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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 computationSat, 29 Nov 2008 12:54:26 -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/t1227988493a65ypfep9c8s392.htm/, Retrieved Sun, 19 May 2024 05:57:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26360, Retrieved Sun, 19 May 2024 05:57:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146

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] [Q3] [2008-11-29 19:54:26] [270782e2502ae87124d0ebdcd1862d6a] [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'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26360&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26360&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26360&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)49.0039438877755Range30Trim Var.32.5819905715345
V(Y[t],d=1,D=0)1.00200400801603Range2Trim Var.NA
V(Y[t],d=2,D=0)1.90742850678367Range4Trim Var.0
V(Y[t],d=3,D=0)5.68546764457714Range8Trim Var.2.53548832711701
V(Y[t],d=0,D=1)11.6840980240347Range18Trim Var.4.40377074630688
V(Y[t],d=1,D=1)1.97530864197531Range4Trim Var.0
V(Y[t],d=2,D=1)3.69484536082474Range8Trim Var.2.21709006928406
V(Y[t],d=3,D=1)10.9173383317713Range16Trim Var.6.29014817328357
V(Y[t],d=0,D=2)23.9592392746572Range28Trim Var.13.3522185286891
V(Y[t],d=1,D=2)5.84794137241839Range8Trim Var.2.59458372021046
V(Y[t],d=2,D=2)11.1455919215707Range16Trim Var.6.36271691812273
V(Y[t],d=3,D=2)33.1016949152542Range28Trim Var.21.0801000113649

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 49.0039438877755 & Range & 30 & Trim Var. & 32.5819905715345 \tabularnewline
V(Y[t],d=1,D=0) & 1.00200400801603 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.90742850678367 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.68546764457714 & Range & 8 & Trim Var. & 2.53548832711701 \tabularnewline
V(Y[t],d=0,D=1) & 11.6840980240347 & Range & 18 & Trim Var. & 4.40377074630688 \tabularnewline
V(Y[t],d=1,D=1) & 1.97530864197531 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.69484536082474 & Range & 8 & Trim Var. & 2.21709006928406 \tabularnewline
V(Y[t],d=3,D=1) & 10.9173383317713 & Range & 16 & Trim Var. & 6.29014817328357 \tabularnewline
V(Y[t],d=0,D=2) & 23.9592392746572 & Range & 28 & Trim Var. & 13.3522185286891 \tabularnewline
V(Y[t],d=1,D=2) & 5.84794137241839 & Range & 8 & Trim Var. & 2.59458372021046 \tabularnewline
V(Y[t],d=2,D=2) & 11.1455919215707 & Range & 16 & Trim Var. & 6.36271691812273 \tabularnewline
V(Y[t],d=3,D=2) & 33.1016949152542 & Range & 28 & Trim Var. & 21.0801000113649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26360&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]49.0039438877755[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]32.5819905715345[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00200400801603[/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]1.90742850678367[/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]5.68546764457714[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.53548832711701[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.6840980240347[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]4.40377074630688[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.97530864197531[/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]3.69484536082474[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.21709006928406[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.9173383317713[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.29014817328357[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]23.9592392746572[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]13.3522185286891[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.84794137241839[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.59458372021046[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.1455919215707[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.36271691812273[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]33.1016949152542[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]21.0801000113649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26360&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26360&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)49.0039438877755Range30Trim Var.32.5819905715345
V(Y[t],d=1,D=0)1.00200400801603Range2Trim Var.NA
V(Y[t],d=2,D=0)1.90742850678367Range4Trim Var.0
V(Y[t],d=3,D=0)5.68546764457714Range8Trim Var.2.53548832711701
V(Y[t],d=0,D=1)11.6840980240347Range18Trim Var.4.40377074630688
V(Y[t],d=1,D=1)1.97530864197531Range4Trim Var.0
V(Y[t],d=2,D=1)3.69484536082474Range8Trim Var.2.21709006928406
V(Y[t],d=3,D=1)10.9173383317713Range16Trim Var.6.29014817328357
V(Y[t],d=0,D=2)23.9592392746572Range28Trim Var.13.3522185286891
V(Y[t],d=1,D=2)5.84794137241839Range8Trim Var.2.59458372021046
V(Y[t],d=2,D=2)11.1455919215707Range16Trim Var.6.36271691812273
V(Y[t],d=3,D=2)33.1016949152542Range28Trim Var.21.0801000113649


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')