FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 06:28:43 -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/t1228224573l8mn0jtvywovyo3.htm/, Retrieved Tue, 10 Feb 2026 14:14:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27752, Retrieved Tue, 10 Feb 2026 14:14:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact407

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] [] [2008-12-02 13:28:43] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-12-04 09:52:51 [72e979bcc364082694890d2eccc1a66f] [reply] 
Er is hier inderdaad geen eenduidig antwoord uit op te maken aangezien de varianties heel dicht bij elkaar. Het lijkt me dan ook een goed idee om ze allebei te testen.
2008-12-05 20:00:57 [Bert Moons] [reply] 
Het is inderdaad opvallend dat de variaties zo dicht bij elkaar liggen, beiden proberen is dus geen overbodige luxe.
2008-12-06 16:28:43 [Bénédicte Soens] [reply] 
Aangezien er hier twijfel is over het aantal keer dat er gedifferentieerd moet worden, zou ik voorstellen aan de student om te kijken naar de autocorrelatie en de spectraal analyse. Daarbij kan je de verschillende differentiaties uitproberen en zien wat er de beste zijn in de grafiek of tabel.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4,56
4,41
4,33
4,20
4,25
4,25
4,19
4,17
4,21
4,21
4,17
4,16
4,19
4,08
4,06
3,98
3,82
3,82
3,72
3,56
3,57
3,49
3,32
3,23
3,04
3,00
2,82
2,73
2,59
2,58
2,53
2,31
2,31
2,30
2,07
2,07
2,06
2,06
2,05
2,05
2,05
2,05
2,05
2,06
2,07
2,08
2,05
2,03
2,02
2,02
2,01
2,01
2,01
2,01
2,01
2,01
2,03
2,04
2,03
2,05
2,08
2,06
2,09
2,19
2,56
2,54
2,63
2,78
2,84
3,02
3,28
3,29
3,29
3,29
3,32
3,34
3,32
3,30
3,30
3,30
3,31
3,35
3,48
3,76
4,06
4,51
4,52
4,53
4,63
4,79
4,77
4,77
4,77
4,81
4,83
4,76
4,61

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' @ 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27752&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27752&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27752&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' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.95300612113402Range2.82Trim Var.0.8043181232493
V(Y[t],d=1,D=0)0.0118513048245614Range0.68Trim Var.0.00408623803009576
V(Y[t],d=2,D=0)0.0117425531914894Range0.71Trim Var.0.00449193277310925
V(Y[t],d=3,D=0)0.0329318348204072Range1.16Trim Var.0.0139502438324728
V(Y[t],d=0,D=1)0.715847675070028Range2.75Trim Var.0.546695834875972
V(Y[t],d=1,D=1)0.0198761904761905Range0.9Trim Var.0.00691144020733061
V(Y[t],d=2,D=1)0.022229356450191Range0.87Trim Var.0.00966411719939116
V(Y[t],d=3,D=1)0.0619583258054803Range1.36Trim Var.0.0304478090766823
V(Y[t],d=0,D=2)0.441470852359209Range2.32Trim Var.0.342123653846154
V(Y[t],d=1,D=2)0.0531217527386541Range1.27Trim Var.0.0209499007936508
V(Y[t],d=2,D=2)0.0619175855130784Range1.42Trim Var.0.0290544290834613
V(Y[t],d=3,D=2)0.168605714285714Range2.34Trim Var.0.0954670809095715

