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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 computationTue, 02 Dec 2008 13:07:37 -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/02/t1228248504w0nfuvdfv79ixk4.htm/, Retrieved Fri, 17 May 2024 04:18:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28326, Retrieved Fri, 17 May 2024 04:18:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

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] [] [2008-12-02 20:07:37] [52492148dbcac26917ed19e489351f79] [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=28326&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=28326&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28326&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)72.9398957915832Range37Trim Var.46.0822229849908
V(Y[t],d=1,D=0)0.999492961827269Range2Trim Var.NA
V(Y[t],d=2,D=0)1.98791140416798Range4Trim Var.0
V(Y[t],d=3,D=0)5.87096774193548Range8Trim Var.2.69782636009549
V(Y[t],d=0,D=1)12.2177096307268Range18Trim Var.4.12109036117072
V(Y[t],d=1,D=1)1.86829585688815Range4Trim Var.0
V(Y[t],d=2,D=1)3.85152942174706Range8Trim Var.2.36057651184672
V(Y[t],d=3,D=1)11.6528244014655Range16Trim Var.6.51420617374928
V(Y[t],d=0,D=2)22.5093321539142Range26Trim Var.12.5301103242280
V(Y[t],d=1,D=2)5.32487674883411Range8Trim Var.2.61372869288437
V(Y[t],d=2,D=2)11.2896227509121Range16Trim Var.6.74124977746128
V(Y[t],d=3,D=2)34.3304905579245Range30Trim Var.21.1608171817706

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 72.9398957915832 & Range & 37 & Trim Var. & 46.0822229849908 \tabularnewline
V(Y[t],d=1,D=0) & 0.999492961827269 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.98791140416798 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.87096774193548 & Range & 8 & Trim Var. & 2.69782636009549 \tabularnewline
V(Y[t],d=0,D=1) & 12.2177096307268 & Range & 18 & Trim Var. & 4.12109036117072 \tabularnewline
V(Y[t],d=1,D=1) & 1.86829585688815 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.85152942174706 & Range & 8 & Trim Var. & 2.36057651184672 \tabularnewline
V(Y[t],d=3,D=1) & 11.6528244014655 & Range & 16 & Trim Var. & 6.51420617374928 \tabularnewline
V(Y[t],d=0,D=2) & 22.5093321539142 & Range & 26 & Trim Var. & 12.5301103242280 \tabularnewline
V(Y[t],d=1,D=2) & 5.32487674883411 & Range & 8 & Trim Var. & 2.61372869288437 \tabularnewline
V(Y[t],d=2,D=2) & 11.2896227509121 & Range & 16 & Trim Var. & 6.74124977746128 \tabularnewline
V(Y[t],d=3,D=2) & 34.3304905579245 & Range & 30 & Trim Var. & 21.1608171817706 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28326&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]72.9398957915832[/C][C]Range[/C][C]37[/C][C]Trim Var.[/C][C]46.0822229849908[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.999492961827269[/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]1.98791140416798[/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]5.87096774193548[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.69782636009549[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.2177096307268[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]4.12109036117072[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.86829585688815[/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]3.85152942174706[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.36057651184672[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.6528244014655[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.51420617374928[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]22.5093321539142[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]12.5301103242280[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.32487674883411[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.61372869288437[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.2896227509121[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.74124977746128[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]34.3304905579245[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]21.1608171817706[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28326&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28326&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)72.9398957915832Range37Trim Var.46.0822229849908
V(Y[t],d=1,D=0)0.999492961827269Range2Trim Var.NA
V(Y[t],d=2,D=0)1.98791140416798Range4Trim Var.0
V(Y[t],d=3,D=0)5.87096774193548Range8Trim Var.2.69782636009549
V(Y[t],d=0,D=1)12.2177096307268Range18Trim Var.4.12109036117072
V(Y[t],d=1,D=1)1.86829585688815Range4Trim Var.0
V(Y[t],d=2,D=1)3.85152942174706Range8Trim Var.2.36057651184672
V(Y[t],d=3,D=1)11.6528244014655Range16Trim Var.6.51420617374928
V(Y[t],d=0,D=2)22.5093321539142Range26Trim Var.12.5301103242280
V(Y[t],d=1,D=2)5.32487674883411Range8Trim Var.2.61372869288437
V(Y[t],d=2,D=2)11.2896227509121Range16Trim Var.6.74124977746128
V(Y[t],d=3,D=2)34.3304905579245Range30Trim Var.21.1608171817706


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
Parameters (R input):
par1 = 500 ; par2 = 0.5 ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')