FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 11:45:24 -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/t1228157172nb8yntj03shegq4.htm/, Retrieved Sun, 12 May 2024 01:12:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27129, Retrieved Sun, 12 May 2024 01:12:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact225

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] [Random Walk] [2008-11-29 12:49:16] [6743688719638b0cb1c0a6e0bf433315]
-           [Law of Averages] [q2] [2008-12-01 18:45:24] [5d823194959040fa9b19b8c8302177e6] [Current]
Feedback Forum

Post a new message

Dataset

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 & 0 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27129&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]0 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=27129&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27129&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 time0 seconds
R Server'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)200.360416833667Range58Trim Var.148.578244600275
V(Y[t],d=1,D=0)0.992346138059251Range2Trim Var.NA
V(Y[t],d=2,D=0)1.97181482469112Range4Trim Var.0
V(Y[t],d=3,D=0)5.90322580645161Range8Trim Var.2.63977304964539
V(Y[t],d=0,D=1)12.3603864409062Range20Trim Var.6.89117238183503
V(Y[t],d=1,D=1)2.12284837883743Range4Trim Var.0
V(Y[t],d=2,D=1)4.27216494845361Range8Trim Var.2.28470806302132
V(Y[t],d=3,D=1)12.7851069268126Range16Trim Var.6.41362986215713
V(Y[t],d=0,D=2)26.2492525431225Range32Trim Var.12.7650172612198
V(Y[t],d=1,D=2)6.52318898512103Range8Trim Var.2.76998447472831
V(Y[t],d=2,D=2)13.2938689217759Range16Trim Var.6.49123376623377
V(Y[t],d=3,D=2)39.9913641738632Range28Trim Var.25.315173738432

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 200.360416833667 & Range & 58 & Trim Var. & 148.578244600275 \tabularnewline
V(Y[t],d=1,D=0) & 0.992346138059251 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.97181482469112 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.90322580645161 & Range & 8 & Trim Var. & 2.63977304964539 \tabularnewline
V(Y[t],d=0,D=1) & 12.3603864409062 & Range & 20 & Trim Var. & 6.89117238183503 \tabularnewline
V(Y[t],d=1,D=1) & 2.12284837883743 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.27216494845361 & Range & 8 & Trim Var. & 2.28470806302132 \tabularnewline
V(Y[t],d=3,D=1) & 12.7851069268126 & Range & 16 & Trim Var. & 6.41362986215713 \tabularnewline
V(Y[t],d=0,D=2) & 26.2492525431225 & Range & 32 & Trim Var. & 12.7650172612198 \tabularnewline
V(Y[t],d=1,D=2) & 6.52318898512103 & Range & 8 & Trim Var. & 2.76998447472831 \tabularnewline
V(Y[t],d=2,D=2) & 13.2938689217759 & Range & 16 & Trim Var. & 6.49123376623377 \tabularnewline
V(Y[t],d=3,D=2) & 39.9913641738632 & Range & 28 & Trim Var. & 25.315173738432 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27129&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]200.360416833667[/C][C]Range[/C][C]58[/C][C]Trim Var.[/C][C]148.578244600275[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.992346138059251[/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]1.97181482469112[/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]5.90322580645161[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.63977304964539[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.3603864409062[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]6.89117238183503[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.12284837883743[/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]4.27216494845361[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.28470806302132[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.7851069268126[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.41362986215713[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]26.2492525431225[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]12.7650172612198[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.52318898512103[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.76998447472831[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.2938689217759[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.49123376623377[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]39.9913641738632[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]25.315173738432[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27129&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27129&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)200.360416833667Range58Trim Var.148.578244600275
V(Y[t],d=1,D=0)0.992346138059251Range2Trim Var.NA
V(Y[t],d=2,D=0)1.97181482469112Range4Trim Var.0
V(Y[t],d=3,D=0)5.90322580645161Range8Trim Var.2.63977304964539
V(Y[t],d=0,D=1)12.3603864409062Range20Trim Var.6.89117238183503
V(Y[t],d=1,D=1)2.12284837883743Range4Trim Var.0
V(Y[t],d=2,D=1)4.27216494845361Range8Trim Var.2.28470806302132
V(Y[t],d=3,D=1)12.7851069268126Range16Trim Var.6.41362986215713
V(Y[t],d=0,D=2)26.2492525431225Range32Trim Var.12.7650172612198
V(Y[t],d=1,D=2)6.52318898512103Range8Trim Var.2.76998447472831
V(Y[t],d=2,D=2)13.2938689217759Range16Trim Var.6.49123376623377
V(Y[t],d=3,D=2)39.9913641738632Range28Trim Var.25.315173738432


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')