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.95300612113402 & Range & 2.82 & Trim Var. & 0.8043181232493 \tabularnewline
V(Y[t],d=1,D=0) & 0.0118513048245614 & Range & 0.68 & Trim Var. & 0.00408623803009576 \tabularnewline
V(Y[t],d=2,D=0) & 0.0117425531914894 & Range & 0.71 & Trim Var. & 0.00449193277310925 \tabularnewline
V(Y[t],d=3,D=0) & 0.0329318348204072 & Range & 1.16 & Trim Var. & 0.0139502438324728 \tabularnewline
V(Y[t],d=0,D=1) & 0.715847675070028 & Range & 2.75 & Trim Var. & 0.546695834875972 \tabularnewline
V(Y[t],d=1,D=1) & 0.0198761904761905 & Range & 0.9 & Trim Var. & 0.00691144020733061 \tabularnewline
V(Y[t],d=2,D=1) & 0.022229356450191 & Range & 0.87 & Trim Var. & 0.00966411719939116 \tabularnewline
V(Y[t],d=3,D=1) & 0.0619583258054803 & Range & 1.36 & Trim Var. & 0.0304478090766823 \tabularnewline
V(Y[t],d=0,D=2) & 0.441470852359209 & Range & 2.32 & Trim Var. & 0.342123653846154 \tabularnewline
V(Y[t],d=1,D=2) & 0.0531217527386541 & Range & 1.27 & Trim Var. & 0.0209499007936508 \tabularnewline
V(Y[t],d=2,D=2) & 0.0619175855130784 & Range & 1.42 & Trim Var. & 0.0290544290834613 \tabularnewline
V(Y[t],d=3,D=2) & 0.168605714285714 & Range & 2.34 & Trim Var. & 0.0954670809095715 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27752&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.95300612113402[/C][C]Range[/C][C]2.82[/C][C]Trim Var.[/C][C]0.8043181232493[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.0118513048245614[/C][C]Range[/C][C]0.68[/C][C]Trim Var.[/C][C]0.00408623803009576[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.0117425531914894[/C][C]Range[/C][C]0.71[/C][C]Trim Var.[/C][C]0.00449193277310925[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]0.0329318348204072[/C][C]Range[/C][C]1.16[/C][C]Trim Var.[/C][C]0.0139502438324728[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.715847675070028[/C][C]Range[/C][C]2.75[/C][C]Trim Var.[/C][C]0.546695834875972[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.0198761904761905[/C][C]Range[/C][C]0.9[/C][C]Trim Var.[/C][C]0.00691144020733061[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.022229356450191[/C][C]Range[/C][C]0.87[/C][C]Trim Var.[/C][C]0.00966411719939116[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.0619583258054803[/C][C]Range[/C][C]1.36[/C][C]Trim Var.[/C][C]0.0304478090766823[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.441470852359209[/C][C]Range[/C][C]2.32[/C][C]Trim Var.[/C][C]0.342123653846154[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.0531217527386541[/C][C]Range[/C][C]1.27[/C][C]Trim Var.[/C][C]0.0209499007936508[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.0619175855130784[/C][C]Range[/C][C]1.42[/C][C]Trim Var.[/C][C]0.0290544290834613[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]0.168605714285714[/C][C]Range[/C][C]2.34[/C][C]Trim Var.[/C][C]0.0954670809095715[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27752&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27752&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)0.95300612113402Range2.82Trim Var.0.8043181232493
V(Y[t],d=1,D=0)0.0118513048245614Range0.68Trim Var.0.00408623803009576
V(Y[t],d=2,D=0)0.0117425531914894Range0.71Trim Var.0.00449193277310925
V(Y[t],d=3,D=0)0.0329318348204072Range1.16Trim Var.0.0139502438324728
V(Y[t],d=0,D=1)0.715847675070028Range2.75Trim Var.0.546695834875972
V(Y[t],d=1,D=1)0.0198761904761905Range0.9Trim Var.0.00691144020733061
V(Y[t],d=2,D=1)0.022229356450191Range0.87Trim Var.0.00966411719939116
V(Y[t],d=3,D=1)0.0619583258054803Range1.36Trim Var.0.0304478090766823
V(Y[t],d=0,D=2)0.441470852359209Range2.32Trim Var.0.342123653846154
V(Y[t],d=1,D=2)0.0531217527386541Range1.27Trim Var.0.0209499007936508
V(Y[t],d=2,D=2)0.0619175855130784Range1.42Trim Var.0.0290544290834613
V(Y[t],d=3,D=2)0.168605714285714Range2.34Trim Var.0.0954670809095715


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')