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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

Tue, 07 Dec 2010 16:53:41 +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/07/t1291741388ke1mmqx3j9mpir8.htm/, Retrieved Sun, 22 Jun 2025 02:12:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106533, Retrieved Sun, 22 Jun 2025 02:12:52 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

243

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
-    D        [Standard Deviation-Mean Plot] [standard deviatio...] [2009-11-24 21:20:13] [8b1aef4e7013bd33fbc2a5833375c5f5]
-                 [Standard Deviation-Mean Plot] [paper Fase 2: SDMP 2] [2010-12-07 16:53:41] [da925928e5a77063c5ecc7b801d712e1] [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' @ 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=106533&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=106533&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106533&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	156.983333333333	1.81350155191218	6
2	162.916666666667	1.54026758792888	4.90000000000001
3	167.958333333333	1.60479867518601	4.69999999999999
4	172.133333333333	1.31241161318553	4
5	175.591666666667	0.792531425626805	2.79999999999998
6	179.233333333333	1.16489042273069	4.09999999999999
7	182.95	1.23029929839708	4
8	187.55	1.26167277129142	4.09999999999999
9	192.641666666667	2.22729282613071	6.30000000000001
10	196.716666666667	1.14561085994514	3.59999999999999
11	202.366666666667	2.04465304162004	5.9
12	207.258333333333	1.49146562044510	4.29999999999998
13	211.35	1.29087708026893	3.70000000000002
14	215.975	1.57545087341543	4.40000000000001
15	221.133333333333	1.55407577522832	4.5
16	226.275	1.57718102955875	5
17	229.825	0.970590260895631	3.19999999999999
18	236.991666666667	2.62140085149952	8.29999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 156.983333333333 & 1.81350155191218 & 6 \tabularnewline
2 & 162.916666666667 & 1.54026758792888 & 4.90000000000001 \tabularnewline
3 & 167.958333333333 & 1.60479867518601 & 4.69999999999999 \tabularnewline
4 & 172.133333333333 & 1.31241161318553 & 4 \tabularnewline
5 & 175.591666666667 & 0.792531425626805 & 2.79999999999998 \tabularnewline
6 & 179.233333333333 & 1.16489042273069 & 4.09999999999999 \tabularnewline
7 & 182.95 & 1.23029929839708 & 4 \tabularnewline
8 & 187.55 & 1.26167277129142 & 4.09999999999999 \tabularnewline
9 & 192.641666666667 & 2.22729282613071 & 6.30000000000001 \tabularnewline
10 & 196.716666666667 & 1.14561085994514 & 3.59999999999999 \tabularnewline
11 & 202.366666666667 & 2.04465304162004 & 5.9 \tabularnewline
12 & 207.258333333333 & 1.49146562044510 & 4.29999999999998 \tabularnewline
13 & 211.35 & 1.29087708026893 & 3.70000000000002 \tabularnewline
14 & 215.975 & 1.57545087341543 & 4.40000000000001 \tabularnewline
15 & 221.133333333333 & 1.55407577522832 & 4.5 \tabularnewline
16 & 226.275 & 1.57718102955875 & 5 \tabularnewline
17 & 229.825 & 0.970590260895631 & 3.19999999999999 \tabularnewline
18 & 236.991666666667 & 2.62140085149952 & 8.29999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106533&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]156.983333333333[/C][C]1.81350155191218[/C][C]6[/C][/ROW]
[ROW][C]2[/C][C]162.916666666667[/C][C]1.54026758792888[/C][C]4.90000000000001[/C][/ROW]
[ROW][C]3[/C][C]167.958333333333[/C][C]1.60479867518601[/C][C]4.69999999999999[/C][/ROW]
[ROW][C]4[/C][C]172.133333333333[/C][C]1.31241161318553[/C][C]4[/C][/ROW]
[ROW][C]5[/C][C]175.591666666667[/C][C]0.792531425626805[/C][C]2.79999999999998[/C][/ROW]
[ROW][C]6[/C][C]179.233333333333[/C][C]1.16489042273069[/C][C]4.09999999999999[/C][/ROW]
[ROW][C]7[/C][C]182.95[/C][C]1.23029929839708[/C][C]4[/C][/ROW]
[ROW][C]8[/C][C]187.55[/C][C]1.26167277129142[/C][C]4.09999999999999[/C][/ROW]
[ROW][C]9[/C][C]192.641666666667[/C][C]2.22729282613071[/C][C]6.30000000000001[/C][/ROW]
[ROW][C]10[/C][C]196.716666666667[/C][C]1.14561085994514[/C][C]3.59999999999999[/C][/ROW]
[ROW][C]11[/C][C]202.366666666667[/C][C]2.04465304162004[/C][C]5.9[/C][/ROW]
[ROW][C]12[/C][C]207.258333333333[/C][C]1.49146562044510[/C][C]4.29999999999998[/C][/ROW]
[ROW][C]13[/C][C]211.35[/C][C]1.29087708026893[/C][C]3.70000000000002[/C][/ROW]
[ROW][C]14[/C][C]215.975[/C][C]1.57545087341543[/C][C]4.40000000000001[/C][/ROW]
[ROW][C]15[/C][C]221.133333333333[/C][C]1.55407577522832[/C][C]4.5[/C][/ROW]
[ROW][C]16[/C][C]226.275[/C][C]1.57718102955875[/C][C]5[/C][/ROW]
[ROW][C]17[/C][C]229.825[/C][C]0.970590260895631[/C][C]3.19999999999999[/C][/ROW]
[ROW][C]18[/C][C]236.991666666667[/C][C]2.62140085149952[/C][C]8.29999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106533&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106533&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	156.983333333333	1.81350155191218	6
2	162.916666666667	1.54026758792888	4.90000000000001
3	167.958333333333	1.60479867518601	4.69999999999999
4	172.133333333333	1.31241161318553	4
5	175.591666666667	0.792531425626805	2.79999999999998
6	179.233333333333	1.16489042273069	4.09999999999999
7	182.95	1.23029929839708	4
8	187.55	1.26167277129142	4.09999999999999
9	192.641666666667	2.22729282613071	6.30000000000001
10	196.716666666667	1.14561085994514	3.59999999999999
11	202.366666666667	2.04465304162004	5.9
12	207.258333333333	1.49146562044510	4.29999999999998
13	211.35	1.29087708026893	3.70000000000002
14	215.975	1.57545087341543	4.40000000000001
15	221.133333333333	1.55407577522832	4.5
16	226.275	1.57718102955875	5
17	229.825	0.970590260895631	3.19999999999999
18	236.991666666667	2.62140085149952	8.29999999999998

