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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

Sun, 27 Dec 2009 04:57:57 -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/2009/Dec/27/t1261915127c6ngto7bny356mh.htm/, Retrieved Thu, 02 May 2024 23:45:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70856, Retrieved Thu, 02 May 2024 23:45:14 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

124

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

-       [Standard Deviation-Mean Plot] [Toon Nauwelaerts] [2009-12-27 11:57:57] [b7e924d6f720297f82cd59f42434ec05] [Current]

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Dataseries X:

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Histogram

Boxplots

7.3
7.1
7.1
6.8
6.5
6.3
6.1
6.1
6.3
6.3
6
6.2
6.4
6.8
7.5
7.5
7.6
7.6
7.4
7.3
7.1
6.9
6.8
7.5
7.6
7.8
8
8.1
8.2
8.3
8.2
8
7.9
7.6
7.6
8.2
8.3
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.5
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.6
8.2
8.1
8
8.6
8.7
8.8
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.1
8.2
8.1
8.1
7.9
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.6
6.2
6.2
6.8
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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70856&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70856&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70856&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	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	6.50833333333333	0.45016831868926	1.3
2	7.2	0.393122696553448	1.2
3	7.95833333333333	0.257464325272219	0.700000000000001
4	8.25833333333333	0.559964825735158	1.7
5	8.53333333333333	0.422833157152888	1.3
6	8.5	0.217422922601844	0.700000000000001
7	7.85	0.264575131106459	0.9
8	6.875	0.376889180722204	1.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6.50833333333333 & 0.45016831868926 & 1.3 \tabularnewline
2 & 7.2 & 0.393122696553448 & 1.2 \tabularnewline
3 & 7.95833333333333 & 0.257464325272219 & 0.700000000000001 \tabularnewline
4 & 8.25833333333333 & 0.559964825735158 & 1.7 \tabularnewline
5 & 8.53333333333333 & 0.422833157152888 & 1.3 \tabularnewline
6 & 8.5 & 0.217422922601844 & 0.700000000000001 \tabularnewline
7 & 7.85 & 0.264575131106459 & 0.9 \tabularnewline
8 & 6.875 & 0.376889180722204 & 1.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70856&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]6.50833333333333[/C][C]0.45016831868926[/C][C]1.3[/C][/ROW]
[ROW][C]2[/C][C]7.2[/C][C]0.393122696553448[/C][C]1.2[/C][/ROW]
[ROW][C]3[/C][C]7.95833333333333[/C][C]0.257464325272219[/C][C]0.700000000000001[/C][/ROW]
[ROW][C]4[/C][C]8.25833333333333[/C][C]0.559964825735158[/C][C]1.7[/C][/ROW]
[ROW][C]5[/C][C]8.53333333333333[/C][C]0.422833157152888[/C][C]1.3[/C][/ROW]
[ROW][C]6[/C][C]8.5[/C][C]0.217422922601844[/C][C]0.700000000000001[/C][/ROW]
[ROW][C]7[/C][C]7.85[/C][C]0.264575131106459[/C][C]0.9[/C][/ROW]
[ROW][C]8[/C][C]6.875[/C][C]0.376889180722204[/C][C]1.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70856&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70856&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	6.50833333333333	0.45016831868926	1.3
2	7.2	0.393122696553448	1.2
3	7.95833333333333	0.257464325272219	0.700000000000001
4	8.25833333333333	0.559964825735158	1.7
5	8.53333333333333	0.422833157152888	1.3
6	8.5	0.217422922601844	0.700000000000001
7	7.85	0.264575131106459	0.9
8	6.875	0.376889180722204	1.1

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.612129970251369
beta	-0.0316876390842066
S.D.	0.0601913371314476
T-STAT	-0.526448498975961
p-value	0.617461451845384

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.612129970251369 \tabularnewline
beta & -0.0316876390842066 \tabularnewline
S.D. & 0.0601913371314476 \tabularnewline
T-STAT & -0.526448498975961 \tabularnewline
p-value & 0.617461451845384 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70856&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.612129970251369[/C][/ROW]
[ROW][C]beta[/C][C]-0.0316876390842066[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0601913371314476[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.526448498975961[/C][/ROW]
[ROW][C]p-value[/C][C]0.617461451845384[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70856&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70856&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	0.612129970251369
beta	-0.0316876390842066
S.D.	0.0601913371314476
T-STAT	-0.526448498975961
p-value	0.617461451845384

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.892067071218492
beta	-0.950452405063625
S.D.	1.24583082294191
T-STAT	-0.762906477798663
p-value	0.474435417501438
Lambda	1.95045240506362

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.892067071218492 \tabularnewline
beta & -0.950452405063625 \tabularnewline
S.D. & 1.24583082294191 \tabularnewline
T-STAT & -0.762906477798663 \tabularnewline
p-value & 0.474435417501438 \tabularnewline
Lambda & 1.95045240506362 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70856&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.892067071218492[/C][/ROW]
[ROW][C]beta[/C][C]-0.950452405063625[/C][/ROW]
[ROW][C]S.D.[/C][C]1.24583082294191[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.762906477798663[/C][/ROW]
[ROW][C]p-value[/C][C]0.474435417501438[/C][/ROW]
[ROW][C]Lambda[/C][C]1.95045240506362[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70856&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70856&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	0.892067071218492
beta	-0.950452405063625
S.D.	1.24583082294191
T-STAT	-0.762906477798663
p-value	0.474435417501438
Lambda	1.95045240506362

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