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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 19 Dec 2007 05:05:12 -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/2007/Dec/19/t119806492559zxphqwodbmx8w.htm/, Retrieved Mon, 06 May 2024 20:27:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4641, Retrieved Mon, 06 May 2024 20:27:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact219

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [l] [2007-12-19 12:05:12] [e2f7a6e26aa7cf06a3d27eb5298a4843] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1
1.04
1.02
1.07
1.12
1.08
1.02
1.01
1.04
0.98
0.95
0.94
0.94
0.96
0.97
1.03
1.01
0.99
1
1
1.02
1.01
0.99
0.98
1.01
1.03
1.03
1
0.96
0.97
0.98
1.02
1.04
1.01
1.01
1
1.01
1.02
1.03
1.06
1.12
1.12
1.13
1.13
1.13
1.17
1.14
1.08
1.07
1.12
1.14
1.21
1.2
1.23
1.29
1.31
1.37
1.35
1.26
1.26
1.28
1.28
1.27
1.35
1.37
1.37
1.4
1.4
1.28
1.23
1.23
1.25
1.21
1.22
1.29
1.32
1.36
1.36
1.37
1.32

Tables (Output of Computation)





Summary of compuational 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 compuational 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=4641&T=0

[TABLE]
[ROW][C]Summary of compuational 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=4641&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4641&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 compuational 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






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11.02250.05241876832516460.18
20.9916666666666670.02587850400809470.07
31.0050.02467976720090590.07
41.0950.05317210478505360.17
51.234166666666670.09179605193860550.41
61.309166666666670.06444988656923980.43

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.0225 & 0.0524187683251646 & 0.18 \tabularnewline
2 & 0.991666666666667 & 0.0258785040080947 & 0.07 \tabularnewline
3 & 1.005 & 0.0246797672009059 & 0.07 \tabularnewline
4 & 1.095 & 0.0531721047850536 & 0.17 \tabularnewline
5 & 1.23416666666667 & 0.0917960519386055 & 0.41 \tabularnewline
6 & 1.30916666666667 & 0.0644498865692398 & 0.43 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4641&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]1.0225[/C][C]0.0524187683251646[/C][C]0.18[/C][/ROW]
[ROW][C]2[/C][C]0.991666666666667[/C][C]0.0258785040080947[/C][C]0.07[/C][/ROW]
[ROW][C]3[/C][C]1.005[/C][C]0.0246797672009059[/C][C]0.07[/C][/ROW]
[ROW][C]4[/C][C]1.095[/C][C]0.0531721047850536[/C][C]0.17[/C][/ROW]
[ROW][C]5[/C][C]1.23416666666667[/C][C]0.0917960519386055[/C][C]0.41[/C][/ROW]
[ROW][C]6[/C][C]1.30916666666667[/C][C]0.0644498865692398[/C][C]0.43[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4641&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4641&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:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11.02250.05241876832516460.18
20.9916666666666670.02587850400809470.07
31.0050.02467976720090590.07
41.0950.05317210478505360.17
51.234166666666670.09179605193860550.41
61.309166666666670.06444988656923980.43






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.115981290171656
beta0.151450668247390
S.D.0.0571768600471921
T-STAT2.64881051744337
p-value0.0570526147225001

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.115981290171656 \tabularnewline
beta & 0.151450668247390 \tabularnewline
S.D. & 0.0571768600471921 \tabularnewline
T-STAT & 2.64881051744337 \tabularnewline
p-value & 0.0570526147225001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4641&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.115981290171656[/C][/ROW]
[ROW][C]beta[/C][C]0.151450668247390[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0571768600471921[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.64881051744337[/C][/ROW]
[ROW][C]p-value[/C][C]0.0570526147225001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4641&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4641&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.115981290171656
beta0.151450668247390
S.D.0.0571768600471921
T-STAT2.64881051744337
p-value0.0570526147225001






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.41460775288589
beta3.5947191074525
S.D.1.31716917293219
T-STAT2.72912483933267
p-value0.0524903112356863
Lambda-2.5947191074525

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.41460775288589 \tabularnewline
beta & 3.5947191074525 \tabularnewline
S.D. & 1.31716917293219 \tabularnewline
T-STAT & 2.72912483933267 \tabularnewline
p-value & 0.0524903112356863 \tabularnewline
Lambda & -2.5947191074525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4641&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.41460775288589[/C][/ROW]
[ROW][C]beta[/C][C]3.5947191074525[/C][/ROW]
[ROW][C]S.D.[/C][C]1.31716917293219[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.72912483933267[/C][/ROW]
[ROW][C]p-value[/C][C]0.0524903112356863[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.5947191074525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4641&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4641&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.41460775288589
beta3.5947191074525
S.D.1.31716917293219
T-STAT2.72912483933267
p-value0.0524903112356863
Lambda-2.5947191074525


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[j,],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')