FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationTue, 02 Dec 2008 13:18:57 -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/02/t1228249173txrcv5r41vz4i5y.htm/, Retrieved Sat, 18 May 2024 06:32:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28358, Retrieved Sat, 18 May 2024 06:32:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176

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] [Non stationary ti...] [2008-12-02 20:15:47] [1a689e9ccc515e1757f0522229a687e9]
-         [Law of Averages] [Non stationary ti...] [2008-12-02 20:17:35] [1a689e9ccc515e1757f0522229a687e9]
-             [Law of Averages] [Non stationary ti...] [2008-12-02 20:18:57] [74a138e5b32af267311b5ad4cd13bf7e] [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=28358&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=28358&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28358&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)23.7724408817635Range20Trim Var.17.8467384551667
V(Y[t],d=1,D=0)1.00190742931646Range2Trim Var.NA
V(Y[t],d=2,D=0)2.06036217303823Range4Trim Var.0
V(Y[t],d=3,D=0)6.14509638476017Range8Trim Var.2.78347781744008
V(Y[t],d=0,D=1)11.8380011445114Range18Trim Var.6.80841533763149
V(Y[t],d=1,D=1)1.90919461556012Range4Trim Var.0
V(Y[t],d=2,D=1)3.9092104704934Range8Trim Var.2.25988750027359
V(Y[t],d=3,D=1)11.7190082644628Range16Trim Var.6.52088671571969
V(Y[t],d=0,D=2)25.4701459531181Range28Trim Var.13.5228361545832
V(Y[t],d=1,D=2)5.53579391516767Range8Trim Var.2.62655421267716
V(Y[t],d=2,D=2)11.2727094316732Range16Trim Var.6.36785080780478
V(Y[t],d=3,D=2)34.0163041530799Range32Trim Var.21.1061167747915

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 23.7724408817635 & Range & 20 & Trim Var. & 17.8467384551667 \tabularnewline
V(Y[t],d=1,D=0) & 1.00190742931646 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.06036217303823 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.14509638476017 & Range & 8 & Trim Var. & 2.78347781744008 \tabularnewline
V(Y[t],d=0,D=1) & 11.8380011445114 & Range & 18 & Trim Var. & 6.80841533763149 \tabularnewline
V(Y[t],d=1,D=1) & 1.90919461556012 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.9092104704934 & Range & 8 & Trim Var. & 2.25988750027359 \tabularnewline
V(Y[t],d=3,D=1) & 11.7190082644628 & Range & 16 & Trim Var. & 6.52088671571969 \tabularnewline
V(Y[t],d=0,D=2) & 25.4701459531181 & Range & 28 & Trim Var. & 13.5228361545832 \tabularnewline
V(Y[t],d=1,D=2) & 5.53579391516767 & Range & 8 & Trim Var. & 2.62655421267716 \tabularnewline
V(Y[t],d=2,D=2) & 11.2727094316732 & Range & 16 & Trim Var. & 6.36785080780478 \tabularnewline
V(Y[t],d=3,D=2) & 34.0163041530799 & Range & 32 & Trim Var. & 21.1061167747915 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28358&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]23.7724408817635[/C][C]Range[/C][C]20[/C][C]Trim Var.[/C][C]17.8467384551667[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00190742931646[/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]2.06036217303823[/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]6.14509638476017[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.78347781744008[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]11.8380011445114[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.80841533763149[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.90919461556012[/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]3.9092104704934[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.25988750027359[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.7190082644628[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.52088671571969[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]25.4701459531181[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]13.5228361545832[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.53579391516767[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.62655421267716[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.2727094316732[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.36785080780478[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]34.0163041530799[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]21.1061167747915[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28358&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28358&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)23.7724408817635Range20Trim Var.17.8467384551667
V(Y[t],d=1,D=0)1.00190742931646Range2Trim Var.NA
V(Y[t],d=2,D=0)2.06036217303823Range4Trim Var.0
V(Y[t],d=3,D=0)6.14509638476017Range8Trim Var.2.78347781744008
V(Y[t],d=0,D=1)11.8380011445114Range18Trim Var.6.80841533763149
V(Y[t],d=1,D=1)1.90919461556012Range4Trim Var.0
V(Y[t],d=2,D=1)3.9092104704934Range8Trim Var.2.25988750027359
V(Y[t],d=3,D=1)11.7190082644628Range16Trim Var.6.52088671571969
V(Y[t],d=0,D=2)25.4701459531181Range28Trim Var.13.5228361545832
V(Y[t],d=1,D=2)5.53579391516767Range8Trim Var.2.62655421267716
V(Y[t],d=2,D=2)11.2727094316732Range16Trim Var.6.36785080780478
V(Y[t],d=3,D=2)34.0163041530799Range32Trim Var.21.1061167747915


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
Parameters (R input):
par1 = 500 ; par2 = 0.5 ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')