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 computationSun, 30 Nov 2008 07:44:32 -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/t122805632428i8ndfwdudcqet.htm/, Retrieved Tue, 28 May 2024 01:04:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26533, Retrieved Tue, 28 May 2024 01:04:09 +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] [taak 7 Q3] [2008-11-30 14:44:32] [bda7fba231d49184c6a1b627868bbb81] [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'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=26533&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=26533&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26533&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)54.8274308617234Range31Trim Var.36.6621660799337
V(Y[t],d=1,D=0)1.00152111451819Range2Trim Var.NA
V(Y[t],d=2,D=0)2.00400798364484Range4Trim Var.0
V(Y[t],d=3,D=0)6.01612903225806Range8Trim Var.2.65124771758977
V(Y[t],d=0,D=1)12.9287878277847Range18Trim Var.5.90521529955542
V(Y[t],d=1,D=1)2.04923061322788Range4Trim Var.0
V(Y[t],d=2,D=1)4.2803954011285Range8Trim Var.2.26939060590187
V(Y[t],d=3,D=1)13.1734855584902Range16Trim Var.6.16407633287429
V(Y[t],d=0,D=2)24.9703847854931Range26Trim Var.13.1274005881601
V(Y[t],d=1,D=2)6.31195203197868Range8Trim Var.2.68972103543604
V(Y[t],d=2,D=2)13.4291041114709Range16Trim Var.6.3949377101048
V(Y[t],d=3,D=2)41.8220159816534Range32Trim Var.23.6620396530968

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 54.8274308617234 & Range & 31 & Trim Var. & 36.6621660799337 \tabularnewline
V(Y[t],d=1,D=0) & 1.00152111451819 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.00400798364484 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.01612903225806 & Range & 8 & Trim Var. & 2.65124771758977 \tabularnewline
V(Y[t],d=0,D=1) & 12.9287878277847 & Range & 18 & Trim Var. & 5.90521529955542 \tabularnewline
V(Y[t],d=1,D=1) & 2.04923061322788 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.2803954011285 & Range & 8 & Trim Var. & 2.26939060590187 \tabularnewline
V(Y[t],d=3,D=1) & 13.1734855584902 & Range & 16 & Trim Var. & 6.16407633287429 \tabularnewline
V(Y[t],d=0,D=2) & 24.9703847854931 & Range & 26 & Trim Var. & 13.1274005881601 \tabularnewline
V(Y[t],d=1,D=2) & 6.31195203197868 & Range & 8 & Trim Var. & 2.68972103543604 \tabularnewline
V(Y[t],d=2,D=2) & 13.4291041114709 & Range & 16 & Trim Var. & 6.3949377101048 \tabularnewline
V(Y[t],d=3,D=2) & 41.8220159816534 & Range & 32 & Trim Var. & 23.6620396530968 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26533&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]54.8274308617234[/C][C]Range[/C][C]31[/C][C]Trim Var.[/C][C]36.6621660799337[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00152111451819[/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]2.00400798364484[/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]6.01612903225806[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.65124771758977[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.9287878277847[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]5.90521529955542[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.04923061322788[/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]4.2803954011285[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.26939060590187[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]13.1734855584902[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.16407633287429[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]24.9703847854931[/C][C]Range[/C][C]26[/C][C]Trim Var.[/C][C]13.1274005881601[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.31195203197868[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.68972103543604[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]13.4291041114709[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.3949377101048[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]41.8220159816534[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]23.6620396530968[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26533&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26533&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)54.8274308617234Range31Trim Var.36.6621660799337
V(Y[t],d=1,D=0)1.00152111451819Range2Trim Var.NA
V(Y[t],d=2,D=0)2.00400798364484Range4Trim Var.0
V(Y[t],d=3,D=0)6.01612903225806Range8Trim Var.2.65124771758977
V(Y[t],d=0,D=1)12.9287878277847Range18Trim Var.5.90521529955542
V(Y[t],d=1,D=1)2.04923061322788Range4Trim Var.0
V(Y[t],d=2,D=1)4.2803954011285Range8Trim Var.2.26939060590187
V(Y[t],d=3,D=1)13.1734855584902Range16Trim Var.6.16407633287429
V(Y[t],d=0,D=2)24.9703847854931Range26Trim Var.13.1274005881601
V(Y[t],d=1,D=2)6.31195203197868Range8Trim Var.2.68972103543604
V(Y[t],d=2,D=2)13.4291041114709Range16Trim Var.6.3949377101048
V(Y[t],d=3,D=2)41.8220159816534Range32Trim Var.23.6620396530968


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')