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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 computationMon, 01 Dec 2008 11:25:50 -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/t1228155993ys28g75awtu9sph.htm/, Retrieved Sun, 27 Sep 2026 01:31:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27096, Retrieved Sun, 27 Sep 2026 01:31:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact483

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] [Q3] [2008-12-01 18:25:50] [577b699a0819d2125728ba9ae2c57238] [Current]
Feedback Forum
2008-12-07 17:03:09 [Chi-Kwong Man] [reply] 
In de eerste kolom van de variance reduction matrix vindt je de berekening van de variantie. De kleine 'd' staat voor differentiëren (lange termijn effect zuiveren,waardoor men een stabieler gemiddelde krijgt). V(Y[t],d=1,D=0) betekent dat men '1x' differentiërt. De tweede kolom geeft de variantie weer (de kleinste kan men vinden in de tweede rij (1.00181085061690).

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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=27096&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=27096&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27096&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)38.379254509018Range30Trim Var.24.5072685856285
V(Y[t],d=1,D=0)1.00181085061690Range2Trim Var.NA
V(Y[t],d=2,D=0)1.97181482469112Range4Trim Var.0
V(Y[t],d=3,D=0)5.91935483870968Range8Trim Var.2.59505956903844
V(Y[t],d=0,D=1)14.1893661426600Range16Trim Var.7.18699693617905
V(Y[t],d=1,D=1)1.95884773662551Range4Trim Var.0
V(Y[t],d=2,D=1)4.00824742268041Range8Trim Var.2.34310782729162
V(Y[t],d=3,D=1)12.3139814262588Range16Trim Var.6.52178017695259
V(Y[t],d=0,D=2)28.0935515258735Range30Trim Var.15.5552169702124
V(Y[t],d=1,D=2)5.86481900954919Range8Trim Var.2.61835345094398
V(Y[t],d=2,D=2)12.2704525383360Range16Trim Var.6.4919575501854
V(Y[t],d=3,D=2)38.1016232486473Range28Trim Var.19.6481867663453

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 38.379254509018 & Range & 30 & Trim Var. & 24.5072685856285 \tabularnewline
V(Y[t],d=1,D=0) & 1.00181085061690 & 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) & 5.91935483870968 & Range & 8 & Trim Var. & 2.59505956903844 \tabularnewline
V(Y[t],d=0,D=1) & 14.1893661426600 & Range & 16 & Trim Var. & 7.18699693617905 \tabularnewline
V(Y[t],d=1,D=1) & 1.95884773662551 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.00824742268041 & Range & 8 & Trim Var. & 2.34310782729162 \tabularnewline
V(Y[t],d=3,D=1) & 12.3139814262588 & Range & 16 & Trim Var. & 6.52178017695259 \tabularnewline
V(Y[t],d=0,D=2) & 28.0935515258735 & Range & 30 & Trim Var. & 15.5552169702124 \tabularnewline
V(Y[t],d=1,D=2) & 5.86481900954919 & Range & 8 & Trim Var. & 2.61835345094398 \tabularnewline
V(Y[t],d=2,D=2) & 12.2704525383360 & Range & 16 & Trim Var. & 6.4919575501854 \tabularnewline
V(Y[t],d=3,D=2) & 38.1016232486473 & Range & 28 & Trim Var. & 19.6481867663453 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27096&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]38.379254509018[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]24.5072685856285[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00181085061690[/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]5.91935483870968[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.59505956903844[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]14.1893661426600[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]7.18699693617905[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.95884773662551[/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]4.00824742268041[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.34310782729162[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.3139814262588[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.52178017695259[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]28.0935515258735[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]15.5552169702124[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.86481900954919[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.61835345094398[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.2704525383360[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.4919575501854[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]38.1016232486473[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]19.6481867663453[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27096&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27096&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)38.379254509018Range30Trim Var.24.5072685856285
V(Y[t],d=1,D=0)1.00181085061690Range2Trim Var.NA
V(Y[t],d=2,D=0)1.97181482469112Range4Trim Var.0
V(Y[t],d=3,D=0)5.91935483870968Range8Trim Var.2.59505956903844
V(Y[t],d=0,D=1)14.1893661426600Range16Trim Var.7.18699693617905
V(Y[t],d=1,D=1)1.95884773662551Range4Trim Var.0
V(Y[t],d=2,D=1)4.00824742268041Range8Trim Var.2.34310782729162
V(Y[t],d=3,D=1)12.3139814262588Range16Trim Var.6.52178017695259
V(Y[t],d=0,D=2)28.0935515258735Range30Trim Var.15.5552169702124
V(Y[t],d=1,D=2)5.86481900954919Range8Trim Var.2.61835345094398
V(Y[t],d=2,D=2)12.2704525383360Range16Trim Var.6.4919575501854
V(Y[t],d=3,D=2)38.1016232486473Range28Trim Var.19.6481867663453


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')