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 computationMon, 01 Dec 2008 08:44:47 -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/t1228146360mbzkn2rjzn43qa7.htm/, Retrieved Sun, 05 May 2024 14:19:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26952, Retrieved Sun, 05 May 2024 14:19:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact186

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] [2008-12-01 15:44:47] [7ed4ec9f8cdf7df79ef87b9dc09dff20] [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=26952&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=26952&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26952&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)113.901306613226Range42Trim Var.82.884107716791
V(Y[t],d=1,D=0)1.00055532752251Range2Trim Var.NA
V(Y[t],d=2,D=0)2.07645875251509Range4Trim Var.0
V(Y[t],d=3,D=0)6.32251573959888Range8Trim Var.2.69135764680675
V(Y[t],d=0,D=1)10.8125357659811Range18Trim Var.5.17217348436467
V(Y[t],d=1,D=1)1.9833869918287Range4Trim Var.0
V(Y[t],d=2,D=1)4.11544694752026Range8Trim Var.2.30822573200797
V(Y[t],d=3,D=1)12.4132231404959Range16Trim Var.6.35399095465102
V(Y[t],d=0,D=2)19.0642016806723Range24Trim Var.11.4001643570375
V(Y[t],d=1,D=2)5.84808349988896Range8Trim Var.2.74013864922956
V(Y[t],d=2,D=2)12.1522020320961Range16Trim Var.6.74997506234414
V(Y[t],d=3,D=2)36.6693302755581Range32Trim Var.22.5530454406545

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 113.901306613226 & Range & 42 & Trim Var. & 82.884107716791 \tabularnewline
V(Y[t],d=1,D=0) & 1.00055532752251 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 2.07645875251509 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 6.32251573959888 & Range & 8 & Trim Var. & 2.69135764680675 \tabularnewline
V(Y[t],d=0,D=1) & 10.8125357659811 & Range & 18 & Trim Var. & 5.17217348436467 \tabularnewline
V(Y[t],d=1,D=1) & 1.9833869918287 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.11544694752026 & Range & 8 & Trim Var. & 2.30822573200797 \tabularnewline
V(Y[t],d=3,D=1) & 12.4132231404959 & Range & 16 & Trim Var. & 6.35399095465102 \tabularnewline
V(Y[t],d=0,D=2) & 19.0642016806723 & Range & 24 & Trim Var. & 11.4001643570375 \tabularnewline
V(Y[t],d=1,D=2) & 5.84808349988896 & Range & 8 & Trim Var. & 2.74013864922956 \tabularnewline
V(Y[t],d=2,D=2) & 12.1522020320961 & Range & 16 & Trim Var. & 6.74997506234414 \tabularnewline
V(Y[t],d=3,D=2) & 36.6693302755581 & Range & 32 & Trim Var. & 22.5530454406545 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26952&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]113.901306613226[/C][C]Range[/C][C]42[/C][C]Trim Var.[/C][C]82.884107716791[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00055532752251[/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]2.07645875251509[/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]6.32251573959888[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.69135764680675[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.8125357659811[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]5.17217348436467[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1.9833869918287[/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]4.11544694752026[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.30822573200797[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]12.4132231404959[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.35399095465102[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]19.0642016806723[/C][C]Range[/C][C]24[/C][C]Trim Var.[/C][C]11.4001643570375[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5.84808349988896[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.74013864922956[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.1522020320961[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.74997506234414[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.6693302755581[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]22.5530454406545[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26952&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26952&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)113.901306613226Range42Trim Var.82.884107716791
V(Y[t],d=1,D=0)1.00055532752251Range2Trim Var.NA
V(Y[t],d=2,D=0)2.07645875251509Range4Trim Var.0
V(Y[t],d=3,D=0)6.32251573959888Range8Trim Var.2.69135764680675
V(Y[t],d=0,D=1)10.8125357659811Range18Trim Var.5.17217348436467
V(Y[t],d=1,D=1)1.9833869918287Range4Trim Var.0
V(Y[t],d=2,D=1)4.11544694752026Range8Trim Var.2.30822573200797
V(Y[t],d=3,D=1)12.4132231404959Range16Trim Var.6.35399095465102
V(Y[t],d=0,D=2)19.0642016806723Range24Trim Var.11.4001643570375
V(Y[t],d=1,D=2)5.84808349988896Range8Trim Var.2.74013864922956
V(Y[t],d=2,D=2)12.1522020320961Range16Trim Var.6.74997506234414
V(Y[t],d=3,D=2)36.6693302755581Range32Trim Var.22.5530454406545


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')