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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationMon, 01 Dec 2008 14:36:50 -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/t1228167440fdetjr6rny2x5k6.htm/, Retrieved Sun, 05 May 2024 10:31:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27432, Retrieved Sun, 05 May 2024 10:31:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117

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]
F       [Law of Averages] [Q3] [2008-11-28 12:56:39] [87cabf13a90315c7085b765dcebb7412]
-           [Law of Averages] [] [2008-12-01 21:36:50] [f6a332ba2d530c028d935c5a5bbb53af] [Current]
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Dataset

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'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=27432&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=27432&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27432&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'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)58.7473507014028Range30Trim Var.41.2040444567423
V(Y[t],d=1,D=0)1.00197181511618Range2Trim Var.NA
V(Y[t],d=2,D=0)1.85110663983903Range4Trim Var.0
V(Y[t],d=3,D=0)5.49993509443759Range8Trim Var.2.43739177489178
V(Y[t],d=0,D=1)14.5373817618743Range16Trim Var.8.49257517063272
V(Y[t],d=1,D=1)2.01630880252829Range4Trim Var.0
V(Y[t],d=2,D=1)3.65359127741717Range8Trim Var.0.936833365267931
V(Y[t],d=3,D=1)10.6942148760331Range16Trim Var.6.2503902939471
V(Y[t],d=0,D=2)25.0909862892525Range28Trim Var.11.9337903100171
V(Y[t],d=1,D=2)6.18549411503442Range8Trim Var.2.63136053749629
V(Y[t],d=2,D=2)11.0697496008064Range16Trim Var.6.47499880147658
V(Y[t],d=3,D=2)32.0507757910202Range30Trim Var.19.2156844307577

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 58.7473507014028 & Range & 30 & Trim Var. & 41.2040444567423 \tabularnewline
V(Y[t],d=1,D=0) & 1.00197181511618 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.85110663983903 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.49993509443759 & Range & 8 & Trim Var. & 2.43739177489178 \tabularnewline
V(Y[t],d=0,D=1) & 14.5373817618743 & Range & 16 & Trim Var. & 8.49257517063272 \tabularnewline
V(Y[t],d=1,D=1) & 2.01630880252829 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.65359127741717 & Range & 8 & Trim Var. & 0.936833365267931 \tabularnewline
V(Y[t],d=3,D=1) & 10.6942148760331 & Range & 16 & Trim Var. & 6.2503902939471 \tabularnewline
V(Y[t],d=0,D=2) & 25.0909862892525 & Range & 28 & Trim Var. & 11.9337903100171 \tabularnewline
V(Y[t],d=1,D=2) & 6.18549411503442 & Range & 8 & Trim Var. & 2.63136053749629 \tabularnewline
V(Y[t],d=2,D=2) & 11.0697496008064 & Range & 16 & Trim Var. & 6.47499880147658 \tabularnewline
V(Y[t],d=3,D=2) & 32.0507757910202 & Range & 30 & Trim Var. & 19.2156844307577 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27432&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]58.7473507014028[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]41.2040444567423[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00197181511618[/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]1.85110663983903[/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]5.49993509443759[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.43739177489178[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]14.5373817618743[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]8.49257517063272[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.01630880252829[/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]3.65359127741717[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.936833365267931[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.6942148760331[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.2503902939471[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]25.0909862892525[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]11.9337903100171[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.18549411503442[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.63136053749629[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.0697496008064[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.47499880147658[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]32.0507757910202[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]19.2156844307577[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27432&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27432&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)58.7473507014028Range30Trim Var.41.2040444567423
V(Y[t],d=1,D=0)1.00197181511618Range2Trim Var.NA
V(Y[t],d=2,D=0)1.85110663983903Range4Trim Var.0
V(Y[t],d=3,D=0)5.49993509443759Range8Trim Var.2.43739177489178
V(Y[t],d=0,D=1)14.5373817618743Range16Trim Var.8.49257517063272
V(Y[t],d=1,D=1)2.01630880252829Range4Trim Var.0
V(Y[t],d=2,D=1)3.65359127741717Range8Trim Var.0.936833365267931
V(Y[t],d=3,D=1)10.6942148760331Range16Trim Var.6.2503902939471
V(Y[t],d=0,D=2)25.0909862892525Range28Trim Var.11.9337903100171
V(Y[t],d=1,D=2)6.18549411503442Range8Trim Var.2.63136053749629
V(Y[t],d=2,D=2)11.0697496008064Range16Trim Var.6.47499880147658
V(Y[t],d=3,D=2)32.0507757910202Range30Trim Var.19.2156844307577


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')