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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 08:19:20 -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/t1228058440xfkmpsh31j21ciu.htm/, Retrieved Tue, 28 May 2024 07:22:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26560, Retrieved Tue, 28 May 2024 07:22:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact214

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: Variance Redu...] [2008-11-30 15:19:20] [924502d03698cd41cacbcd1327858815] [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'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=26560&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=26560&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26560&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)33.2015390781563Range24Trim Var.22.8082624809244
V(Y[t],d=1,D=0)1.00181085061690Range2Trim Var.NA
V(Y[t],d=2,D=0)2.02010456312170Range4Trim Var.0
V(Y[t],d=3,D=0)5.98387096774194Range8Trim Var.2.75188652482269
V(Y[t],d=0,D=1)8.5065304473693Range16Trim Var.3.62979368532068
V(Y[t],d=1,D=1)1.86001470327275Range4Trim Var.0
V(Y[t],d=2,D=1)3.52989690721649Range8Trim Var.0.92378526645768
V(Y[t],d=3,D=1)10.1900656044986Range16Trim Var.5.99979832610669
V(Y[t],d=0,D=2)19.5534011499337Range28Trim Var.12.1223529411765
V(Y[t],d=1,D=2)5.45140572951366Range8Trim Var.2.52291105121294
V(Y[t],d=2,D=2)10.3763035120115Range16Trim Var.6.21377672209026
V(Y[t],d=3,D=2)29.9574658687784Range30Trim Var.16.3056386651323

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 33.2015390781563 & Range & 24 & Trim Var. & 22.8082624809244 \tabularnewline
V(Y[t],d=1,D=0) & 1.00181085061690 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.02010456312170 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.98387096774194 & Range & 8 & Trim Var. & 2.75188652482269 \tabularnewline
V(Y[t],d=0,D=1) & 8.5065304473693 & Range & 16 & Trim Var. & 3.62979368532068 \tabularnewline
V(Y[t],d=1,D=1) & 1.86001470327275 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.52989690721649 & Range & 8 & Trim Var. & 0.92378526645768 \tabularnewline
V(Y[t],d=3,D=1) & 10.1900656044986 & Range & 16 & Trim Var. & 5.99979832610669 \tabularnewline
V(Y[t],d=0,D=2) & 19.5534011499337 & Range & 28 & Trim Var. & 12.1223529411765 \tabularnewline
V(Y[t],d=1,D=2) & 5.45140572951366 & Range & 8 & Trim Var. & 2.52291105121294 \tabularnewline
V(Y[t],d=2,D=2) & 10.3763035120115 & Range & 16 & Trim Var. & 6.21377672209026 \tabularnewline
V(Y[t],d=3,D=2) & 29.9574658687784 & Range & 30 & Trim Var. & 16.3056386651323 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26560&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]33.2015390781563[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]22.8082624809244[/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]2.02010456312170[/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]5.98387096774194[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.75188652482269[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]8.5065304473693[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]3.62979368532068[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.86001470327275[/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]3.52989690721649[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]0.92378526645768[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]10.1900656044986[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.99979832610669[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]19.5534011499337[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]12.1223529411765[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.45140572951366[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.52291105121294[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]10.3763035120115[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.21377672209026[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]29.9574658687784[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]16.3056386651323[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26560&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26560&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)33.2015390781563Range24Trim Var.22.8082624809244
V(Y[t],d=1,D=0)1.00181085061690Range2Trim Var.NA
V(Y[t],d=2,D=0)2.02010456312170Range4Trim Var.0
V(Y[t],d=3,D=0)5.98387096774194Range8Trim Var.2.75188652482269
V(Y[t],d=0,D=1)8.5065304473693Range16Trim Var.3.62979368532068
V(Y[t],d=1,D=1)1.86001470327275Range4Trim Var.0
V(Y[t],d=2,D=1)3.52989690721649Range8Trim Var.0.92378526645768
V(Y[t],d=3,D=1)10.1900656044986Range16Trim Var.5.99979832610669
V(Y[t],d=0,D=2)19.5534011499337Range28Trim Var.12.1223529411765
V(Y[t],d=1,D=2)5.45140572951366Range8Trim Var.2.52291105121294
V(Y[t],d=2,D=2)10.3763035120115Range16Trim Var.6.21377672209026
V(Y[t],d=3,D=2)29.9574658687784Range30Trim Var.16.3056386651323


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')