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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 computationWed, 29 Dec 2010 18:13:34 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/29/t1293646335lqr7n6pyrubf831.htm/, Retrieved Fri, 03 May 2024 14:20:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117013, Retrieved Fri, 03 May 2024 14:20:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

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...] [2010-12-29 18:13:34] [76d5107cfd0c78d23318a36a1ce43bff] [Current]
- R P     [Variance Reduction Matrix] [] [2011-12-21 20:42:17] [3931071255a6f7f4a767409781cc5f7d]
-   P       [Variance Reduction Matrix] [] [2011-12-21 21:15:28] [3931071255a6f7f4a767409781cc5f7d]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5.921
4.561
4.399
4.249
4.211
4.081
4.131
4.071
3.841
4.109
4.354
4.402
4.954
4.137
4.561
4.210
4.429
4.190
4.196
4.226
3.878
3.931
4.115
4.679
5.385
4.387
4.552
4.325
4.179
4.054
4.075
4.147
4.046
4.368
4.097
4.821
4.965
4.425
4.601
4.521
4.193
4.039
4.099
4.109
4.024
4.245
4.252
5.136
5.037
4.230
4.408
4.119
4.083
4.010
4.148
3.952
3.843
4.164
4.075
4.708

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' @ www.wessa.org

\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' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117013&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' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117013&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117013&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' @ www.wessa.org






Variance Reduction Matrix
V(Y[t],d=0,D=0)0.148368439548023Range2.08Trim Var.0.0696727798742138
V(Y[t],d=1,D=0)0.154402974868498Range2.244Trim Var.0.0704002343976778
V(Y[t],d=2,D=0)0.338399252571083Range2.945Trim Var.0.179807271116139
V(Y[t],d=3,D=0)1.05155883897243Range4.883Trim Var.0.597813720784314
V(Y[t],d=0,D=1)0.0605515101950355Range1.404Trim Var.0.0268815081300813
V(Y[t],d=1,D=1)0.0617579500462535Range1.148Trim Var.0.0321148512195122
V(Y[t],d=2,D=1)0.134968285990338Range1.807Trim Var.0.0681014557692308
V(Y[t],d=3,D=1)0.442389336363636Range3.209Trim Var.0.217144025641026
V(Y[t],d=0,D=2)0.171203828571429Range2.249Trim Var.0.0731103830645161
V(Y[t],d=1,D=2)0.160471440336134Range1.578Trim Var.0.109331825806452
V(Y[t],d=2,D=2)0.339417198752228Range2.399Trim Var.0.207253481609195
V(Y[t],d=3,D=2)1.10814694318182Range3.909Trim Var.0.760405564039408

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 0.148368439548023 & Range & 2.08 & Trim Var. & 0.0696727798742138 \tabularnewline
V(Y[t],d=1,D=0) & 0.154402974868498 & Range & 2.244 & Trim Var. & 0.0704002343976778 \tabularnewline
V(Y[t],d=2,D=0) & 0.338399252571083 & Range & 2.945 & Trim Var. & 0.179807271116139 \tabularnewline
V(Y[t],d=3,D=0) & 1.05155883897243 & Range & 4.883 & Trim Var. & 0.597813720784314 \tabularnewline
V(Y[t],d=0,D=1) & 0.0605515101950355 & Range & 1.404 & Trim Var. & 0.0268815081300813 \tabularnewline
V(Y[t],d=1,D=1) & 0.0617579500462535 & Range & 1.148 & Trim Var. & 0.0321148512195122 \tabularnewline
V(Y[t],d=2,D=1) & 0.134968285990338 & Range & 1.807 & Trim Var. & 0.0681014557692308 \tabularnewline
V(Y[t],d=3,D=1) & 0.442389336363636 & Range & 3.209 & Trim Var. & 0.217144025641026 \tabularnewline
V(Y[t],d=0,D=2) & 0.171203828571429 & Range & 2.249 & Trim Var. & 0.0731103830645161 \tabularnewline
V(Y[t],d=1,D=2) & 0.160471440336134 & Range & 1.578 & Trim Var. & 0.109331825806452 \tabularnewline
V(Y[t],d=2,D=2) & 0.339417198752228 & Range & 2.399 & Trim Var. & 0.207253481609195 \tabularnewline
V(Y[t],d=3,D=2) & 1.10814694318182 & Range & 3.909 & Trim Var. & 0.760405564039408 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117013&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]0.148368439548023[/C][C]Range[/C][C]2.08[/C][C]Trim Var.[/C][C]0.0696727798742138[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.154402974868498[/C][C]Range[/C][C]2.244[/C][C]Trim Var.[/C][C]0.0704002343976778[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]0.338399252571083[/C][C]Range[/C][C]2.945[/C][C]Trim Var.[/C][C]0.179807271116139[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1.05155883897243[/C][C]Range[/C][C]4.883[/C][C]Trim Var.[/C][C]0.597813720784314[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]0.0605515101950355[/C][C]Range[/C][C]1.404[/C][C]Trim Var.[/C][C]0.0268815081300813[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]0.0617579500462535[/C][C]Range[/C][C]1.148[/C][C]Trim Var.[/C][C]0.0321148512195122[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]0.134968285990338[/C][C]Range[/C][C]1.807[/C][C]Trim Var.[/C][C]0.0681014557692308[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]0.442389336363636[/C][C]Range[/C][C]3.209[/C][C]Trim Var.[/C][C]0.217144025641026[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]0.171203828571429[/C][C]Range[/C][C]2.249[/C][C]Trim Var.[/C][C]0.0731103830645161[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]0.160471440336134[/C][C]Range[/C][C]1.578[/C][C]Trim Var.[/C][C]0.109331825806452[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]0.339417198752228[/C][C]Range[/C][C]2.399[/C][C]Trim Var.[/C][C]0.207253481609195[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1.10814694318182[/C][C]Range[/C][C]3.909[/C][C]Trim Var.[/C][C]0.760405564039408[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117013&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117013&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)0.148368439548023Range2.08Trim Var.0.0696727798742138
V(Y[t],d=1,D=0)0.154402974868498Range2.244Trim Var.0.0704002343976778
V(Y[t],d=2,D=0)0.338399252571083Range2.945Trim Var.0.179807271116139
V(Y[t],d=3,D=0)1.05155883897243Range4.883Trim Var.0.597813720784314
V(Y[t],d=0,D=1)0.0605515101950355Range1.404Trim Var.0.0268815081300813
V(Y[t],d=1,D=1)0.0617579500462535Range1.148Trim Var.0.0321148512195122
V(Y[t],d=2,D=1)0.134968285990338Range1.807Trim Var.0.0681014557692308
V(Y[t],d=3,D=1)0.442389336363636Range3.209Trim Var.0.217144025641026
V(Y[t],d=0,D=2)0.171203828571429Range2.249Trim Var.0.0731103830645161
V(Y[t],d=1,D=2)0.160471440336134Range1.578Trim Var.0.109331825806452
V(Y[t],d=2,D=2)0.339417198752228Range2.399Trim Var.0.207253481609195
V(Y[t],d=3,D=2)1.10814694318182Range3.909Trim Var.0.760405564039408


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(myx,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')
bitmap(file='pic0.png')
op <- par(mfrow=c(2,2))
plot(x,type='l',xlab='time',ylab='value',main='d=0, D=0')
plot(diff(x,lag=1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=0')
plot(diff(x,lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=0, D=1')
plot(diff(diff(x,lag=1,differences=1),lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=1')
par(op)
dev.off()