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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationSat, 29 Nov 2008 01:38:57 -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/29/t12279479645qd5tt4t0rd04vl.htm/, Retrieved Sun, 19 May 2024 07:44:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26177, Retrieved Sun, 19 May 2024 07:44:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact190

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]
- R       [Law of Averages] [Question 3 ] [2008-11-29 08:38:57] [d41d8cd98f00b204e9800998ecf8427e] [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 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=26177&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=26177&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26177&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)86.2384769539078Range33Trim Var.65.7463579289947
V(Y[t],d=1,D=0)1.00084506362122Range2Trim Var.NA
V(Y[t],d=2,D=0)1.99597585513078Range4Trim Var.0
V(Y[t],d=3,D=0)6.04030635425456Range8Trim Var.2.61009301984912
V(Y[t],d=0,D=1)11.3333557747332Range20Trim Var.5.88235294117647
V(Y[t],d=1,D=1)2.06569151857767Range4Trim Var.0
V(Y[t],d=2,D=1)4.14013830554495Range8Trim Var.2.33648163366392
V(Y[t],d=3,D=1)12.6115020874159Range16Trim Var.6.79701741886347
V(Y[t],d=0,D=2)27.0528615656789Range30Trim Var.14.1426455722984
V(Y[t],d=1,D=2)6.16033755274262Range8Trim Var.2.78638306045038
V(Y[t],d=2,D=2)12.4228151399185Range16Trim Var.7.06509993576907
V(Y[t],d=3,D=2)38.1355215537320Range28Trim Var.22.3060326183752

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 86.2384769539078 & Range & 33 & Trim Var. & 65.7463579289947 \tabularnewline
V(Y[t],d=1,D=0) & 1.00084506362122 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.99597585513078 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.04030635425456 & Range & 8 & Trim Var. & 2.61009301984912 \tabularnewline
V(Y[t],d=0,D=1) & 11.3333557747332 & Range & 20 & Trim Var. & 5.88235294117647 \tabularnewline
V(Y[t],d=1,D=1) & 2.06569151857767 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.14013830554495 & Range & 8 & Trim Var. & 2.33648163366392 \tabularnewline
V(Y[t],d=3,D=1) & 12.6115020874159 & Range & 16 & Trim Var. & 6.79701741886347 \tabularnewline
V(Y[t],d=0,D=2) & 27.0528615656789 & Range & 30 & Trim Var. & 14.1426455722984 \tabularnewline
V(Y[t],d=1,D=2) & 6.16033755274262 & Range & 8 & Trim Var. & 2.78638306045038 \tabularnewline
V(Y[t],d=2,D=2) & 12.4228151399185 & Range & 16 & Trim Var. & 7.06509993576907 \tabularnewline
V(Y[t],d=3,D=2) & 38.1355215537320 & Range & 28 & Trim Var. & 22.3060326183752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26177&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]86.2384769539078[/C][C]Range[/C][C]33[/C][C]Trim Var.[/C][C]65.7463579289947[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00084506362122[/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]1.99597585513078[/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]6.04030635425456[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.61009301984912[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.3333557747332[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]5.88235294117647[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.06569151857767[/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]4.14013830554495[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.33648163366392[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.6115020874159[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.79701741886347[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]27.0528615656789[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]14.1426455722984[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.16033755274262[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.78638306045038[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.4228151399185[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.06509993576907[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]38.1355215537320[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]22.3060326183752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26177&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26177&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)86.2384769539078Range33Trim Var.65.7463579289947
V(Y[t],d=1,D=0)1.00084506362122Range2Trim Var.NA
V(Y[t],d=2,D=0)1.99597585513078Range4Trim Var.0
V(Y[t],d=3,D=0)6.04030635425456Range8Trim Var.2.61009301984912
V(Y[t],d=0,D=1)11.3333557747332Range20Trim Var.5.88235294117647
V(Y[t],d=1,D=1)2.06569151857767Range4Trim Var.0
V(Y[t],d=2,D=1)4.14013830554495Range8Trim Var.2.33648163366392
V(Y[t],d=3,D=1)12.6115020874159Range16Trim Var.6.79701741886347
V(Y[t],d=0,D=2)27.0528615656789Range30Trim Var.14.1426455722984
V(Y[t],d=1,D=2)6.16033755274262Range8Trim Var.2.78638306045038
V(Y[t],d=2,D=2)12.4228151399185Range16Trim Var.7.06509993576907
V(Y[t],d=3,D=2)38.1355215537320Range28Trim Var.22.3060326183752


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')