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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 computationFri, 28 Nov 2008 06:25:56 -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/Nov/28/t1227878795subu7upe1g6yswg.htm/, Retrieved Sun, 19 May 2024 10:46:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26094, Retrieved Sun, 19 May 2024 10:46:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166

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] [] [2008-11-28 13:25:56] [f6a332ba2d530c028d935c5a5bbb53af] [Current]
- RM D      [Variance Reduction Matrix] [] [2008-11-28 14:33:43] [d2d412c7f4d35ffbf5ee5ee89db327d4]
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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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26094&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26094&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26094&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)53.6065090180361Range30Trim Var.38.93422683529
V(Y[t],d=1,D=0)1.00110260682007Range2Trim Var.NA
V(Y[t],d=2,D=0)2.11668403998287Range4Trim Var.0
V(Y[t],d=3,D=0)6.2258064516129Range8Trim Var.2.96589697022111
V(Y[t],d=0,D=1)9.35925876056148Range14Trim Var.4.16835946577721
V(Y[t],d=1,D=1)1.95878013537151Range4Trim Var.0
V(Y[t],d=2,D=1)4.04946756607696Range8Trim Var.2.19002375296912
V(Y[t],d=3,D=1)11.9172872113828Range16Trim Var.6.33702665633013
V(Y[t],d=0,D=2)18.8533038478549Range24Trim Var.9.0726012603721
V(Y[t],d=1,D=2)5.76355318676438Range8Trim Var.2.67005870841487
V(Y[t],d=2,D=2)12.0422119338811Range16Trim Var.6.19085401947079
V(Y[t],d=3,D=2)35.5677786935178Range32Trim Var.20.8172556175504

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 53.6065090180361 & Range & 30 & Trim Var. & 38.93422683529 \tabularnewline
V(Y[t],d=1,D=0) & 1.00110260682007 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.11668403998287 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.2258064516129 & Range & 8 & Trim Var. & 2.96589697022111 \tabularnewline
V(Y[t],d=0,D=1) & 9.35925876056148 & Range & 14 & Trim Var. & 4.16835946577721 \tabularnewline
V(Y[t],d=1,D=1) & 1.95878013537151 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.04946756607696 & Range & 8 & Trim Var. & 2.19002375296912 \tabularnewline
V(Y[t],d=3,D=1) & 11.9172872113828 & Range & 16 & Trim Var. & 6.33702665633013 \tabularnewline
V(Y[t],d=0,D=2) & 18.8533038478549 & Range & 24 & Trim Var. & 9.0726012603721 \tabularnewline
V(Y[t],d=1,D=2) & 5.76355318676438 & Range & 8 & Trim Var. & 2.67005870841487 \tabularnewline
V(Y[t],d=2,D=2) & 12.0422119338811 & Range & 16 & Trim Var. & 6.19085401947079 \tabularnewline
V(Y[t],d=3,D=2) & 35.5677786935178 & Range & 32 & Trim Var. & 20.8172556175504 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26094&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]53.6065090180361[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]38.93422683529[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00110260682007[/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]2.11668403998287[/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]6.2258064516129[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.96589697022111[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]9.35925876056148[/C][C]Range[/C][C]14[/C][C]Trim Var.[/C][C]4.16835946577721[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.95878013537151[/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]4.04946756607696[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.19002375296912[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.9172872113828[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.33702665633013[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]18.8533038478549[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]9.0726012603721[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.76355318676438[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.67005870841487[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.0422119338811[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.19085401947079[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]35.5677786935178[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]20.8172556175504[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26094&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26094&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)53.6065090180361Range30Trim Var.38.93422683529
V(Y[t],d=1,D=0)1.00110260682007Range2Trim Var.NA
V(Y[t],d=2,D=0)2.11668403998287Range4Trim Var.0
V(Y[t],d=3,D=0)6.2258064516129Range8Trim Var.2.96589697022111
V(Y[t],d=0,D=1)9.35925876056148Range14Trim Var.4.16835946577721
V(Y[t],d=1,D=1)1.95878013537151Range4Trim Var.0
V(Y[t],d=2,D=1)4.04946756607696Range8Trim Var.2.19002375296912
V(Y[t],d=3,D=1)11.9172872113828Range16Trim Var.6.33702665633013
V(Y[t],d=0,D=2)18.8533038478549Range24Trim Var.9.0726012603721
V(Y[t],d=1,D=2)5.76355318676438Range8Trim Var.2.67005870841487
V(Y[t],d=2,D=2)12.0422119338811Range16Trim Var.6.19085401947079
V(Y[t],d=3,D=2)35.5677786935178Range32Trim Var.20.8172556175504


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')