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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationWed, 03 Dec 2008 03:35:47 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/03/t1228300599ps1lpu5gq6gqme9.htm/, Retrieved Fri, 17 May 2024 05:02:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28606, Retrieved Fri, 17 May 2024 05:02:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact196

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Variance Reduction Matrix] [] [2008-12-03 10:35:47] [ed75e673b8609ce7f7795f94157397be] [Current]
Feedback Forum
2008-12-07 19:26:38 [Jasmine Hendrikx] [reply] 
Evaluatie Q8:
De student heeft hier gebruik gemaakt van de VRM. Dit is inderdaad een methode om deze vraag op te lossen. De kleinste variantie is inderdaad terug te vinden bij d=2 en D=1. Als we naar de getrimde variantie kijken zien we dat de kleinste variantie zich bevindt bij d=1 en D=0. Er is dus blijkbaar een invloed van outliers, wat de student ook correct concludeert.

Zoals ik hiervoor ook al vermeldde, is de VRM slechts één methode en zou je ook nog gebruik moeten maken van de ACF en van Spectral Analysis om de resultaten uit de VRM te controleren. Het is namelijk zo dat deze niet altijd overeenkomen en wanneer de VRM en de ACF een verschillend resultaat geven, zou men eerder geneigd moeten zijn om de ACF te gebruiken. Je zou dus ook van de andere methodes gebruik moeten maken ter controle.

Ook is de optimale lambda niet berekend. Deze moet je berekenen via de methode Standard Deviation – Mean plot. Met die optimale lambda zou je dan de variantie kunnen stabiliseren om zo de tijdreeks meer stationair te maken.
2008-12-08 19:41:45 [Erik Geysen] [reply] 
Er zijn 3 methodes om een trend te analyseren.
1) VRM
2) ACF
3) Spectraal analyse

De student heeft hier enkel de VRM gebruikt. Het is nodig om minstens ACF ook te berekenen om de uitkomsten te controleren. Deze komen niet altijd overeen en als dit het geval is zijn we geneigd om ACF te geloven. Je hebt de Standard deviation mean-plot nodig om de lambda te berekenen.

je vindt inderdaad de kleinste variantie bij d=2 en D=1, voor de getrimde variantie is dit bij d=1 en D=0 wat betekent dat de outliers een grote invloed hebben. De student vermeld dit ook.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6.8
6.9
6.8
6.2
6.2
6.6
6.8
7.1
7.3
7.2
7
7
7
7.3
7.5
7.2
7.7
8
7.9
8
8
7.9
7.9
7.9
8.1
8.1
8.2
8.1
8.3
8.5
8.6
8.7
8.7
8.5
8.4
8.5
8.8
8.7
8.6
8
8.1
8.2
8.6
8.6
8.5
8.3
8.2
8.7
9.3
9.3
8.8
7.5
7.2
7.5
8.3
8.8
8.9
8.6
8.4
8.4
8.4

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'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28606&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28606&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28606&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.55675956284153Range3.1Trim Var.0.304753401360544
V(Y[t],d=1,D=0)0.101649717514124Range2.1Trim Var.0.0363197586726998
V(Y[t],d=2,D=0)0.12947983635301Range1.8Trim Var.0.072564705882353
V(Y[t],d=3,D=0)0.270163339382940Range2.8Trim Var.0.134328808446456
V(Y[t],d=0,D=1)0.308333333333333Range2.4Trim Var.0.179623477297896
V(Y[t],d=1,D=1)0.0775487588652483Range1.2Trim Var.0.0382307692307692
V(Y[t],d=2,D=1)0.0757909343200741Range1.2Trim Var.0.0438397435897437
V(Y[t],d=3,D=1)0.160425120772947Range1.5Trim Var.0.0981987179487183
V(Y[t],d=0,D=2)0.248693693693694Range2.3Trim Var.0.155587121212121
V(Y[t],d=1,D=2)0.129230158730159Range1.50000000000000Trim Var.0.0761290322580644
V(Y[t],d=2,D=2)0.151042016806723Range1.70000000000000Trim Var.0.0849462365591397
V(Y[t],d=3,D=2)0.411203208556149Range2.59999999999999Trim Var.0.235402298850575

