hier geblogd:  
Spectrum d=1 en D=1 
 
http://www.freestatistics.org/blog/index.php?v=date/2009/Dec/08/t1260298450kf8i2alpqlye926.htm/ 
 
spectrum d=2 en D=1 
 
http://www.freestatistics.org/blog/index.php?v=date/2009/Dec/08/t1260298560m9o5ffosedxe09y.htm/ 
 
Ik zou aan de hand van deze output durven stellen dat d=2 en D=1 de beste mogelijkheid is omdat bij deze differentiatie het cumulatief periodogram het best binnen het 95% betrouwbaarheidsinterval ligt.

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Dataseries X:

Download CSV

Histogram

Boxplots

9,3
9,3
8,7
8,2
8,3
8,5
8,6
8,5
8,2
8,1
7,9
8,6
8,7
8,7
8,5
8,4
8,5
8,7
8,7
8,6
8,5
8,3
8
8,2
8,1
8,1
8
7,9
7,9
8
8
7,9
8
7,7
7,2
7,5
7,3
7
7
7
7,2
7,3
7,1
6,8
6,4
6,1
6,5
7,7
7,9
7,5
6,9
6,6
6,9
7,7
8
8
7,7
7,3
7,4
8,1

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59274&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59274&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59274&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Variance Reduction Matrix
V(Y[t],d=0,D=0)	0.501387005649717	Range	3.2	Trim Var.	0.300261224489796
V(Y[t],d=1,D=0)	0.111303331385155	Range	1.8	Trim Var.	0.0417411764705882
V(Y[t],d=2,D=0)	0.145641258318209	Range	1.9	Trim Var.	0.0881749622926093
V(Y[t],d=3,D=0)	0.282763157894737	Range	2.8	Trim Var.	0.120031372549020
V(Y[t],d=0,D=1)	0.48040780141844	Range	2.9	Trim Var.	0.282346109175378
V(Y[t],d=1,D=1)	0.102580943570768	Range	1.5	Trim Var.	0.0442439024390244
V(Y[t],d=2,D=1)	0.0912125603864735	Range	1.40000000000000	Trim Var.	0.0491025641025642
V(Y[t],d=3,D=1)	0.143	Range	1.7	Trim Var.	0.0741430499325237
V(Y[t],d=0,D=2)	1.21139682539683	Range	4	Trim Var.	0.804475806451613
V(Y[t],d=1,D=2)	0.271731092436975	Range	2.5	Trim Var.	0.132129032258064
V(Y[t],d=2,D=2)	0.210374331550802	Range	2.1	Trim Var.	0.11351724137931
V(Y[t],d=3,D=2)	0.357178030303029	Range	2.60000000000000	Trim Var.	0.184630541871921

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.501387005649717 & Range & 3.2 & Trim Var. & 0.300261224489796 \tabularnewline
V(Y[t],d=1,D=0) & 0.111303331385155 & Range & 1.8 & Trim Var. & 0.0417411764705882 \tabularnewline
V(Y[t],d=2,D=0) & 0.145641258318209 & Range & 1.9 & Trim Var. & 0.0881749622926093 \tabularnewline
V(Y[t],d=3,D=0) & 0.282763157894737 & Range & 2.8 & Trim Var. & 0.120031372549020 \tabularnewline
V(Y[t],d=0,D=1) & 0.48040780141844 & Range & 2.9 & Trim Var. & 0.282346109175378 \tabularnewline
V(Y[t],d=1,D=1) & 0.102580943570768 & Range & 1.5 & Trim Var. & 0.0442439024390244 \tabularnewline
V(Y[t],d=2,D=1) & 0.0912125603864735 & Range & 1.40000000000000 & Trim Var. & 0.0491025641025642 \tabularnewline
V(Y[t],d=3,D=1) & 0.143 & Range & 1.7 & Trim Var. & 0.0741430499325237 \tabularnewline
V(Y[t],d=0,D=2) & 1.21139682539683 & Range & 4 & Trim Var. & 0.804475806451613 \tabularnewline
V(Y[t],d=1,D=2) & 0.271731092436975 & Range & 2.5 & Trim Var. & 0.132129032258064 \tabularnewline
V(Y[t],d=2,D=2) & 0.210374331550802 & Range & 2.1 & Trim Var. & 0.11351724137931 \tabularnewline
V(Y[t],d=3,D=2) & 0.357178030303029 & Range & 2.60000000000000 & Trim Var. & 0.184630541871921 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59274&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.501387005649717[/C][C]Range[/C][C]3.2[/C][C]Trim Var.[/C][C]0.300261224489796[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.111303331385155[/C][C]Range[/C][C]1.8[/C][C]Trim Var.[/C][C]0.0417411764705882[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.145641258318209[/C][C]Range[/C][C]1.9[/C][C]Trim Var.[/C][C]0.0881749622926093[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.282763157894737[/C][C]Range[/C][C]2.8[/C][C]Trim Var.[/C][C]0.120031372549020[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.48040780141844[/C][C]Range[/C][C]2.9[/C][C]Trim Var.[/C][C]0.282346109175378[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.102580943570768[/C][C]Range[/C][C]1.5[/C][C]Trim Var.[/C][C]0.0442439024390244[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.0912125603864735[/C][C]Range[/C][C]1.40000000000000[/C][C]Trim Var.[/C][C]0.0491025641025642[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.143[/C][C]Range[/C][C]1.7[/C][C]Trim Var.[/C][C]0.0741430499325237[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1.21139682539683[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0.804475806451613[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.271731092436975[/C][C]Range[/C][C]2.5[/C][C]Trim Var.[/C][C]0.132129032258064[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.210374331550802[/C][C]Range[/C][C]2.1[/C][C]Trim Var.[/C][C]0.11351724137931[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.357178030303029[/C][C]Range[/C][C]2.60000000000000[/C][C]Trim Var.[/C][C]0.184630541871921[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59274&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59274&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Variance Reduction Matrix
V(Y[t],d=0,D=0)	0.501387005649717	Range	3.2	Trim Var.	0.300261224489796
V(Y[t],d=1,D=0)	0.111303331385155	Range	1.8	Trim Var.	0.0417411764705882
V(Y[t],d=2,D=0)	0.145641258318209	Range	1.9	Trim Var.	0.0881749622926093
V(Y[t],d=3,D=0)	0.282763157894737	Range	2.8	Trim Var.	0.120031372549020
V(Y[t],d=0,D=1)	0.48040780141844	Range	2.9	Trim Var.	0.282346109175378
V(Y[t],d=1,D=1)	0.102580943570768	Range	1.5	Trim Var.	0.0442439024390244
V(Y[t],d=2,D=1)	0.0912125603864735	Range	1.40000000000000	Trim Var.	0.0491025641025642
V(Y[t],d=3,D=1)	0.143	Range	1.7	Trim Var.	0.0741430499325237
V(Y[t],d=0,D=2)	1.21139682539683	Range	4	Trim Var.	0.804475806451613
V(Y[t],d=1,D=2)	0.271731092436975	Range	2.5	Trim Var.	0.132129032258064
V(Y[t],d=2,D=2)	0.210374331550802	Range	2.1	Trim Var.	0.11351724137931
V(Y[t],d=3,D=2)	0.357178030303029	Range	2.60000000000000	Trim Var.	0.184630541871921

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(x,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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code