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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, 24 Nov 2009 14:12:18 -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/Nov/24/t1259097406952384k1ag2vosg.htm/, Retrieved Tue, 04 Nov 2025 15:49:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59292, Retrieved Tue, 04 Nov 2025 15:49:49 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

672

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] [ws 8] [2009-11-24 21:12:18] [f7d3e79b917995ba1c8c80042fc22ef9] [Current]
-    D            [Standard Deviation-Mean Plot] [WS8 SDMP] [2009-11-27 16:05:59] [37a8d600db9abe09a2528d150ccff095] 
-    D            [Standard Deviation-Mean Plot] [ws 9] [2009-12-06 10:43:30] [b5908418e3090fddbd22f5f0f774653d] 
-    D              [Standard Deviation-Mean Plot] [ws 9] [2009-12-06 11:20:00] [b5908418e3090fddbd22f5f0f774653d] 

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Dataseries X:

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Histogram

Boxplots

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

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=59292&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=59292&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59292&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	8.51666666666667	0.434497271323859	1.4
2	8.48333333333333	0.224957908520818	0.700
3	7.85833333333333	0.267847763183537	0.9
4	6.95	0.442102415119557	1.6
5	7.5	0.493595344018117	1.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.51666666666667 & 0.434497271323859 & 1.4 \tabularnewline
2 & 8.48333333333333 & 0.224957908520818 & 0.700 \tabularnewline
3 & 7.85833333333333 & 0.267847763183537 & 0.9 \tabularnewline
4 & 6.95 & 0.442102415119557 & 1.6 \tabularnewline
5 & 7.5 & 0.493595344018117 & 1.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59292&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]8.51666666666667[/C][C]0.434497271323859[/C][C]1.4[/C][/ROW]
[ROW][C]2[/C][C]8.48333333333333[/C][C]0.224957908520818[/C][C]0.700[/C][/ROW]
[ROW][C]3[/C][C]7.85833333333333[/C][C]0.267847763183537[/C][C]0.9[/C][/ROW]
[ROW][C]4[/C][C]6.95[/C][C]0.442102415119557[/C][C]1.6[/C][/ROW]
[ROW][C]5[/C][C]7.5[/C][C]0.493595344018117[/C][C]1.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59292&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59292&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	8.51666666666667	0.434497271323859	1.4
2	8.48333333333333	0.224957908520818	0.700
3	7.85833333333333	0.267847763183537	0.9
4	6.95	0.442102415119557	1.6
5	7.5	0.493595344018117	1.5

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.07150446017643
beta	-0.0889002738702464
S.D.	0.0887762927013865
T-STAT	-1.00139655717858
p-value	0.390425150352976

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.07150446017643 \tabularnewline
beta & -0.0889002738702464 \tabularnewline
S.D. & 0.0887762927013865 \tabularnewline
T-STAT & -1.00139655717858 \tabularnewline
p-value & 0.390425150352976 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59292&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.07150446017643[/C][/ROW]
[ROW][C]beta[/C][C]-0.0889002738702464[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0887762927013865[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.00139655717858[/C][/ROW]
[ROW][C]p-value[/C][C]0.390425150352976[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59292&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59292&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	1.07150446017643
beta	-0.0889002738702464
S.D.	0.0887762927013865
T-STAT	-1.00139655717858
p-value	0.390425150352976

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	3.21265634507503
beta	-2.06192926973093
S.D.	2.01292580283106
T-STAT	-1.02434439800560
p-value	0.381057914699529
Lambda	3.06192926973093

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.21265634507503 \tabularnewline
beta & -2.06192926973093 \tabularnewline
S.D. & 2.01292580283106 \tabularnewline
T-STAT & -1.02434439800560 \tabularnewline
p-value & 0.381057914699529 \tabularnewline
Lambda & 3.06192926973093 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59292&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.21265634507503[/C][/ROW]
[ROW][C]beta[/C][C]-2.06192926973093[/C][/ROW]
[ROW][C]S.D.[/C][C]2.01292580283106[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.02434439800560[/C][/ROW]
[ROW][C]p-value[/C][C]0.381057914699529[/C][/ROW]
[ROW][C]Lambda[/C][C]3.06192926973093[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59292&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59292&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	3.21265634507503
beta	-2.06192926973093
S.D.	2.01292580283106
T-STAT	-1.02434439800560
p-value	0.381057914699529
Lambda	3.06192926973093

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