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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Thu, 18 Dec 2008 08:09:25 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/18/t1229613016ra7so4uwq8waevv.htm/, Retrieved Sun, 12 May 2024 11:30:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34826, Retrieved Sun, 12 May 2024 11:30:43 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

k_vanderheggen

Estimated Impact

178

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F     [Standard Deviation-Mean Plot] [eigen tijdreeks A...] [2008-12-09 16:57:22] [42e82fcd8ee0f4c6e81d502bb09e62b7]
-         [Standard Deviation-Mean Plot] [Paper SDMP] [2008-12-18 15:09:25] [547f3960ab1cda94661cd6e0871d2c7b] [Current]

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Dataseries X:

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Histogram

Boxplots

5,5
5,3
5,2
5,3
5,3
5
4,8
4,9
5,3
6
6,2
6,4
6,4
6,4
6,2
6,1
6
5,9
6,2
6,2
6,4
6,8
6,9
7
7
6,9
6,7
6,6
6,5
6,4
6,5
6,5
6,6
6,7
6,8
7,2
7,6
7,6
7,3
6,4
6,1
6,3
7,1
7,5
7,4
7,1
6,8
6,9
7,2
7,4
7,3
6,9
6,9
6,8
7,1
7,2
7,1
7
6,9
7
7,4
7,5
7,5
7,4
7,3
7
6,7
6,5
6,5
6,5
6,6
6,8
6,9
6,9
6,8
6,8
6,5
6,1
6
5,9
5,8
5,9
5,9
6,2
6,3
6,2
6
5,8
5,5
5,5
5,7
5,8

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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=34826&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=34826&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34826&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	5.43333333333333	0.508711980189064	1.6
2	6.375	0.354516315818917	1.1
3	6.7	0.23741027013092	0.8
4	7.00833333333333	0.517789591056117	1.5
5	7.06666666666667	0.182574185835055	0.6
6	6.975	0.420227211268986	1
7	6.30833333333333	0.439955231882297	1.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5.43333333333333 & 0.508711980189064 & 1.6 \tabularnewline
2 & 6.375 & 0.354516315818917 & 1.1 \tabularnewline
3 & 6.7 & 0.23741027013092 & 0.8 \tabularnewline
4 & 7.00833333333333 & 0.517789591056117 & 1.5 \tabularnewline
5 & 7.06666666666667 & 0.182574185835055 & 0.6 \tabularnewline
6 & 6.975 & 0.420227211268986 & 1 \tabularnewline
7 & 6.30833333333333 & 0.439955231882297 & 1.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34826&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]5.43333333333333[/C][C]0.508711980189064[/C][C]1.6[/C][/ROW]
[ROW][C]2[/C][C]6.375[/C][C]0.354516315818917[/C][C]1.1[/C][/ROW]
[ROW][C]3[/C][C]6.7[/C][C]0.23741027013092[/C][C]0.8[/C][/ROW]
[ROW][C]4[/C][C]7.00833333333333[/C][C]0.517789591056117[/C][C]1.5[/C][/ROW]
[ROW][C]5[/C][C]7.06666666666667[/C][C]0.182574185835055[/C][C]0.6[/C][/ROW]
[ROW][C]6[/C][C]6.975[/C][C]0.420227211268986[/C][C]1[/C][/ROW]
[ROW][C]7[/C][C]6.30833333333333[/C][C]0.439955231882297[/C][C]1.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34826&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34826&T=1

As an alternative you can also use a QR Code:

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

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	5.43333333333333	0.508711980189064	1.6
2	6.375	0.354516315818917	1.1
3	6.7	0.23741027013092	0.8
4	7.00833333333333	0.517789591056117	1.5
5	7.06666666666667	0.182574185835055	0.6
6	6.975	0.420227211268986	1
7	6.30833333333333	0.439955231882297	1.1

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.02011660363127
beta	-0.0976663831229108
S.D.	0.0899128609553385
T-STAT	-1.08623373881322
p-value	0.326946075736779

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.02011660363127 \tabularnewline
beta & -0.0976663831229108 \tabularnewline
S.D. & 0.0899128609553385 \tabularnewline
T-STAT & -1.08623373881322 \tabularnewline
p-value & 0.326946075736779 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34826&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.02011660363127[/C][/ROW]
[ROW][C]beta[/C][C]-0.0976663831229108[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0899128609553385[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.08623373881322[/C][/ROW]
[ROW][C]p-value[/C][C]0.326946075736779[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34826&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34826&T=2

As an alternative you can also use a QR Code:

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

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.02011660363127
beta	-0.0976663831229108
S.D.	0.0899128609553385
T-STAT	-1.08623373881322
p-value	0.326946075736779

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.54106893075445
beta	-1.90236405060300
S.D.	1.71561108454999
T-STAT	-1.10885507078779
p-value	0.317958245814863
Lambda	2.90236405060300

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.54106893075445 \tabularnewline
beta & -1.90236405060300 \tabularnewline
S.D. & 1.71561108454999 \tabularnewline
T-STAT & -1.10885507078779 \tabularnewline
p-value & 0.317958245814863 \tabularnewline
Lambda & 2.90236405060300 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34826&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.54106893075445[/C][/ROW]
[ROW][C]beta[/C][C]-1.90236405060300[/C][/ROW]
[ROW][C]S.D.[/C][C]1.71561108454999[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.10885507078779[/C][/ROW]
[ROW][C]p-value[/C][C]0.317958245814863[/C][/ROW]
[ROW][C]Lambda[/C][C]2.90236405060300[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34826&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34826&T=3

As an alternative you can also use a QR Code:

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

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.54106893075445
beta	-1.90236405060300
S.D.	1.71561108454999
T-STAT	-1.10885507078779
p-value	0.317958245814863
Lambda	2.90236405060300

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = ; 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):

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code