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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 computationTue, 09 Dec 2008 10:09:17 -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/09/t12288426930rxl91prqs630nb.htm/, Retrieved Mon, 27 May 2024 23:11:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31596, Retrieved Mon, 27 May 2024 23:11:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsk_vanderheggen
Estimated Impact190

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] [eigen tijdreeks w...] [2008-12-09 17:09:17] [2731fa16c50d4727d0297daf34574cde] [Current]
-         [Variance Reduction Matrix] [Paper VRM] [2008-12-18 15:13:24] [1640119c345fbfa2091dc1243f79f7a6]
Feedback Forum
2008-12-14 13:53:44 [Jasmine Hendrikx] [reply] 
Evaluatie stap 2 VRM:
De berekening is goed uitgevoerd en de conclusie is juist, maar onvolledig. Het is inderdaad zo dat we de kleinste variantie vinden bij d=2 en D=0, maar als we echter kijken naar de getrimde variantie, zien we dat we de kleinste variantie vinden bij d=1 en D=0. Omdat er toch wel sprake lijkt te zijn van outliers, zou ik meer vertrouwen op de getrimde variantie, dus d=1 en D=0. De student heeft echter in stap 3 telkens gewerkt D=0 en d=2. Dit zou dan ook uitgetest moeten worden met d=1 en D=0.
2008-12-16 14:01:47 [Peter Van Doninck] [reply] 
Het klopt dat de gewone variantie het kleinste is bij d=2 en D=0. Omdat we echter te maken hebben met een grote invloed van outliers (zie vorige vraag), moeten we de getrimde variantie onderzoeken! Deze houdt geen rekening met de outliers! We krijgen dan andere waarden, namelijk d=1 en D=0. Doordat de studente de 'verkeerde' parameters beschouwd heeft, zullen de toekomstige berekeningen enerzijds verschillend zijn.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5.5
5.3
5.2
5.3
5.3
5
4.8
4.9
5.3
6
6.2
6.4
6.4
6.4
6.2
6.1
6
5.9
6.2
6.2
6.4
6.8
6.9
7
7
6.9
6.7
6.6
6.5
6.4
6.5
6.5
6.6
6.7
6.8
7.2
7.6
7.6
7.3
6.4
6.1
6.3
7.1
7.5
7.4
7.1
6.8
6.9
7.2
7.4
7.3
6.9
6.9
6.8
7.1
7.2
7.1
7
6.9
7
7.4
7.5
7.5
7.4
7.3
7
6.7
6.5
6.5
6.5
6.6
6.8
6.9
6.9
6.8
6.8
6.5
6.1
6
5.9
5.8
5.9
5.9
6.2
6.3
6.2
6
5.8
5.5
5.5
5.7
5.8

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=31596&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=31596&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31596&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)0.44673674151935Range2.8Trim Var.0.253667640376501
V(Y[t],d=1,D=0)0.0592112332112332Range1.7Trim Var.0.0301234567901234
V(Y[t],d=2,D=0)0.0580786516853932Range1.2Trim Var.0.0341708860759494
V(Y[t],d=3,D=0)0.109767620020429Range2.20000000000000Trim Var.0.0529470950989938
V(Y[t],d=0,D=1)0.372094936708861Range2.4Trim Var.0.274969818913481
V(Y[t],d=1,D=1)0.0649659201557936Range1.5Trim Var.0.0339047619047619
V(Y[t],d=2,D=1)0.0701298701298702Range1.30000000000000Trim Var.0.0402855924978687
V(Y[t],d=3,D=1)0.127098427887902Range2.20000000000000Trim Var.0.0729326513213983
V(Y[t],d=0,D=2)0.298375768217735Range2.5Trim Var.0.184455535390200
V(Y[t],d=1,D=2)0.164400723654455Range2.5Trim Var.0.0740327293980129
V(Y[t],d=2,D=2)0.179039627039627Range2.10000000000000Trim Var.0.105251058681186
V(Y[t],d=3,D=2)0.328711538461539Range3.1Trim Var.0.166773182957394

