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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationSat, 13 Dec 2008 07:05:35 -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/13/t1229177288f5z07u4q4w8913m.htm/, Retrieved Thu, 12 Feb 2026 13:43:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33106, Retrieved Thu, 12 Feb 2026 13:43:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact508

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [Variance reductio...] [2007-11-30 14:45:44] [6c50c82828af94f83a614a64264ea782]
-    D    [Variance Reduction Matrix] [VRM: Bel 20] [2008-12-13 14:05:35] [81dc0ee785f23261ccd6abf7aef76c2a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3032,93
3045,78
3110,52
3013,24
2987,1
2995,55
2833,18
2848,96
2794,83
2845,26
2915,02
2892,63
2604,42
2641,65
2659,81
2638,53
2720,25
2745,88
2735,7
2811,7
2799,43
2555,28
2304,98
2214,95
2065,81
1940,49
2042
1995,37
1946,81
1765,9
1635,25
1833,42
1910,43
1959,67
1969,6
2061,41
2093,48
2120,88
2174,56
2196,72
2350,44
2440,25
2408,64
2472,81
2407,6
2454,62
2448,05
2497,84
2645,64
2756,76
2849,27
2921,44
2981,85
3080,58
3106,22
3119,31
3061,26
3097,31
3161,69
3257,16
3277,01
3295,32
3363,99
3494,17
3667,03
3813,06
3917,96
3895,51
3801,06
3570,12
3701,61
3862,27
3970,1
4138,52
4199,75
4290,89
4443,91
4502,64
4356,98
4591,27
4696,96
4621,4
4562,84
4202,52
4296,49
4435,23
4105,18
4116,68
3844,49
3720,98
3674,4
3857,62
3801,06
3504,37
3032,6
3047,03
2962,34
2197,82
2014,45

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=33106&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=33106&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33106&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)631167.526877386Range3061.71Trim Var.480007.146104826
V(Y[t],d=1,D=0)23271.5594052598Range998.81Trim Var.10889.6867585031
V(Y[t],d=2,D=0)33369.1774374141Range1260.98Trim Var.14198.2223864475
V(Y[t],d=3,D=0)89333.0528701316Range1886.22Trim Var.38645.9883220384
V(Y[t],d=0,D=1)548597.603251243Range3288.69Trim Var.363369.792156801
V(Y[t],d=1,D=1)36910.6986129685Range1278.01Trim Var.15217.5771823684
V(Y[t],d=2,D=1)59444.5703390756Range1774.54Trim Var.19407.3166689009
V(Y[t],d=3,D=1)143673.059402696Range3115.91Trim Var.43060.3844156979
V(Y[t],d=0,D=2)821099.220138739Range4407.96Trim Var.448933.047758254
V(Y[t],d=1,D=2)82126.5325679377Range1769.31Trim Var.42688.8309361539
V(Y[t],d=2,D=2)128837.614222222Range2472.07000000000Trim Var.44352.4338033653
V(Y[t],d=3,D=2)289925.442055086Range4299.74Trim Var.104581.029328943

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 631167.526877386 & Range & 3061.71 & Trim Var. & 480007.146104826 \tabularnewline
V(Y[t],d=1,D=0) & 23271.5594052598 & Range & 998.81 & Trim Var. & 10889.6867585031 \tabularnewline
V(Y[t],d=2,D=0) & 33369.1774374141 & Range & 1260.98 & Trim Var. & 14198.2223864475 \tabularnewline
V(Y[t],d=3,D=0) & 89333.0528701316 & Range & 1886.22 & Trim Var. & 38645.9883220384 \tabularnewline
V(Y[t],d=0,D=1) & 548597.603251243 & Range & 3288.69 & Trim Var. & 363369.792156801 \tabularnewline
V(Y[t],d=1,D=1) & 36910.6986129685 & Range & 1278.01 & Trim Var. & 15217.5771823684 \tabularnewline
V(Y[t],d=2,D=1) & 59444.5703390756 & Range & 1774.54 & Trim Var. & 19407.3166689009 \tabularnewline
V(Y[t],d=3,D=1) & 143673.059402696 & Range & 3115.91 & Trim Var. & 43060.3844156979 \tabularnewline
V(Y[t],d=0,D=2) & 821099.220138739 & Range & 4407.96 & Trim Var. & 448933.047758254 \tabularnewline
V(Y[t],d=1,D=2) & 82126.5325679377 & Range & 1769.31 & Trim Var. & 42688.8309361539 \tabularnewline
V(Y[t],d=2,D=2) & 128837.614222222 & Range & 2472.07000000000 & Trim Var. & 44352.4338033653 \tabularnewline
V(Y[t],d=3,D=2) & 289925.442055086 & Range & 4299.74 & Trim Var. & 104581.029328943 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33106&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]631167.526877386[/C][C]Range[/C][C]3061.71[/C][C]Trim Var.[/C][C]480007.146104826[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]23271.5594052598[/C][C]Range[/C][C]998.81[/C][C]Trim Var.[/C][C]10889.6867585031[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]33369.1774374141[/C][C]Range[/C][C]1260.98[/C][C]Trim Var.[/C][C]14198.2223864475[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]89333.0528701316[/C][C]Range[/C][C]1886.22[/C][C]Trim Var.[/C][C]38645.9883220384[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]548597.603251243[/C][C]Range[/C][C]3288.69[/C][C]Trim Var.[/C][C]363369.792156801[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]36910.6986129685[/C][C]Range[/C][C]1278.01[/C][C]Trim Var.[/C][C]15217.5771823684[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]59444.5703390756[/C][C]Range[/C][C]1774.54[/C][C]Trim Var.[/C][C]19407.3166689009[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]143673.059402696[/C][C]Range[/C][C]3115.91[/C][C]Trim Var.[/C][C]43060.3844156979[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]821099.220138739[/C][C]Range[/C][C]4407.96[/C][C]Trim Var.[/C][C]448933.047758254[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]82126.5325679377[/C][C]Range[/C][C]1769.31[/C][C]Trim Var.[/C][C]42688.8309361539[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]128837.614222222[/C][C]Range[/C][C]2472.07000000000[/C][C]Trim Var.[/C][C]44352.4338033653[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]289925.442055086[/C][C]Range[/C][C]4299.74[/C][C]Trim Var.[/C][C]104581.029328943[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33106&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33106&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)631167.526877386Range3061.71Trim Var.480007.146104826
V(Y[t],d=1,D=0)23271.5594052598Range998.81Trim Var.10889.6867585031
V(Y[t],d=2,D=0)33369.1774374141Range1260.98Trim Var.14198.2223864475
V(Y[t],d=3,D=0)89333.0528701316Range1886.22Trim Var.38645.9883220384
V(Y[t],d=0,D=1)548597.603251243Range3288.69Trim Var.363369.792156801
V(Y[t],d=1,D=1)36910.6986129685Range1278.01Trim Var.15217.5771823684
V(Y[t],d=2,D=1)59444.5703390756Range1774.54Trim Var.19407.3166689009
V(Y[t],d=3,D=1)143673.059402696Range3115.91Trim Var.43060.3844156979
V(Y[t],d=0,D=2)821099.220138739Range4407.96Trim Var.448933.047758254
V(Y[t],d=1,D=2)82126.5325679377Range1769.31Trim Var.42688.8309361539
V(Y[t],d=2,D=2)128837.614222222Range2472.07000000000Trim Var.44352.4338033653
V(Y[t],d=3,D=2)289925.442055086Range4299.74Trim Var.104581.029328943


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')