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.652474068308027
beta	0.00438885327955577
S.D.	0.00447711574728643
T-STAT	0.980285864223154
p-value	0.341536197888881

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.652474068308027 \tabularnewline
beta & 0.00438885327955577 \tabularnewline
S.D. & 0.00447711574728643 \tabularnewline
T-STAT & 0.980285864223154 \tabularnewline
p-value & 0.341536197888881 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106533&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.652474068308027[/C][/ROW]
[ROW][C]beta[/C][C]0.00438885327955577[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00447711574728643[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.980285864223154[/C][/ROW]
[ROW][C]p-value[/C][C]0.341536197888881[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106533&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106533&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	0.652474068308027
beta	0.00438885327955577
S.D.	0.00447711574728643
T-STAT	0.980285864223154
p-value	0.341536197888881

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.86097976704424
beta	0.423996886114892
S.D.	0.571125813735332
T-STAT	0.742387887078377
p-value	0.468612008528257
Lambda	0.576003113885108

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.86097976704424 \tabularnewline
beta & 0.423996886114892 \tabularnewline
S.D. & 0.571125813735332 \tabularnewline
T-STAT & 0.742387887078377 \tabularnewline
p-value & 0.468612008528257 \tabularnewline
Lambda & 0.576003113885108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106533&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.86097976704424[/C][/ROW]
[ROW][C]beta[/C][C]0.423996886114892[/C][/ROW]
[ROW][C]S.D.[/C][C]0.571125813735332[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.742387887078377[/C][/ROW]
[ROW][C]p-value[/C][C]0.468612008528257[/C][/ROW]
[ROW][C]Lambda[/C][C]0.576003113885108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106533&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106533&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	-1.86097976704424
beta	0.423996886114892
S.D.	0.571125813735332
T-STAT	0.742387887078377
p-value	0.468612008528257
Lambda	0.576003113885108

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code