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 computationFri, 28 Nov 2008 05:42:17 -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/28/t1227876270gaicc03jn25wgby.htm/, Retrieved Sun, 19 May 2024 11:31:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26049, Retrieved Sun, 19 May 2024 11:31:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVariance Reduction matrix- Q3
Estimated Impact168

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] [Variance reductio...] [2008-11-28 12:42:17] [0cdfeda4aa2f9e551c2e529c44a404df] [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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26049&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26049&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26049&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'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)41.7434869739479Range29Trim Var.25.8797724217892
V(Y[t],d=1,D=0)1.00197181511618Range2Trim Var.NA
V(Y[t],d=2,D=0)2.11668403998287Range4Trim Var.0
V(Y[t],d=3,D=0)6.45966119296424Range8Trim Var.2.77686310514931
V(Y[t],d=0,D=1)10.1184064361935Range20Trim Var.4.47052053948606
V(Y[t],d=1,D=1)2.14813124783465Range4Trim Var.0
V(Y[t],d=2,D=1)4.63505154639175Range8Trim Var.2.45661704485234
V(Y[t],d=3,D=1)14.0907557297435Range16Trim Var.6.99989177489177
V(Y[t],d=0,D=2)21.2968244139761Range24Trim Var.13.2404818729401
V(Y[t],d=1,D=2)6.66659560293138Range8Trim Var.2.79175550817342
V(Y[t],d=2,D=2)14.7228838279766Range16Trim Var.6.74514275559768
V(Y[t],d=3,D=2)45.135593220339Range30Trim Var.27.8307741444120

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 41.7434869739479 & Range & 29 & Trim Var. & 25.8797724217892 \tabularnewline
V(Y[t],d=1,D=0) & 1.00197181511618 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.11668403998287 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.45966119296424 & Range & 8 & Trim Var. & 2.77686310514931 \tabularnewline
V(Y[t],d=0,D=1) & 10.1184064361935 & Range & 20 & Trim Var. & 4.47052053948606 \tabularnewline
V(Y[t],d=1,D=1) & 2.14813124783465 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.63505154639175 & Range & 8 & Trim Var. & 2.45661704485234 \tabularnewline
V(Y[t],d=3,D=1) & 14.0907557297435 & Range & 16 & Trim Var. & 6.99989177489177 \tabularnewline
V(Y[t],d=0,D=2) & 21.2968244139761 & Range & 24 & Trim Var. & 13.2404818729401 \tabularnewline
V(Y[t],d=1,D=2) & 6.66659560293138 & Range & 8 & Trim Var. & 2.79175550817342 \tabularnewline
V(Y[t],d=2,D=2) & 14.7228838279766 & Range & 16 & Trim Var. & 6.74514275559768 \tabularnewline
V(Y[t],d=3,D=2) & 45.135593220339 & Range & 30 & Trim Var. & 27.8307741444120 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26049&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]41.7434869739479[/C][C]Range[/C][C]29[/C][C]Trim Var.[/C][C]25.8797724217892[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00197181511618[/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]2.11668403998287[/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]6.45966119296424[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.77686310514931[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.1184064361935[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]4.47052053948606[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.14813124783465[/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]4.63505154639175[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.45661704485234[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]14.0907557297435[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.99989177489177[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]21.2968244139761[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]13.2404818729401[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.66659560293138[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.79175550817342[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]14.7228838279766[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.74514275559768[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]45.135593220339[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]27.8307741444120[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26049&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26049&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)41.7434869739479Range29Trim Var.25.8797724217892
V(Y[t],d=1,D=0)1.00197181511618Range2Trim Var.NA
V(Y[t],d=2,D=0)2.11668403998287Range4Trim Var.0
V(Y[t],d=3,D=0)6.45966119296424Range8Trim Var.2.77686310514931
V(Y[t],d=0,D=1)10.1184064361935Range20Trim Var.4.47052053948606
V(Y[t],d=1,D=1)2.14813124783465Range4Trim Var.0
V(Y[t],d=2,D=1)4.63505154639175Range8Trim Var.2.45661704485234
V(Y[t],d=3,D=1)14.0907557297435Range16Trim Var.6.99989177489177
V(Y[t],d=0,D=2)21.2968244139761Range24Trim Var.13.2404818729401
V(Y[t],d=1,D=2)6.66659560293138Range8Trim Var.2.79175550817342
V(Y[t],d=2,D=2)14.7228838279766Range16Trim Var.6.74514275559768
V(Y[t],d=3,D=2)45.135593220339Range30Trim Var.27.8307741444120


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')