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.55675956284153 & Range & 3.1 & Trim Var. & 0.304753401360544 \tabularnewline
V(Y[t],d=1,D=0) & 0.101649717514124 & Range & 2.1 & Trim Var. & 0.0363197586726998 \tabularnewline
V(Y[t],d=2,D=0) & 0.12947983635301 & Range & 1.8 & Trim Var. & 0.072564705882353 \tabularnewline
V(Y[t],d=3,D=0) & 0.270163339382940 & Range & 2.8 & Trim Var. & 0.134328808446456 \tabularnewline
V(Y[t],d=0,D=1) & 0.308333333333333 & Range & 2.4 & Trim Var. & 0.179623477297896 \tabularnewline
V(Y[t],d=1,D=1) & 0.0775487588652483 & Range & 1.2 & Trim Var. & 0.0382307692307692 \tabularnewline
V(Y[t],d=2,D=1) & 0.0757909343200741 & Range & 1.2 & Trim Var. & 0.0438397435897437 \tabularnewline
V(Y[t],d=3,D=1) & 0.160425120772947 & Range & 1.5 & Trim Var. & 0.0981987179487183 \tabularnewline
V(Y[t],d=0,D=2) & 0.248693693693694 & Range & 2.3 & Trim Var. & 0.155587121212121 \tabularnewline
V(Y[t],d=1,D=2) & 0.129230158730159 & Range & 1.50000000000000 & Trim Var. & 0.0761290322580644 \tabularnewline
V(Y[t],d=2,D=2) & 0.151042016806723 & Range & 1.70000000000000 & Trim Var. & 0.0849462365591397 \tabularnewline
V(Y[t],d=3,D=2) & 0.411203208556149 & Range & 2.59999999999999 & Trim Var. & 0.235402298850575 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28606&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.55675956284153[/C][C]Range[/C][C]3.1[/C][C]Trim Var.[/C][C]0.304753401360544[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.101649717514124[/C][C]Range[/C][C]2.1[/C][C]Trim Var.[/C][C]0.0363197586726998[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.12947983635301[/C][C]Range[/C][C]1.8[/C][C]Trim Var.[/C][C]0.072564705882353[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.270163339382940[/C][C]Range[/C][C]2.8[/C][C]Trim Var.[/C][C]0.134328808446456[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.308333333333333[/C][C]Range[/C][C]2.4[/C][C]Trim Var.[/C][C]0.179623477297896[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.0775487588652483[/C][C]Range[/C][C]1.2[/C][C]Trim Var.[/C][C]0.0382307692307692[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.0757909343200741[/C][C]Range[/C][C]1.2[/C][C]Trim Var.[/C][C]0.0438397435897437[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.160425120772947[/C][C]Range[/C][C]1.5[/C][C]Trim Var.[/C][C]0.0981987179487183[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.248693693693694[/C][C]Range[/C][C]2.3[/C][C]Trim Var.[/C][C]0.155587121212121[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.129230158730159[/C][C]Range[/C][C]1.50000000000000[/C][C]Trim Var.[/C][C]0.0761290322580644[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.151042016806723[/C][C]Range[/C][C]1.70000000000000[/C][C]Trim Var.[/C][C]0.0849462365591397[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.411203208556149[/C][C]Range[/C][C]2.59999999999999[/C][C]Trim Var.[/C][C]0.235402298850575[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28606&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28606&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)0.55675956284153Range3.1Trim Var.0.304753401360544
V(Y[t],d=1,D=0)0.101649717514124Range2.1Trim Var.0.0363197586726998
V(Y[t],d=2,D=0)0.12947983635301Range1.8Trim Var.0.072564705882353
V(Y[t],d=3,D=0)0.270163339382940Range2.8Trim Var.0.134328808446456
V(Y[t],d=0,D=1)0.308333333333333Range2.4Trim Var.0.179623477297896
V(Y[t],d=1,D=1)0.0775487588652483Range1.2Trim Var.0.0382307692307692
V(Y[t],d=2,D=1)0.0757909343200741Range1.2Trim Var.0.0438397435897437
V(Y[t],d=3,D=1)0.160425120772947Range1.5Trim Var.0.0981987179487183
V(Y[t],d=0,D=2)0.248693693693694Range2.3Trim Var.0.155587121212121
V(Y[t],d=1,D=2)0.129230158730159Range1.50000000000000Trim Var.0.0761290322580644
V(Y[t],d=2,D=2)0.151042016806723Range1.70000000000000Trim Var.0.0849462365591397
V(Y[t],d=3,D=2)0.411203208556149Range2.59999999999999Trim Var.0.235402298850575


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 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')