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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

Thu, 17 Dec 2009 16:29:15 -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/18/t1261092596uokqnfjo5sbeqoi.htm/, Retrieved Tue, 17 Jun 2025 06:22:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69148, Retrieved Tue, 17 Jun 2025 06:22:57 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

266

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]
-   PD        [Standard Deviation-Mean Plot] [Identifying integ...] [2009-11-23 19:29:32] [d46757a0a8c9b00540ab7e7e0c34bfc4]
-   P             [Standard Deviation-Mean Plot] [] [2009-12-17 23:29:15] [f90b018c65398c2fee7b197f24b65ddd] [Current]

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Dataseries X:

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Histogram

Boxplots

8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
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
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.2

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=69148&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=69148&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69148&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	8.33333333333333	0.648541487189571	2.1
2	8.46666666666667	0.365148371670111	1.4
3	8.43333333333333	0.238683256575942	0.700
4	7.79166666666667	0.299873710792131	0.9
5	7	0.513455318052471	1.8
6	7.53333333333333	0.534846338737217	1.7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.33333333333333 & 0.648541487189571 & 2.1 \tabularnewline
2 & 8.46666666666667 & 0.365148371670111 & 1.4 \tabularnewline
3 & 8.43333333333333 & 0.238683256575942 & 0.700 \tabularnewline
4 & 7.79166666666667 & 0.299873710792131 & 0.9 \tabularnewline
5 & 7 & 0.513455318052471 & 1.8 \tabularnewline
6 & 7.53333333333333 & 0.534846338737217 & 1.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69148&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]8.33333333333333[/C][C]0.648541487189571[/C][C]2.1[/C][/ROW]
[ROW][C]2[/C][C]8.46666666666667[/C][C]0.365148371670111[/C][C]1.4[/C][/ROW]
[ROW][C]3[/C][C]8.43333333333333[/C][C]0.238683256575942[/C][C]0.700[/C][/ROW]
[ROW][C]4[/C][C]7.79166666666667[/C][C]0.299873710792131[/C][C]0.9[/C][/ROW]
[ROW][C]5[/C][C]7[/C][C]0.513455318052471[/C][C]1.8[/C][/ROW]
[ROW][C]6[/C][C]7.53333333333333[/C][C]0.534846338737217[/C][C]1.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69148&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69148&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	8.33333333333333	0.648541487189571	2.1
2	8.46666666666667	0.365148371670111	1.4
3	8.43333333333333	0.238683256575942	0.700
4	7.79166666666667	0.299873710792131	0.9
5	7	0.513455318052471	1.8
6	7.53333333333333	0.534846338737217	1.7

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.08776978746855
beta	-0.0825527298081765
S.D.	0.126373492449734
T-STAT	-0.653244032493701
p-value	0.54924439802919

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.08776978746855 \tabularnewline
beta & -0.0825527298081765 \tabularnewline
S.D. & 0.126373492449734 \tabularnewline
T-STAT & -0.653244032493701 \tabularnewline
p-value & 0.54924439802919 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69148&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.08776978746855[/C][/ROW]
[ROW][C]beta[/C][C]-0.0825527298081765[/C][/ROW]
[ROW][C]S.D.[/C][C]0.126373492449734[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.653244032493701[/C][/ROW]
[ROW][C]p-value[/C][C]0.54924439802919[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69148&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69148&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	1.08776978746855
beta	-0.0825527298081765
S.D.	0.126373492449734
T-STAT	-0.653244032493701
p-value	0.54924439802919

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.98448504919170
beta	-1.87611572138014
S.D.	2.33711386161391
T-STAT	-0.80274895981515
p-value	0.467106215117767
Lambda	2.87611572138014

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.98448504919170 \tabularnewline
beta & -1.87611572138014 \tabularnewline
S.D. & 2.33711386161391 \tabularnewline
T-STAT & -0.80274895981515 \tabularnewline
p-value & 0.467106215117767 \tabularnewline
Lambda & 2.87611572138014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69148&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.98448504919170[/C][/ROW]
[ROW][C]beta[/C][C]-1.87611572138014[/C][/ROW]
[ROW][C]S.D.[/C][C]2.33711386161391[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.80274895981515[/C][/ROW]
[ROW][C]p-value[/C][C]0.467106215117767[/C][/ROW]
[ROW][C]Lambda[/C][C]2.87611572138014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69148&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69148&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	2.98448504919170
beta	-1.87611572138014
S.D.	2.33711386161391
T-STAT	-0.80274895981515
p-value	0.467106215117767
Lambda	2.87611572138014

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