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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 11:47:27 -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/t1228157332kmp778odneitkeb.htm/, Retrieved Sun, 05 May 2024 15:17:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27136, Retrieved Sun, 05 May 2024 15:17:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact263

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]
F           [Law of Averages] [q3] [2008-12-01 18:47:27] [5d823194959040fa9b19b8c8302177e6] [Current]
-             [Law of Averages] [Q2] [2008-12-01 20:46:37] [fe7291e888d31b8c4db0b24d6c0f75c6]
-             [Law of Averages] [Q3] [2008-12-01 20:50:15] [fe7291e888d31b8c4db0b24d6c0f75c6]
Feedback Forum
2008-12-07 12:37:28 [Dana Molenberghs] [reply] 
Hoe groter de variantie wordt (2de kolom), hoe groter de onzekerheid wordt. Daarom is de beste combinatie diegene met de kleinste variantie.

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'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=27136&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=27136&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27136&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)112.194084168337Range45Trim Var.76.940224307986
V(Y[t],d=1,D=0)0.997078494338074Range2Trim Var.NA
V(Y[t],d=2,D=0)1.9476861167002Range4Trim Var.0
V(Y[t],d=3,D=0)5.77412864282469Range8Trim Var.2.60630467990557
V(Y[t],d=0,D=1)15.1503517689433Range22Trim Var.6.52852869800779
V(Y[t],d=1,D=1)2.08228762643547Range4Trim Var.0
V(Y[t],d=2,D=1)3.95876288659794Range8Trim Var.2.16033074518504
V(Y[t],d=3,D=1)11.9421317202011Range16Trim Var.6.56824392348627
V(Y[t],d=0,D=2)32.8168244139761Range38Trim Var.16.4460575534239
V(Y[t],d=1,D=2)6.29535864978903Range8Trim Var.2.81830536225952
V(Y[t],d=2,D=2)11.9577167019027Range16Trim Var.5.93847797878025
V(Y[t],d=3,D=2)36.4660837782635Range32Trim Var.21.0075533661741

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 112.194084168337 & Range & 45 & Trim Var. & 76.940224307986 \tabularnewline
V(Y[t],d=1,D=0) & 0.997078494338074 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.9476861167002 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.77412864282469 & Range & 8 & Trim Var. & 2.60630467990557 \tabularnewline
V(Y[t],d=0,D=1) & 15.1503517689433 & Range & 22 & Trim Var. & 6.52852869800779 \tabularnewline
V(Y[t],d=1,D=1) & 2.08228762643547 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.95876288659794 & Range & 8 & Trim Var. & 2.16033074518504 \tabularnewline
V(Y[t],d=3,D=1) & 11.9421317202011 & Range & 16 & Trim Var. & 6.56824392348627 \tabularnewline
V(Y[t],d=0,D=2) & 32.8168244139761 & Range & 38 & Trim Var. & 16.4460575534239 \tabularnewline
V(Y[t],d=1,D=2) & 6.29535864978903 & Range & 8 & Trim Var. & 2.81830536225952 \tabularnewline
V(Y[t],d=2,D=2) & 11.9577167019027 & Range & 16 & Trim Var. & 5.93847797878025 \tabularnewline
V(Y[t],d=3,D=2) & 36.4660837782635 & Range & 32 & Trim Var. & 21.0075533661741 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27136&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]112.194084168337[/C][C]Range[/C][C]45[/C][C]Trim Var.[/C][C]76.940224307986[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.997078494338074[/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]1.9476861167002[/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]5.77412864282469[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.60630467990557[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]15.1503517689433[/C][C]Range[/C][C]22[/C][C]Trim Var.[/C][C]6.52852869800779[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.08228762643547[/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]3.95876288659794[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.16033074518504[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.9421317202011[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.56824392348627[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]32.8168244139761[/C][C]Range[/C][C]38[/C][C]Trim Var.[/C][C]16.4460575534239[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.29535864978903[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.81830536225952[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.9577167019027[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.93847797878025[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.4660837782635[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]21.0075533661741[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27136&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27136&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)112.194084168337Range45Trim Var.76.940224307986
V(Y[t],d=1,D=0)0.997078494338074Range2Trim Var.NA
V(Y[t],d=2,D=0)1.9476861167002Range4Trim Var.0
V(Y[t],d=3,D=0)5.77412864282469Range8Trim Var.2.60630467990557
V(Y[t],d=0,D=1)15.1503517689433Range22Trim Var.6.52852869800779
V(Y[t],d=1,D=1)2.08228762643547Range4Trim Var.0
V(Y[t],d=2,D=1)3.95876288659794Range8Trim Var.2.16033074518504
V(Y[t],d=3,D=1)11.9421317202011Range16Trim Var.6.56824392348627
V(Y[t],d=0,D=2)32.8168244139761Range38Trim Var.16.4460575534239
V(Y[t],d=1,D=2)6.29535864978903Range8Trim Var.2.81830536225952
V(Y[t],d=2,D=2)11.9577167019027Range16Trim Var.5.93847797878025
V(Y[t],d=3,D=2)36.4660837782635Range32Trim Var.21.0075533661741


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')