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 computationMon, 01 Dec 2008 12:21:38 -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/t1228159343pzh2949fy53z13q.htm/, Retrieved Sun, 05 May 2024 08:57:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27218, Retrieved Sun, 05 May 2024 08:57:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact221

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 reproduce] [2008-12-01 19:21:38] [c040f376c7eef5bfe1cb52dcc7980437] [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 time0 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27218&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]0 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=27218&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27218&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 time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)75.5230460921844Range36Trim Var.52.233571693416
V(Y[t],d=1,D=0)0.99862375353116Range2Trim Var.NA
V(Y[t],d=2,D=0)1.90742850678367Range4Trim Var.0
V(Y[t],d=3,D=0)5.83062893489972Range8Trim Var.2.40289250210127
V(Y[t],d=0,D=1)12.9862322011647Range18Trim Var.5.76102196603832
V(Y[t],d=1,D=1)1.82709289257316Range4Trim Var.0
V(Y[t],d=2,D=1)3.76082474226804Range8Trim Var.2.09801046203681
V(Y[t],d=3,D=1)11.6694214876033Range16Trim Var.5.75330727054865
V(Y[t],d=0,D=2)18.2803361344538Range22Trim Var.8.99106882569634
V(Y[t],d=1,D=2)5.33269375971575Range8Trim Var.2.51551773049645
V(Y[t],d=2,D=2)11.0950660565026Range16Trim Var.6.08385331143952
V(Y[t],d=3,D=2)34.1779481850432Range30Trim Var.19.3860204228391

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 75.5230460921844 & Range & 36 & Trim Var. & 52.233571693416 \tabularnewline
V(Y[t],d=1,D=0) & 0.99862375353116 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.90742850678367 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.83062893489972 & Range & 8 & Trim Var. & 2.40289250210127 \tabularnewline
V(Y[t],d=0,D=1) & 12.9862322011647 & Range & 18 & Trim Var. & 5.76102196603832 \tabularnewline
V(Y[t],d=1,D=1) & 1.82709289257316 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.76082474226804 & Range & 8 & Trim Var. & 2.09801046203681 \tabularnewline
V(Y[t],d=3,D=1) & 11.6694214876033 & Range & 16 & Trim Var. & 5.75330727054865 \tabularnewline
V(Y[t],d=0,D=2) & 18.2803361344538 & Range & 22 & Trim Var. & 8.99106882569634 \tabularnewline
V(Y[t],d=1,D=2) & 5.33269375971575 & Range & 8 & Trim Var. & 2.51551773049645 \tabularnewline
V(Y[t],d=2,D=2) & 11.0950660565026 & Range & 16 & Trim Var. & 6.08385331143952 \tabularnewline
V(Y[t],d=3,D=2) & 34.1779481850432 & Range & 30 & Trim Var. & 19.3860204228391 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27218&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]75.5230460921844[/C][C]Range[/C][C]36[/C][C]Trim Var.[/C][C]52.233571693416[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.99862375353116[/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]1.90742850678367[/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]5.83062893489972[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.40289250210127[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12.9862322011647[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]5.76102196603832[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.82709289257316[/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]3.76082474226804[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.09801046203681[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.6694214876033[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]5.75330727054865[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]18.2803361344538[/C][C]Range[/C][C]22[/C][C]Trim Var.[/C][C]8.99106882569634[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.33269375971575[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.51551773049645[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.0950660565026[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.08385331143952[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]34.1779481850432[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]19.3860204228391[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27218&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27218&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)75.5230460921844Range36Trim Var.52.233571693416
V(Y[t],d=1,D=0)0.99862375353116Range2Trim Var.NA
V(Y[t],d=2,D=0)1.90742850678367Range4Trim Var.0
V(Y[t],d=3,D=0)5.83062893489972Range8Trim Var.2.40289250210127
V(Y[t],d=0,D=1)12.9862322011647Range18Trim Var.5.76102196603832
V(Y[t],d=1,D=1)1.82709289257316Range4Trim Var.0
V(Y[t],d=2,D=1)3.76082474226804Range8Trim Var.2.09801046203681
V(Y[t],d=3,D=1)11.6694214876033Range16Trim Var.5.75330727054865
V(Y[t],d=0,D=2)18.2803361344538Range22Trim Var.8.99106882569634
V(Y[t],d=1,D=2)5.33269375971575Range8Trim Var.2.51551773049645
V(Y[t],d=2,D=2)11.0950660565026Range16Trim Var.6.08385331143952
V(Y[t],d=3,D=2)34.1779481850432Range30Trim Var.19.3860204228391


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')