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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, 02 Dec 2008 08:54:25 -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/02/t1228233401iqnr6atuhjobxij.htm/, Retrieved Fri, 29 May 2026 15:20:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27980, Retrieved Fri, 29 May 2026 15:20:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact379

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:31:28] [b98453cac15ba1066b407e146608df68]
F RMPD    [Variance Reduction Matrix] [W7Q8] [2008-12-02 15:54:25] [823d674fbf3a4e0ec71bbbd5140f82c6] [Current]
Feedback Forum
2008-12-08 16:03:07 [Kevin Vermeiren] [reply] 
De student geeft een beperkt antwoord. Het klopt dat via de variance reduction matrix de waarden voor de parameters het gemakkelijkst kunnen worden afgelezen. Hier had nog wel vermeld mogen worden dat deze methode minder betrouwbaar is daar deze gevoelig is voor outliers. Indien deze aanwezig zijn is het beter te werken met de getrimde varianties. Hier uit zijn de 5% hoogste en laagste waarden uit de reeks weggelaten. Dit geeft dan een betrouwbaarder beeld. Het klopt dat de parameter d de waarde 1 krijgt en D de waarde 0. Dit is duidelijk te zien in de tabel.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
94,6
97,9
101,7
102,3
103,5
103,6
102,3
101,6
104,3
110,8
112,1
111,1
114,4
115
115,3
114,1
114,8
114,5
114,1
112,3
113
112,2
113,7
113,6
115,8
117,9
120,1
118,8
114,7
110,9
112,9
113,3
114,3
116,5
114,3
115,9
120,1
122,6
122,4
123,1
127,9
130,9
135
134,9
130,2
130,8
132,6
138,6
146,2
149,3
149,9
156,8
158,8
156,7
159,9
158,2
157,5
159,1
160,6
161,6
161,3
159,7
162,4
161,4
161,7
164,3
165,4
156,6
151,5
131,3

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=27980&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=27980&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27980&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)456.9333436853Range70.8Trim Var.378.696491274458
V(Y[t],d=1,D=0)14.0477919863598Range27.8Trim Var.3.65014207650274
V(Y[t],d=2,D=0)13.2929653204566Range21.4Trim Var.6.61214406779663
V(Y[t],d=3,D=0)30.5452691090006Range32.4000000000000Trim Var.15.6175511396845
V(Y[t],d=0,D=1)133.574047186933Range61.5Trim Var.86.026798642534
V(Y[t],d=1,D=1)21.2983897243108Range30.7Trim Var.8.97113725490199
V(Y[t],d=2,D=1)23.0330097402598Range24.9Trim Var.13.0442000000000
V(Y[t],d=3,D=1)49.5549966329969Range36.3Trim Var.25.2884183673472
V(Y[t],d=0,D=2)335.82129468599Range85.5Trim Var.205.117634615385
V(Y[t],d=1,D=2)51.0705858585859Range36.5000000000000Trim Var.26.4410256410257
V(Y[t],d=2,D=2)56.9402748414378Range31.1000000000001Trim Var.33.5088762446659
V(Y[t],d=3,D=2)123.619534883722Range52.8000000000001Trim Var.63.4714114114117

