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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 computationSun, 30 Nov 2008 06:45:34 -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/30/t12280527871bgyfyv9342su36.htm/, Retrieved Sat, 07 Nov 2026 15:33:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26506, Retrieved Sat, 07 Nov 2026 15:33:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact449

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] [nsts Q3] [2008-11-30 13:45:34] [821c4b3d195be8e737cf8c9dc649d3cf] [Current]
Feedback Forum
2008-12-08 16:10:34 [Charis Berrevoets] [reply] 
Heel goed, je geeft een beknopt maar volledig antwoord op de vraag.
2008-12-08 19:23:19 [Gert-Jan Geudens] [reply] 
Goede conclusie maar je bent de getrimde variantie vergeten te vermelden. Via de getrimde variantie kunnen we het effect van outliers wegwerken. Door een logaritme toe te voegen worden de 5% hoogste en laagste gegevens verwijderd. Uiteraard is dit niet van toepassing op deze vraag aangezien we hier geen outliers hebben.

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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'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26506&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26506&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26506&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'George Udny Yule' @ 72.249.76.132






Variance Reduction Matrix
V(Y[t],d=0,D=0)307.180857715431Range69Trim Var.235.895344384542
V(Y[t],d=1,D=0)0.986036329687487Range2Trim Var.NA
V(Y[t],d=2,D=0)1.85913876835309Range4Trim Var.0
V(Y[t],d=3,D=0)5.60482248328682Range8Trim Var.2.36175531176226
V(Y[t],d=0,D=1)12.4944962466759Range18Trim Var.5.86093386606238
V(Y[t],d=1,D=1)1.87627280486053Range4Trim Var.0
V(Y[t],d=2,D=1)3.57938144329897Range8Trim Var.0.915117838666411
V(Y[t],d=3,D=1)10.8099173553719Range16Trim Var.6.01591034864416
V(Y[t],d=0,D=2)21.1715701017249Range24Trim Var.12.6226756623334
V(Y[t],d=1,D=2)5.54428603153453Range8Trim Var.2.56251373324544
V(Y[t],d=2,D=2)10.5961766621172Range16Trim Var.6.07783514331494
V(Y[t],d=3,D=2)32.0930590891174Range28Trim Var.17.693094629156

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 307.180857715431 & Range & 69 & Trim Var. & 235.895344384542 \tabularnewline
V(Y[t],d=1,D=0) & 0.986036329687487 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.85913876835309 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.60482248328682 & Range & 8 & Trim Var. & 2.36175531176226 \tabularnewline
V(Y[t],d=0,D=1) & 12.4944962466759 & Range & 18 & Trim Var. & 5.86093386606238 \tabularnewline
V(Y[t],d=1,D=1) & 1.87627280486053 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.57938144329897 & Range & 8 & Trim Var. & 0.915117838666411 \tabularnewline
V(Y[t],d=3,D=1) & 10.8099173553719 & Range & 16 & Trim Var. & 6.01591034864416 \tabularnewline
V(Y[t],d=0,D=2) & 21.1715701017249 & Range & 24 & Trim Var. & 12.6226756623334 \tabularnewline
V(Y[t],d=1,D=2) & 5.54428603153453 & Range & 8 & Trim Var. & 2.56251373324544 \tabularnewline
V(Y[t],d=2,D=2) & 10.5961766621172 & Range & 16 & Trim Var. & 6.07783514331494 \tabularnewline
V(Y[t],d=3,D=2) & 32.0930590891174 & Range & 28 & Trim Var. & 17.693094629156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26506&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]307.180857715431[/C][C]Range[/C][C]69[/C][C]Trim Var.[/C][C]235.895344384542[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.986036329687487[/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]1.85913876835309[/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]5.60482248328682[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.36175531176226[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.4944962466759[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]5.86093386606238[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.87627280486053[/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]3.57938144329897[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.915117838666411[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.8099173553719[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.01591034864416[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]21.1715701017249[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]12.6226756623334[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.54428603153453[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.56251373324544[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]10.5961766621172[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.07783514331494[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]32.0930590891174[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]17.693094629156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26506&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26506&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)307.180857715431Range69Trim Var.235.895344384542
V(Y[t],d=1,D=0)0.986036329687487Range2Trim Var.NA
V(Y[t],d=2,D=0)1.85913876835309Range4Trim Var.0
V(Y[t],d=3,D=0)5.60482248328682Range8Trim Var.2.36175531176226
V(Y[t],d=0,D=1)12.4944962466759Range18Trim Var.5.86093386606238
V(Y[t],d=1,D=1)1.87627280486053Range4Trim Var.0
V(Y[t],d=2,D=1)3.57938144329897Range8Trim Var.0.915117838666411
V(Y[t],d=3,D=1)10.8099173553719Range16Trim Var.6.01591034864416
V(Y[t],d=0,D=2)21.1715701017249Range24Trim Var.12.6226756623334
V(Y[t],d=1,D=2)5.54428603153453Range8Trim Var.2.56251373324544
V(Y[t],d=2,D=2)10.5961766621172Range16Trim Var.6.07783514331494
V(Y[t],d=3,D=2)32.0930590891174Range28Trim Var.17.693094629156


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')