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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

Wed, 22 Dec 2010 16:04:08 +0000

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/2010/Dec/22/t1293033835szq24fbtukb85p6.htm/, Retrieved Mon, 06 May 2024 09:15:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114342, Retrieved Mon, 06 May 2024 09:15:14 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [Standard Deviation-Mean Plot] [Paper Standard De...] [2010-12-22 16:04:08] [f38914513f1f4d866974b642cdd0baea] [Current]

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Histogram

Boxplots

0,504208603
0,457969746
0,509923035
0,606622221
0,626210885
0,626631316
0,676731276
0,613117455
0,486215861
0,452529881
0,467150592
0,494624486
0,444567428
0,478862605
0,544458459
0,628201498
0,672578445
0,652706633
0,645430599
0,576334011
0,618334234
0,639896351
0,72850438
0,694655375
0,689773225
0,712244845
0,760337031
0,837816503
0,90688735
0,976018259
0,962066806
0,837593417
0,767638807
0,580006349
0,387740568
0,331274078
0,345251272
0,380172806
0,399838692
0,425742404
0,524183377
0,597115327
0,541489699
0,615039426
0,547924872
0,574540743
0,603438956
0,577492342
0,614198564
0,584776957
0,62752366
0,676859979
0,645996894
0,596059959
0,585961029
0,607617528
0,598462423
0,638703699
0,64923164

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114342&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114342&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114342&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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	0.543494613083333	0.0798266402827084	0.224201395
2	0.6103775015	0.0850090618592825	0.283936952
3	0.7291164365	0.207090872344423	0.644744181
4	0.511019159666667	0.0962594148385083	0.269788154

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 0.543494613083333 & 0.0798266402827084 & 0.224201395 \tabularnewline
2 & 0.6103775015 & 0.0850090618592825 & 0.283936952 \tabularnewline
3 & 0.7291164365 & 0.207090872344423 & 0.644744181 \tabularnewline
4 & 0.511019159666667 & 0.0962594148385083 & 0.269788154 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114342&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]0.543494613083333[/C][C]0.0798266402827084[/C][C]0.224201395[/C][/ROW]
[ROW][C]2[/C][C]0.6103775015[/C][C]0.0850090618592825[/C][C]0.283936952[/C][/ROW]
[ROW][C]3[/C][C]0.7291164365[/C][C]0.207090872344423[/C][C]0.644744181[/C][/ROW]
[ROW][C]4[/C][C]0.511019159666667[/C][C]0.0962594148385083[/C][C]0.269788154[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114342&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114342&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	0.543494613083333	0.0798266402827084	0.224201395
2	0.6103775015	0.0850090618592825	0.283936952
3	0.7291164365	0.207090872344423	0.644744181
4	0.511019159666667	0.0962594148385083	0.269788154

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-0.210248946252271
beta	0.54685779350471
S.D.	0.216521317484687
T-STAT	2.52565336225328
p-value	0.127471551881751

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.210248946252271 \tabularnewline
beta & 0.54685779350471 \tabularnewline
S.D. & 0.216521317484687 \tabularnewline
T-STAT & 2.52565336225328 \tabularnewline
p-value & 0.127471551881751 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114342&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.210248946252271[/C][/ROW]
[ROW][C]beta[/C][C]0.54685779350471[/C][/ROW]
[ROW][C]S.D.[/C][C]0.216521317484687[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.52565336225328[/C][/ROW]
[ROW][C]p-value[/C][C]0.127471551881751[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114342&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114342&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	-0.210248946252271
beta	0.54685779350471
S.D.	0.216521317484687
T-STAT	2.52565336225328
p-value	0.127471551881751

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.0066211786431
beta	2.33498639605248
S.D.	1.12738936084732
T-STAT	2.07114460819246
p-value	0.17415693004637
Lambda	-1.33498639605248

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.0066211786431 \tabularnewline
beta & 2.33498639605248 \tabularnewline
S.D. & 1.12738936084732 \tabularnewline
T-STAT & 2.07114460819246 \tabularnewline
p-value & 0.17415693004637 \tabularnewline
Lambda & -1.33498639605248 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114342&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.0066211786431[/C][/ROW]
[ROW][C]beta[/C][C]2.33498639605248[/C][/ROW]
[ROW][C]S.D.[/C][C]1.12738936084732[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.07114460819246[/C][/ROW]
[ROW][C]p-value[/C][C]0.17415693004637[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.33498639605248[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114342&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114342&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	-1.0066211786431
beta	2.33498639605248
S.D.	1.12738936084732
T-STAT	2.07114460819246
p-value	0.17415693004637
Lambda	-1.33498639605248

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 ;

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