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 456.9333436853 & Range & 70.8 & Trim Var. & 378.696491274458 \tabularnewline
V(Y[t],d=1,D=0) & 14.0477919863598 & Range & 27.8 & Trim Var. & 3.65014207650274 \tabularnewline
V(Y[t],d=2,D=0) & 13.2929653204566 & Range & 21.4 & Trim Var. & 6.61214406779663 \tabularnewline
V(Y[t],d=3,D=0) & 30.5452691090006 & Range & 32.4000000000000 & Trim Var. & 15.6175511396845 \tabularnewline
V(Y[t],d=0,D=1) & 133.574047186933 & Range & 61.5 & Trim Var. & 86.026798642534 \tabularnewline
V(Y[t],d=1,D=1) & 21.2983897243108 & Range & 30.7 & Trim Var. & 8.97113725490199 \tabularnewline
V(Y[t],d=2,D=1) & 23.0330097402598 & Range & 24.9 & Trim Var. & 13.0442000000000 \tabularnewline
V(Y[t],d=3,D=1) & 49.5549966329969 & Range & 36.3 & Trim Var. & 25.2884183673472 \tabularnewline
V(Y[t],d=0,D=2) & 335.82129468599 & Range & 85.5 & Trim Var. & 205.117634615385 \tabularnewline
V(Y[t],d=1,D=2) & 51.0705858585859 & Range & 36.5000000000000 & Trim Var. & 26.4410256410257 \tabularnewline
V(Y[t],d=2,D=2) & 56.9402748414378 & Range & 31.1000000000001 & Trim Var. & 33.5088762446659 \tabularnewline
V(Y[t],d=3,D=2) & 123.619534883722 & Range & 52.8000000000001 & Trim Var. & 63.4714114114117 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27980&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]456.9333436853[/C][C]Range[/C][C]70.8[/C][C]Trim Var.[/C][C]378.696491274458[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]14.0477919863598[/C][C]Range[/C][C]27.8[/C][C]Trim Var.[/C][C]3.65014207650274[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]13.2929653204566[/C][C]Range[/C][C]21.4[/C][C]Trim Var.[/C][C]6.61214406779663[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]30.5452691090006[/C][C]Range[/C][C]32.4000000000000[/C][C]Trim Var.[/C][C]15.6175511396845[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]133.574047186933[/C][C]Range[/C][C]61.5[/C][C]Trim Var.[/C][C]86.026798642534[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]21.2983897243108[/C][C]Range[/C][C]30.7[/C][C]Trim Var.[/C][C]8.97113725490199[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]23.0330097402598[/C][C]Range[/C][C]24.9[/C][C]Trim Var.[/C][C]13.0442000000000[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]49.5549966329969[/C][C]Range[/C][C]36.3[/C][C]Trim Var.[/C][C]25.2884183673472[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]335.82129468599[/C][C]Range[/C][C]85.5[/C][C]Trim Var.[/C][C]205.117634615385[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]51.0705858585859[/C][C]Range[/C][C]36.5000000000000[/C][C]Trim Var.[/C][C]26.4410256410257[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]56.9402748414378[/C][C]Range[/C][C]31.1000000000001[/C][C]Trim Var.[/C][C]33.5088762446659[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]123.619534883722[/C][C]Range[/C][C]52.8000000000001[/C][C]Trim Var.[/C][C]63.4714114114117[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27980&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27980&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)456.9333436853Range70.8Trim Var.378.696491274458
V(Y[t],d=1,D=0)14.0477919863598Range27.8Trim Var.3.65014207650274
V(Y[t],d=2,D=0)13.2929653204566Range21.4Trim Var.6.61214406779663
V(Y[t],d=3,D=0)30.5452691090006Range32.4000000000000Trim Var.15.6175511396845
V(Y[t],d=0,D=1)133.574047186933Range61.5Trim Var.86.026798642534
V(Y[t],d=1,D=1)21.2983897243108Range30.7Trim Var.8.97113725490199
V(Y[t],d=2,D=1)23.0330097402598Range24.9Trim Var.13.0442000000000
V(Y[t],d=3,D=1)49.5549966329969Range36.3Trim Var.25.2884183673472
V(Y[t],d=0,D=2)335.82129468599Range85.5Trim Var.205.117634615385
V(Y[t],d=1,D=2)51.0705858585859Range36.5000000000000Trim Var.26.4410256410257
V(Y[t],d=2,D=2)56.9402748414378Range31.1000000000001Trim Var.33.5088762446659
V(Y[t],d=3,D=2)123.619534883722Range52.8000000000001Trim Var.63.4714114114117


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ; par5 = 1 ; par6 = 0 ; par7 = 0 ;
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')