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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

Tue, 06 Dec 2011 18:10:28 -0500

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/2011/Dec/06/t13232130768f00rtbpopiupje.htm/, Retrieved Mon, 29 Apr 2024 06:33:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152030, Retrieved Mon, 29 Apr 2024 06:33:35 +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] [WS9: SMP] [2010-12-03 10:37:40] [1fd136673b2a4fecb5c545b9b4a05d64]
F   P   [Standard Deviation-Mean Plot] [WS9: stationary v...] [2010-12-06 20:16:01] [1fd136673b2a4fecb5c545b9b4a05d64]
- R PD      [Standard Deviation-Mean Plot] [] [2011-12-06 23:10:28] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

6.7
6.9
7.2
7.1
6.5
6.6
6.7
6.9
7.1
7.4
7.6
7.8
8.1
8.5
8.7
8.8
8
8
8.3
8.5
8.7
8.6
8.3
7.9
7.9
8.1
8.3
8.1
7.4
7.3
7.7
8
8
7.7
6.9
6.6
6.9

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	'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152030&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152030&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152030&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	'George Udny Yule' @ yule.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	7.04166666666667	0.405548636996473	1.3
2	8.36666666666667	0.311399577664609	0.9
3	7.66666666666667	0.521071157823144	1.7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 7.04166666666667 & 0.405548636996473 & 1.3 \tabularnewline
2 & 8.36666666666667 & 0.311399577664609 & 0.9 \tabularnewline
3 & 7.66666666666667 & 0.521071157823144 & 1.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152030&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]7.04166666666667[/C][C]0.405548636996473[/C][C]1.3[/C][/ROW]
[ROW][C]2[/C][C]8.36666666666667[/C][C]0.311399577664609[/C][C]0.9[/C][/ROW]
[ROW][C]3[/C][C]7.66666666666667[/C][C]0.521071157823144[/C][C]1.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152030&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152030&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	7.04166666666667	0.405548636996473	1.3
2	8.36666666666667	0.311399577664609	0.9
3	7.66666666666667	0.521071157823144	1.7

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.99420844761622
beta	-0.0756058925401704
S.D.	0.139227977782572
T-STAT	-0.543036634908552
p-value	0.683293540925984

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.99420844761622 \tabularnewline
beta & -0.0756058925401704 \tabularnewline
S.D. & 0.139227977782572 \tabularnewline
T-STAT & -0.543036634908552 \tabularnewline
p-value & 0.683293540925984 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152030&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.99420844761622[/C][/ROW]
[ROW][C]beta[/C][C]-0.0756058925401704[/C][/ROW]
[ROW][C]S.D.[/C][C]0.139227977782572[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.543036634908552[/C][/ROW]
[ROW][C]p-value[/C][C]0.683293540925984[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152030&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152030&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	0.99420844761622
beta	-0.0756058925401704
S.D.	0.139227977782572
T-STAT	-0.543036634908552
p-value	0.683293540925984

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.25571377396824
beta	-1.5521397349295
S.D.	2.55113013353782
T-STAT	-0.608412606838307
p-value	0.65203490732088
Lambda	2.5521397349295

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.25571377396824 \tabularnewline
beta & -1.5521397349295 \tabularnewline
S.D. & 2.55113013353782 \tabularnewline
T-STAT & -0.608412606838307 \tabularnewline
p-value & 0.65203490732088 \tabularnewline
Lambda & 2.5521397349295 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152030&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.25571377396824[/C][/ROW]
[ROW][C]beta[/C][C]-1.5521397349295[/C][/ROW]
[ROW][C]S.D.[/C][C]2.55113013353782[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.608412606838307[/C][/ROW]
[ROW][C]p-value[/C][C]0.65203490732088[/C][/ROW]
[ROW][C]Lambda[/C][C]2.5521397349295[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152030&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152030&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	2.25571377396824
beta	-1.5521397349295
S.D.	2.55113013353782
T-STAT	-0.608412606838307
p-value	0.65203490732088
Lambda	2.5521397349295

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