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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, 02 Dec 2008 12:52:01 -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/2008/Dec/02/t1228247588n5ldjvh62t2aw4m.htm/, Retrieved Sat, 14 Feb 2026 18:18:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28291, Retrieved Sat, 14 Feb 2026 18:18:12 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

gdm

Estimated Impact

482

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 18:40:39] [b98453cac15ba1066b407e146608df68]
F       [Law of Averages] [WS7 Task 4] [2008-11-30 15:52:14] [11ac052cc87d77b9933b02bea117068e]
- RMPD    [Spectral Analysis] [WS7 Task 6d] [2008-12-02 18:21:54] [11ac052cc87d77b9933b02bea117068e]
- RMPD        [Variance Reduction Matrix] [WS7 Task 8c] [2008-12-02 19:52:01] [99f79d508deef838ee89a56fb32f134e] [Current]

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Dataseries X:

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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

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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28291&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28291&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28291&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	'George Udny Yule' @ 72.249.76.132

Variance Reduction Matrix
V(Y[t],d=0,D=0)	0.95300612113402	Range	2.82	Trim Var.	0.8043181232493
V(Y[t],d=1,D=0)	0.0118513048245614	Range	0.68	Trim Var.	0.00408623803009576
V(Y[t],d=2,D=0)	0.0117425531914894	Range	0.71	Trim Var.	0.00449193277310925
V(Y[t],d=3,D=0)	0.0329318348204072	Range	1.16	Trim Var.	0.0139502438324728
V(Y[t],d=0,D=1)	0.715847675070028	Range	2.75	Trim Var.	0.546695834875972
V(Y[t],d=1,D=1)	0.0198761904761905	Range	0.9	Trim Var.	0.00691144020733061
V(Y[t],d=2,D=1)	0.022229356450191	Range	0.87	Trim Var.	0.00966411719939116
V(Y[t],d=3,D=1)	0.0619583258054803	Range	1.36	Trim Var.	0.0304478090766823
V(Y[t],d=0,D=2)	0.441470852359209	Range	2.32	Trim Var.	0.342123653846154
V(Y[t],d=1,D=2)	0.0531217527386541	Range	1.27	Trim Var.	0.0209499007936508
V(Y[t],d=2,D=2)	0.0619175855130784	Range	1.42	Trim Var.	0.0290544290834613
V(Y[t],d=3,D=2)	0.168605714285714	Range	2.34	Trim 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=28291&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=28291&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28291&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)	0.95300612113402	Range	2.82	Trim Var.	0.8043181232493
V(Y[t],d=1,D=0)	0.0118513048245614	Range	0.68	Trim Var.	0.00408623803009576
V(Y[t],d=2,D=0)	0.0117425531914894	Range	0.71	Trim Var.	0.00449193277310925
V(Y[t],d=3,D=0)	0.0329318348204072	Range	1.16	Trim Var.	0.0139502438324728
V(Y[t],d=0,D=1)	0.715847675070028	Range	2.75	Trim Var.	0.546695834875972
V(Y[t],d=1,D=1)	0.0198761904761905	Range	0.9	Trim Var.	0.00691144020733061
V(Y[t],d=2,D=1)	0.022229356450191	Range	0.87	Trim Var.	0.00966411719939116
V(Y[t],d=3,D=1)	0.0619583258054803	Range	1.36	Trim Var.	0.0304478090766823
V(Y[t],d=0,D=2)	0.441470852359209	Range	2.32	Trim Var.	0.342123653846154
V(Y[t],d=1,D=2)	0.0531217527386541	Range	1.27	Trim Var.	0.0209499007936508
V(Y[t],d=2,D=2)	0.0619175855130784	Range	1.42	Trim Var.	0.0290544290834613
V(Y[t],d=3,D=2)	0.168605714285714	Range	2.34	Trim Var.	0.0954670809095715

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code