FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 16 Dec 2015 19:29:45 +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/2015/Dec/16/t1450294192ab3v7crz39i1466.htm/, Retrieved Thu, 16 May 2024 07:15:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286740, Retrieved Thu, 16 May 2024 07:15:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2015-12-16 19:09:29] [c4d175d45982400f45768592120a8602]
- RMP   [Mean Plot] [] [2015-12-16 19:15:48] [c4d175d45982400f45768592120a8602]
- RM        [Variance Reduction Matrix] [] [2015-12-16 19:29:45] [0f06e4fdd8087d4b3abca42184bf2a00] [Current]
- RMP         [(Partial) Autocorrelation Function] [] [2015-12-16 19:34:59] [c4d175d45982400f45768592120a8602]
- RMP         [(Partial) Autocorrelation Function] [] [2015-12-16 19:37:59] [c4d175d45982400f45768592120a8602]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
87.29
88.19
89.1
89.1
103.65
127.75
125.47
125.47
109.11
100.01
95.01
85.01
86.83
86.83
86.83
86.83
100.47
111.38
105.47
102.74
105.01
96.38
94.1
86.83
92.74
93.2
95.47
96.38
99.56
120.47
123.2
114.11
120.93
102.74
101.83
95.47
100.01
100.01
98.2
100.01
103.65
114.56
134.11
131.84
113.65
107.29
102.29
94.56
97.29
98.2
95.47
100.47
116.38
117.29
140.93
120.02
111.38
108.65
105.92
99.1
101.83
102.74
102.74
105.47
108.65
139.57
110.47
118.65
120.02
109.11
108.2
101.38
106.38
108.65
107.74
105.92
129.56
139.11
125.93
123.65
118.65
110.47
110.02
100.47
104.1
106.6
105.5
107.5
117.9
136.3
156.8
135.8
130
117.5
115.8
105.5
111.6
113.2
113.1
112.5
120
147.6
149.9
131.2
134.6
122.2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286740&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286740&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)231.37Range71.79Trim Var.140.243
V(Y[t],d=1,D=0)108.644Range60.02Trim Var.51.2978
V(Y[t],d=2,D=0)212.733Range97.3Trim Var.92.2416
V(Y[t],d=3,D=0)635.383Range185.06Trim Var.266.862
V(Y[t],d=0,D=1)78.086Range61.33Trim Var.29.6646
V(Y[t],d=1,D=1)124.953Range86.42Trim Var.40.0781
V(Y[t],d=2,D=1)383.857Range164.58Trim Var.120.462
V(Y[t],d=3,D=1)1304.9Range290.07Trim Var.389.836
V(Y[t],d=0,D=2)208.769Range83.69Trim Var.77.0407
V(Y[t],d=1,D=2)374.593Range125.49Trim Var.111.69
V(Y[t],d=2,D=2)1196.22Range228.25Trim Var.403.474
V(Y[t],d=3,D=2)4162.28Range432.86Trim Var.1336.52

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 231.37 & Range & 71.79 & Trim Var. & 140.243 \tabularnewline
V(Y[t],d=1,D=0) & 108.644 & Range & 60.02 & Trim Var. & 51.2978 \tabularnewline
V(Y[t],d=2,D=0) & 212.733 & Range & 97.3 & Trim Var. & 92.2416 \tabularnewline
V(Y[t],d=3,D=0) & 635.383 & Range & 185.06 & Trim Var. & 266.862 \tabularnewline
V(Y[t],d=0,D=1) & 78.086 & Range & 61.33 & Trim Var. & 29.6646 \tabularnewline
V(Y[t],d=1,D=1) & 124.953 & Range & 86.42 & Trim Var. & 40.0781 \tabularnewline
V(Y[t],d=2,D=1) & 383.857 & Range & 164.58 & Trim Var. & 120.462 \tabularnewline
V(Y[t],d=3,D=1) & 1304.9 & Range & 290.07 & Trim Var. & 389.836 \tabularnewline
V(Y[t],d=0,D=2) & 208.769 & Range & 83.69 & Trim Var. & 77.0407 \tabularnewline
V(Y[t],d=1,D=2) & 374.593 & Range & 125.49 & Trim Var. & 111.69 \tabularnewline
V(Y[t],d=2,D=2) & 1196.22 & Range & 228.25 & Trim Var. & 403.474 \tabularnewline
V(Y[t],d=3,D=2) & 4162.28 & Range & 432.86 & Trim Var. & 1336.52 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286740&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]231.37[/C][C]Range[/C][C]71.79[/C][C]Trim Var.[/C][C]140.243[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]108.644[/C][C]Range[/C][C]60.02[/C][C]Trim Var.[/C][C]51.2978[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]212.733[/C][C]Range[/C][C]97.3[/C][C]Trim Var.[/C][C]92.2416[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]635.383[/C][C]Range[/C][C]185.06[/C][C]Trim Var.[/C][C]266.862[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]78.086[/C][C]Range[/C][C]61.33[/C][C]Trim Var.[/C][C]29.6646[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]124.953[/C][C]Range[/C][C]86.42[/C][C]Trim Var.[/C][C]40.0781[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]383.857[/C][C]Range[/C][C]164.58[/C][C]Trim Var.[/C][C]120.462[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1304.9[/C][C]Range[/C][C]290.07[/C][C]Trim Var.[/C][C]389.836[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]208.769[/C][C]Range[/C][C]83.69[/C][C]Trim Var.[/C][C]77.0407[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]374.593[/C][C]Range[/C][C]125.49[/C][C]Trim Var.[/C][C]111.69[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1196.22[/C][C]Range[/C][C]228.25[/C][C]Trim Var.[/C][C]403.474[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]4162.28[/C][C]Range[/C][C]432.86[/C][C]Trim Var.[/C][C]1336.52[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286740&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)231.37Range71.79Trim Var.140.243
V(Y[t],d=1,D=0)108.644Range60.02Trim Var.51.2978
V(Y[t],d=2,D=0)212.733Range97.3Trim Var.92.2416
V(Y[t],d=3,D=0)635.383Range185.06Trim Var.266.862
V(Y[t],d=0,D=1)78.086Range61.33Trim Var.29.6646
V(Y[t],d=1,D=1)124.953Range86.42Trim Var.40.0781
V(Y[t],d=2,D=1)383.857Range164.58Trim Var.120.462
V(Y[t],d=3,D=1)1304.9Range290.07Trim Var.389.836
V(Y[t],d=0,D=2)208.769Range83.69Trim Var.77.0407
V(Y[t],d=1,D=2)374.593Range125.49Trim Var.111.69
V(Y[t],d=2,D=2)1196.22Range228.25Trim Var.403.474
V(Y[t],d=3,D=2)4162.28Range432.86Trim Var.1336.52


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.orig <- length(x)
x <- na.omit(x)
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)
if(n.orig!=n) {
a<-table.row.start(a)
a<-table.element(a,'Warning: NAs were removed from the time series! The results shown below will only be correct if the NAs are all located at the start and/or end of the time series.',6,F)
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,signif(var(myx), digits=6))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,signif(max(myx)-min(myx), digits=6))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,signif(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()