FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationMon, 01 Dec 2008 03:06:24 -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/01/t122812601274ueed8pej7j7b9.htm/, Retrieved Sun, 05 May 2024 15:30:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26841, Retrieved Sun, 05 May 2024 15:30:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182

Tree of Dependent Computations

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 18:31:28] [b98453cac15ba1066b407e146608df68]
-         [Law of Averages] [Non Stationary Ti...] [2008-12-01 10:06:24] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message

Dataset

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'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26841&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26841&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26841&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'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)41.3740921843687Range27Trim Var.28.2975342155865
V(Y[t],d=1,D=0)1.00152111451819Range2Trim Var.NA
V(Y[t],d=2,D=0)2.03620114259856Range4Trim Var.0
V(Y[t],d=3,D=0)6.11290322580645Range8Trim Var.2.74408100823195
V(Y[t],d=0,D=1)11.1332514222237Range18Trim Var.6.12864088496365
V(Y[t],d=1,D=1)2.00816285142089Range4Trim Var.0
V(Y[t],d=2,D=1)4.05773195876289Range8Trim Var.2.43524699599466
V(Y[t],d=3,D=1)12.0825764675812Range16Trim Var.6.57865786578658
V(Y[t],d=0,D=2)24.4769570986289Range32Trim Var.12.0386188800763
V(Y[t],d=1,D=2)6.17721518987342Range8Trim Var.2.62068965517241
V(Y[t],d=2,D=2)12.4059018206796Range16Trim Var.7.33697244042072
V(Y[t],d=3,D=2)36.805066829111Range32Trim Var.23.1316835796095

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 41.3740921843687 & Range & 27 & Trim Var. & 28.2975342155865 \tabularnewline
V(Y[t],d=1,D=0) & 1.00152111451819 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.03620114259856 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.11290322580645 & Range & 8 & Trim Var. & 2.74408100823195 \tabularnewline
V(Y[t],d=0,D=1) & 11.1332514222237 & Range & 18 & Trim Var. & 6.12864088496365 \tabularnewline
V(Y[t],d=1,D=1) & 2.00816285142089 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.05773195876289 & Range & 8 & Trim Var. & 2.43524699599466 \tabularnewline
V(Y[t],d=3,D=1) & 12.0825764675812 & Range & 16 & Trim Var. & 6.57865786578658 \tabularnewline
V(Y[t],d=0,D=2) & 24.4769570986289 & Range & 32 & Trim Var. & 12.0386188800763 \tabularnewline
V(Y[t],d=1,D=2) & 6.17721518987342 & Range & 8 & Trim Var. & 2.62068965517241 \tabularnewline
V(Y[t],d=2,D=2) & 12.4059018206796 & Range & 16 & Trim Var. & 7.33697244042072 \tabularnewline
V(Y[t],d=3,D=2) & 36.805066829111 & Range & 32 & Trim Var. & 23.1316835796095 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26841&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]41.3740921843687[/C][C]Range[/C][C]27[/C][C]Trim Var.[/C][C]28.2975342155865[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00152111451819[/C][C]Range[/C][C]2[/C][C]Trim Var.[/C][C]NA[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]2.03620114259856[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]6.11290322580645[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.74408100823195[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.1332514222237[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.12864088496365[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.00816285142089[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]4.05773195876289[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.43524699599466[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.0825764675812[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.57865786578658[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]24.4769570986289[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]12.0386188800763[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.17721518987342[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.62068965517241[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.4059018206796[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.33697244042072[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.805066829111[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]23.1316835796095[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26841&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26841&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)41.3740921843687Range27Trim Var.28.2975342155865
V(Y[t],d=1,D=0)1.00152111451819Range2Trim Var.NA
V(Y[t],d=2,D=0)2.03620114259856Range4Trim Var.0
V(Y[t],d=3,D=0)6.11290322580645Range8Trim Var.2.74408100823195
V(Y[t],d=0,D=1)11.1332514222237Range18Trim Var.6.12864088496365
V(Y[t],d=1,D=1)2.00816285142089Range4Trim Var.0
V(Y[t],d=2,D=1)4.05773195876289Range8Trim Var.2.43524699599466
V(Y[t],d=3,D=1)12.0825764675812Range16Trim Var.6.57865786578658
V(Y[t],d=0,D=2)24.4769570986289Range32Trim Var.12.0386188800763
V(Y[t],d=1,D=2)6.17721518987342Range8Trim Var.2.62068965517241
V(Y[t],d=2,D=2)12.4059018206796Range16Trim Var.7.33697244042072
V(Y[t],d=3,D=2)36.805066829111Range32Trim Var.23.1316835796095


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
Parameters (R input):
par1 = 500 ; par2 = 0.5 ;
R code (references can be found in the software module):
n <- as.numeric(par1)
p <- as.numeric(par2)
heads=rbinom(n-1,1,p)
a=2*(heads)-1
b=diffinv(a,xi=0)
c=1:n
pheads=(diffinv(heads,xi=.5))/c
bitmap(file='test1.png')
op=par(mfrow=c(2,1))
plot(c,b,type='n',main='Law of Averages',xlab='Toss Number',ylab='Excess of Heads',lwd=2,cex.lab=1.5,cex.main=2)
lines(c,b,col='red')
lines(c,rep(0,n),col='black')
plot(c,pheads,type='n',xlab='Toss Number',ylab='Proportion of Heads',lwd=2,cex.lab=1.5)
lines(c,pheads,col='blue')
lines(c,rep(.5,n),col='black')
par(op)
dev.off()
b
par1 <- as.numeric(12)
x <- as.array(b)
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')