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Author's title

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Wed, 07 Dec 2011 16:43:30 -0500

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/2011/Dec/07/t1323294479obgmoxpkdx84jsj.htm/, Retrieved Thu, 02 May 2024 22:49:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152752, Retrieved Thu, 02 May 2024 22:49:28 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

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

-       [Standard Deviation-Mean Plot] [standard deviatio...] [2011-12-07 21:43:30] [77544ad9bc6b823fffe5e8df50f1b7b2] [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	'AstonUniversity' @ aston.wessa.net

\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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152752&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152752&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152752&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	'AstonUniversity' @ aston.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	100	0.712230810392762	2.30000000000001
2	98.6333333333333	0.759585213764526	3.10000000000001
3	97.9916666666667	0.456186431852221	1.59999999999999
4	95.9	0.439007144278168	1.2
5	94.2166666666667	0.693912927906054	2
6	93.7666666666667	0.794679275881252	2.69999999999999
7	94.6166666666667	0.807727826946825	2.40000000000001
8	91.7416666666667	1.86033151167563	4.89999999999999
9	89.575	0.965895721832613	2.89999999999999
10	89.9083333333333	0.742793661956283	2.5
11	89.2416666666667	0.57121614016752	2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100 & 0.712230810392762 & 2.30000000000001 \tabularnewline
2 & 98.6333333333333 & 0.759585213764526 & 3.10000000000001 \tabularnewline
3 & 97.9916666666667 & 0.456186431852221 & 1.59999999999999 \tabularnewline
4 & 95.9 & 0.439007144278168 & 1.2 \tabularnewline
5 & 94.2166666666667 & 0.693912927906054 & 2 \tabularnewline
6 & 93.7666666666667 & 0.794679275881252 & 2.69999999999999 \tabularnewline
7 & 94.6166666666667 & 0.807727826946825 & 2.40000000000001 \tabularnewline
8 & 91.7416666666667 & 1.86033151167563 & 4.89999999999999 \tabularnewline
9 & 89.575 & 0.965895721832613 & 2.89999999999999 \tabularnewline
10 & 89.9083333333333 & 0.742793661956283 & 2.5 \tabularnewline
11 & 89.2416666666667 & 0.57121614016752 & 2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152752&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]100[/C][C]0.712230810392762[/C][C]2.30000000000001[/C][/ROW]
[ROW][C]2[/C][C]98.6333333333333[/C][C]0.759585213764526[/C][C]3.10000000000001[/C][/ROW]
[ROW][C]3[/C][C]97.9916666666667[/C][C]0.456186431852221[/C][C]1.59999999999999[/C][/ROW]
[ROW][C]4[/C][C]95.9[/C][C]0.439007144278168[/C][C]1.2[/C][/ROW]
[ROW][C]5[/C][C]94.2166666666667[/C][C]0.693912927906054[/C][C]2[/C][/ROW]
[ROW][C]6[/C][C]93.7666666666667[/C][C]0.794679275881252[/C][C]2.69999999999999[/C][/ROW]
[ROW][C]7[/C][C]94.6166666666667[/C][C]0.807727826946825[/C][C]2.40000000000001[/C][/ROW]
[ROW][C]8[/C][C]91.7416666666667[/C][C]1.86033151167563[/C][C]4.89999999999999[/C][/ROW]
[ROW][C]9[/C][C]89.575[/C][C]0.965895721832613[/C][C]2.89999999999999[/C][/ROW]
[ROW][C]10[/C][C]89.9083333333333[/C][C]0.742793661956283[/C][C]2.5[/C][/ROW]
[ROW][C]11[/C][C]89.2416666666667[/C][C]0.57121614016752[/C][C]2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152752&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152752&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	100	0.712230810392762	2.30000000000001
2	98.6333333333333	0.759585213764526	3.10000000000001
3	97.9916666666667	0.456186431852221	1.59999999999999
4	95.9	0.439007144278168	1.2
5	94.2166666666667	0.693912927906054	2
6	93.7666666666667	0.794679275881252	2.69999999999999
7	94.6166666666667	0.807727826946825	2.40000000000001
8	91.7416666666667	1.86033151167563	4.89999999999999
9	89.575	0.965895721832613	2.89999999999999
10	89.9083333333333	0.742793661956283	2.5
11	89.2416666666667	0.57121614016752	2

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	3.86168830883235
beta	-0.032517647461276
S.D.	0.0323024282948125
T-STAT	-1.006662631196
p-value	0.340393335667425

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.86168830883235 \tabularnewline
beta & -0.032517647461276 \tabularnewline
S.D. & 0.0323024282948125 \tabularnewline
T-STAT & -1.006662631196 \tabularnewline
p-value & 0.340393335667425 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152752&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.86168830883235[/C][/ROW]
[ROW][C]beta[/C][C]-0.032517647461276[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0323024282948125[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.006662631196[/C][/ROW]
[ROW][C]p-value[/C][C]0.340393335667425[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152752&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152752&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	3.86168830883235
beta	-0.032517647461276
S.D.	0.0323024282948125
T-STAT	-1.006662631196
p-value	0.340393335667425

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	14.95150184935
beta	-3.35637300133514
S.D.	3.05191057853763
T-STAT	-1.09976125281606
p-value	0.29998138497754
Lambda	4.35637300133514

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 14.95150184935 \tabularnewline
beta & -3.35637300133514 \tabularnewline
S.D. & 3.05191057853763 \tabularnewline
T-STAT & -1.09976125281606 \tabularnewline
p-value & 0.29998138497754 \tabularnewline
Lambda & 4.35637300133514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152752&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]14.95150184935[/C][/ROW]
[ROW][C]beta[/C][C]-3.35637300133514[/C][/ROW]
[ROW][C]S.D.[/C][C]3.05191057853763[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.09976125281606[/C][/ROW]
[ROW][C]p-value[/C][C]0.29998138497754[/C][/ROW]
[ROW][C]Lambda[/C][C]4.35637300133514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152752&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152752&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	14.95150184935
beta	-3.35637300133514
S.D.	3.05191057853763
T-STAT	-1.09976125281606
p-value	0.29998138497754
Lambda	4.35637300133514

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