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Author's title

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Wed, 13 Aug 2014 10:59:59 +0100

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/2014/Aug/13/t1407924062dv7qhyhvv7v7849.htm/, Retrieved Thu, 16 May 2024 12:54:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235498, Retrieved Thu, 16 May 2024 12:54:50 +0000

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Estimated Impact

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

-     [(Partial) Autocorrelation Function] [] [2014-08-13 09:41:06] [ba0170e6f15797e8c541ec0953bc1848]
- RMP     [Standard Deviation-Mean Plot] [] [2014-08-13 09:59:59] [b3e3d38149b35cb70244b37a39776b3a] [Current]

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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' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235498&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235498&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235498&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' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	104.5	8.72301032275608	26
2	127.166666666667	15.3376146855508	39
3	167.166666666667	13.7499311293041	36
4	205.416666666667	14.5380899916757	38
5	247.416666666667	20.7691131396134	55
6	311.5	24.3926218353009	70
7	390.583333333333	28.2471505669424	78
8	473.833333333333	30.9687036548288	82
9	564.166666666667	35.6493869214996	99
10	654.666666666667	39.3754268856128	106

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 104.5 & 8.72301032275608 & 26 \tabularnewline
2 & 127.166666666667 & 15.3376146855508 & 39 \tabularnewline
3 & 167.166666666667 & 13.7499311293041 & 36 \tabularnewline
4 & 205.416666666667 & 14.5380899916757 & 38 \tabularnewline
5 & 247.416666666667 & 20.7691131396134 & 55 \tabularnewline
6 & 311.5 & 24.3926218353009 & 70 \tabularnewline
7 & 390.583333333333 & 28.2471505669424 & 78 \tabularnewline
8 & 473.833333333333 & 30.9687036548288 & 82 \tabularnewline
9 & 564.166666666667 & 35.6493869214996 & 99 \tabularnewline
10 & 654.666666666667 & 39.3754268856128 & 106 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235498&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]104.5[/C][C]8.72301032275608[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]127.166666666667[/C][C]15.3376146855508[/C][C]39[/C][/ROW]
[ROW][C]3[/C][C]167.166666666667[/C][C]13.7499311293041[/C][C]36[/C][/ROW]
[ROW][C]4[/C][C]205.416666666667[/C][C]14.5380899916757[/C][C]38[/C][/ROW]
[ROW][C]5[/C][C]247.416666666667[/C][C]20.7691131396134[/C][C]55[/C][/ROW]
[ROW][C]6[/C][C]311.5[/C][C]24.3926218353009[/C][C]70[/C][/ROW]
[ROW][C]7[/C][C]390.583333333333[/C][C]28.2471505669424[/C][C]78[/C][/ROW]
[ROW][C]8[/C][C]473.833333333333[/C][C]30.9687036548288[/C][C]82[/C][/ROW]
[ROW][C]9[/C][C]564.166666666667[/C][C]35.6493869214996[/C][C]99[/C][/ROW]
[ROW][C]10[/C][C]654.666666666667[/C][C]39.3754268856128[/C][C]106[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235498&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235498&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	104.5	8.72301032275608	26
2	127.166666666667	15.3376146855508	39
3	167.166666666667	13.7499311293041	36
4	205.416666666667	14.5380899916757	38
5	247.416666666667	20.7691131396134	55
6	311.5	24.3926218353009	70
7	390.583333333333	28.2471505669424	78
8	473.833333333333	30.9687036548288	82
9	564.166666666667	35.6493869214996	99
10	654.666666666667	39.3754268856128	106

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	5.97614315505707
beta	0.0529782942985899
S.D.	0.00350148254532131
T-STAT	15.1302465778045
p-value	3.60355203347105e-07

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.97614315505707 \tabularnewline
beta & 0.0529782942985899 \tabularnewline
S.D. & 0.00350148254532131 \tabularnewline
T-STAT & 15.1302465778045 \tabularnewline
p-value & 3.60355203347105e-07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235498&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.97614315505707[/C][/ROW]
[ROW][C]beta[/C][C]0.0529782942985899[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00350148254532131[/C][/ROW]
[ROW][C]T-STAT[/C][C]15.1302465778045[/C][/ROW]
[ROW][C]p-value[/C][C]3.60355203347105e-07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235498&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235498&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	5.97614315505707
beta	0.0529782942985899
S.D.	0.00350148254532131
T-STAT	15.1302465778045
p-value	3.60355203347105e-07

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.14645381308243
beta	0.746487931115477
S.D.	0.066790572884601
T-STAT	11.176546312984
p-value	3.67834766631973e-06
Lambda	0.253512068884523

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.14645381308243 \tabularnewline
beta & 0.746487931115477 \tabularnewline
S.D. & 0.066790572884601 \tabularnewline
T-STAT & 11.176546312984 \tabularnewline
p-value & 3.67834766631973e-06 \tabularnewline
Lambda & 0.253512068884523 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235498&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.14645381308243[/C][/ROW]
[ROW][C]beta[/C][C]0.746487931115477[/C][/ROW]
[ROW][C]S.D.[/C][C]0.066790572884601[/C][/ROW]
[ROW][C]T-STAT[/C][C]11.176546312984[/C][/ROW]
[ROW][C]p-value[/C][C]3.67834766631973e-06[/C][/ROW]
[ROW][C]Lambda[/C][C]0.253512068884523[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235498&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235498&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	-1.14645381308243
beta	0.746487931115477
S.D.	0.066790572884601
T-STAT	11.176546312984
p-value	3.67834766631973e-06
Lambda	0.253512068884523

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = 48 ;

Parameters (R input):

par1 = 12 ;

R code (references can be found in the software module):

par1 <- '12'
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