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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

Wed, 22 Dec 2010 18:12:26 +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/22/t1293041423waa4jckxrrdxjc8.htm/, Retrieved Sun, 05 May 2024 23:41:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114457, Retrieved Sun, 05 May 2024 23:41:51 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

128

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

-       [Standard Deviation-Mean Plot] [] [2010-12-22 18:12:26] [b91d9cfbf8712a09013bf3c2e3081c55] [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	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=114457&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=114457&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114457&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	9.7	0.355902608401044	0.8
2	9.525	0.298607881119482	0.700000000000001
3	9.2	0.382970843102536	0.8
4	9.325	0.25	0.6
5	8.475	0.45	1.1
6	6.9	0.316227766016838	0.7
7	6.6	0.616441400296898	1.3
8	7.5	0.496655480858378	1.2
9	8.175	0.340342964277702	0.8
10	8.4	0.725718035235908	1.7
11	8.475	0.262995563967658	0.6
12	8.25	0.341565025531986	0.799999999999999
13	7.5	0.391578004149024	0.9
14	6.975	0.585234995535981	1.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.7 & 0.355902608401044 & 0.8 \tabularnewline
2 & 9.525 & 0.298607881119482 & 0.700000000000001 \tabularnewline
3 & 9.2 & 0.382970843102536 & 0.8 \tabularnewline
4 & 9.325 & 0.25 & 0.6 \tabularnewline
5 & 8.475 & 0.45 & 1.1 \tabularnewline
6 & 6.9 & 0.316227766016838 & 0.7 \tabularnewline
7 & 6.6 & 0.616441400296898 & 1.3 \tabularnewline
8 & 7.5 & 0.496655480858378 & 1.2 \tabularnewline
9 & 8.175 & 0.340342964277702 & 0.8 \tabularnewline
10 & 8.4 & 0.725718035235908 & 1.7 \tabularnewline
11 & 8.475 & 0.262995563967658 & 0.6 \tabularnewline
12 & 8.25 & 0.341565025531986 & 0.799999999999999 \tabularnewline
13 & 7.5 & 0.391578004149024 & 0.9 \tabularnewline
14 & 6.975 & 0.585234995535981 & 1.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114457&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]9.7[/C][C]0.355902608401044[/C][C]0.8[/C][/ROW]
[ROW][C]2[/C][C]9.525[/C][C]0.298607881119482[/C][C]0.700000000000001[/C][/ROW]
[ROW][C]3[/C][C]9.2[/C][C]0.382970843102536[/C][C]0.8[/C][/ROW]
[ROW][C]4[/C][C]9.325[/C][C]0.25[/C][C]0.6[/C][/ROW]
[ROW][C]5[/C][C]8.475[/C][C]0.45[/C][C]1.1[/C][/ROW]
[ROW][C]6[/C][C]6.9[/C][C]0.316227766016838[/C][C]0.7[/C][/ROW]
[ROW][C]7[/C][C]6.6[/C][C]0.616441400296898[/C][C]1.3[/C][/ROW]
[ROW][C]8[/C][C]7.5[/C][C]0.496655480858378[/C][C]1.2[/C][/ROW]
[ROW][C]9[/C][C]8.175[/C][C]0.340342964277702[/C][C]0.8[/C][/ROW]
[ROW][C]10[/C][C]8.4[/C][C]0.725718035235908[/C][C]1.7[/C][/ROW]
[ROW][C]11[/C][C]8.475[/C][C]0.262995563967658[/C][C]0.6[/C][/ROW]
[ROW][C]12[/C][C]8.25[/C][C]0.341565025531986[/C][C]0.799999999999999[/C][/ROW]
[ROW][C]13[/C][C]7.5[/C][C]0.391578004149024[/C][C]0.9[/C][/ROW]
[ROW][C]14[/C][C]6.975[/C][C]0.585234995535981[/C][C]1.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114457&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114457&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	9.7	0.355902608401044	0.8
2	9.525	0.298607881119482	0.700000000000001
3	9.2	0.382970843102536	0.8
4	9.325	0.25	0.6
5	8.475	0.45	1.1
6	6.9	0.316227766016838	0.7
7	6.6	0.616441400296898	1.3
8	7.5	0.496655480858378	1.2
9	8.175	0.340342964277702	0.8
10	8.4	0.725718035235908	1.7
11	8.475	0.262995563967658	0.6
12	8.25	0.341565025531986	0.799999999999999
13	7.5	0.391578004149024	0.9
14	6.975	0.585234995535981	1.4

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.96047039595424
beta	-0.0663682171727473
S.D.	0.0360320288979844
T-STAT	-1.84192284482931
p-value	0.0903235562601148

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.96047039595424 \tabularnewline
beta & -0.0663682171727473 \tabularnewline
S.D. & 0.0360320288979844 \tabularnewline
T-STAT & -1.84192284482931 \tabularnewline
p-value & 0.0903235562601148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114457&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.96047039595424[/C][/ROW]
[ROW][C]beta[/C][C]-0.0663682171727473[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0360320288979844[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.84192284482931[/C][/ROW]
[ROW][C]p-value[/C][C]0.0903235562601148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114457&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114457&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	0.96047039595424
beta	-0.0663682171727473
S.D.	0.0360320288979844
T-STAT	-1.84192284482931
p-value	0.0903235562601148

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	1.75544332444115
beta	-1.27896142622348
S.D.	0.64879676610557
T-STAT	-1.97128206094568
p-value	0.072195821883553
Lambda	2.27896142622348

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.75544332444115 \tabularnewline
beta & -1.27896142622348 \tabularnewline
S.D. & 0.64879676610557 \tabularnewline
T-STAT & -1.97128206094568 \tabularnewline
p-value & 0.072195821883553 \tabularnewline
Lambda & 2.27896142622348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114457&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.75544332444115[/C][/ROW]
[ROW][C]beta[/C][C]-1.27896142622348[/C][/ROW]
[ROW][C]S.D.[/C][C]0.64879676610557[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.97128206094568[/C][/ROW]
[ROW][C]p-value[/C][C]0.072195821883553[/C][/ROW]
[ROW][C]Lambda[/C][C]2.27896142622348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114457&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114457&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	1.75544332444115
beta	-1.27896142622348
S.D.	0.64879676610557
T-STAT	-1.97128206094568
p-value	0.072195821883553
Lambda	2.27896142622348

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 4 ;

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