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.44673674151935 & Range & 2.8 & Trim Var. & 0.253667640376501 \tabularnewline
V(Y[t],d=1,D=0) & 0.0592112332112332 & Range & 1.7 & Trim Var. & 0.0301234567901234 \tabularnewline
V(Y[t],d=2,D=0) & 0.0580786516853932 & Range & 1.2 & Trim Var. & 0.0341708860759494 \tabularnewline
V(Y[t],d=3,D=0) & 0.109767620020429 & Range & 2.20000000000000 & Trim Var. & 0.0529470950989938 \tabularnewline
V(Y[t],d=0,D=1) & 0.372094936708861 & Range & 2.4 & Trim Var. & 0.274969818913481 \tabularnewline
V(Y[t],d=1,D=1) & 0.0649659201557936 & Range & 1.5 & Trim Var. & 0.0339047619047619 \tabularnewline
V(Y[t],d=2,D=1) & 0.0701298701298702 & Range & 1.30000000000000 & Trim Var. & 0.0402855924978687 \tabularnewline
V(Y[t],d=3,D=1) & 0.127098427887902 & Range & 2.20000000000000 & Trim Var. & 0.0729326513213983 \tabularnewline
V(Y[t],d=0,D=2) & 0.298375768217735 & Range & 2.5 & Trim Var. & 0.184455535390200 \tabularnewline
V(Y[t],d=1,D=2) & 0.164400723654455 & Range & 2.5 & Trim Var. & 0.0740327293980129 \tabularnewline
V(Y[t],d=2,D=2) & 0.179039627039627 & Range & 2.10000000000000 & Trim Var. & 0.105251058681186 \tabularnewline
V(Y[t],d=3,D=2) & 0.328711538461539 & Range & 3.1 & Trim Var. & 0.166773182957394 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31596&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.44673674151935[/C][C]Range[/C][C]2.8[/C][C]Trim Var.[/C][C]0.253667640376501[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.0592112332112332[/C][C]Range[/C][C]1.7[/C][C]Trim Var.[/C][C]0.0301234567901234[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.0580786516853932[/C][C]Range[/C][C]1.2[/C][C]Trim Var.[/C][C]0.0341708860759494[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.109767620020429[/C][C]Range[/C][C]2.20000000000000[/C][C]Trim Var.[/C][C]0.0529470950989938[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.372094936708861[/C][C]Range[/C][C]2.4[/C][C]Trim Var.[/C][C]0.274969818913481[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.0649659201557936[/C][C]Range[/C][C]1.5[/C][C]Trim Var.[/C][C]0.0339047619047619[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.0701298701298702[/C][C]Range[/C][C]1.30000000000000[/C][C]Trim Var.[/C][C]0.0402855924978687[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.127098427887902[/C][C]Range[/C][C]2.20000000000000[/C][C]Trim Var.[/C][C]0.0729326513213983[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.298375768217735[/C][C]Range[/C][C]2.5[/C][C]Trim Var.[/C][C]0.184455535390200[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.164400723654455[/C][C]Range[/C][C]2.5[/C][C]Trim Var.[/C][C]0.0740327293980129[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.179039627039627[/C][C]Range[/C][C]2.10000000000000[/C][C]Trim Var.[/C][C]0.105251058681186[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.328711538461539[/C][C]Range[/C][C]3.1[/C][C]Trim Var.[/C][C]0.166773182957394[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31596&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31596&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)0.44673674151935Range2.8Trim Var.0.253667640376501
V(Y[t],d=1,D=0)0.0592112332112332Range1.7Trim Var.0.0301234567901234
V(Y[t],d=2,D=0)0.0580786516853932Range1.2Trim Var.0.0341708860759494
V(Y[t],d=3,D=0)0.109767620020429Range2.20000000000000Trim Var.0.0529470950989938
V(Y[t],d=0,D=1)0.372094936708861Range2.4Trim Var.0.274969818913481
V(Y[t],d=1,D=1)0.0649659201557936Range1.5Trim Var.0.0339047619047619
V(Y[t],d=2,D=1)0.0701298701298702Range1.30000000000000Trim Var.0.0402855924978687
V(Y[t],d=3,D=1)0.127098427887902Range2.20000000000000Trim Var.0.0729326513213983
V(Y[t],d=0,D=2)0.298375768217735Range2.5Trim Var.0.184455535390200
V(Y[t],d=1,D=2)0.164400723654455Range2.5Trim Var.0.0740327293980129
V(Y[t],d=2,D=2)0.179039627039627Range2.10000000000000Trim Var.0.105251058681186
V(Y[t],d=3,D=2)0.328711538461539Range3.1Trim Var.0.166773182957394


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(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')