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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, 29 Dec 2010 17:51:04 +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/29/t1293644969jvxdkroeo68g2hx.htm/, Retrieved Fri, 03 May 2024 10:52:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116998, Retrieved Fri, 03 May 2024 10:52:34 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

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...] [2010-12-29 17:51:04] [95610e892c4b5c84ff80f4c898567a9d] [Current]

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Dataseries X:

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Histogram

Boxplots

0,3
-0,1
-1
-1,2
-0,8
-1,7
-1,1
-0,4
0,6
0,6
1,9
2,3
2,6
3,1
4,7
5,5
5,4
5,9
5,8
5,2
4,2
4,4
3,6
3,5
3,1
2,9
2,2
1,5
1,1
1,4
1,3
1,3
1,8
1,8
1,8
1,7
1,6
1,5
1,2
1,2
1,6
1,6
1,9
2,2
2
1,7
2,4
2,6
2,9
2,6
2,5
3,2
3,1
3,1
2,9
2,5
2,8
3,1
2,6
2,3

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116998&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116998&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116998&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	-0.5	0.716472842006823	1.5
2	-1	0.547722557505166	1.3
3	1.35	0.881286937760152	1.7
4	3.975	1.35492927244684	2.9
5	5.575	0.330403793359983	0.7
6	3.925	0.442530601578392	0.9
7	2.425	0.727438428093173	1.6
8	1.275	0.125830573921179	0.3
9	1.775	0.05	0.1
10	1.375	0.206155281280883	0.4
11	1.825	0.287228132326901	0.6
12	2.175	0.403112887414928	0.9
13	2.8	0.316227766016838	0.7
14	2.9	0.282842712474619	0.6
15	2.7	0.336650164612069	0.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & -0.5 & 0.716472842006823 & 1.5 \tabularnewline
2 & -1 & 0.547722557505166 & 1.3 \tabularnewline
3 & 1.35 & 0.881286937760152 & 1.7 \tabularnewline
4 & 3.975 & 1.35492927244684 & 2.9 \tabularnewline
5 & 5.575 & 0.330403793359983 & 0.7 \tabularnewline
6 & 3.925 & 0.442530601578392 & 0.9 \tabularnewline
7 & 2.425 & 0.727438428093173 & 1.6 \tabularnewline
8 & 1.275 & 0.125830573921179 & 0.3 \tabularnewline
9 & 1.775 & 0.05 & 0.1 \tabularnewline
10 & 1.375 & 0.206155281280883 & 0.4 \tabularnewline
11 & 1.825 & 0.287228132326901 & 0.6 \tabularnewline
12 & 2.175 & 0.403112887414928 & 0.9 \tabularnewline
13 & 2.8 & 0.316227766016838 & 0.7 \tabularnewline
14 & 2.9 & 0.282842712474619 & 0.6 \tabularnewline
15 & 2.7 & 0.336650164612069 & 0.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116998&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]-0.5[/C][C]0.716472842006823[/C][C]1.5[/C][/ROW]
[ROW][C]2[/C][C]-1[/C][C]0.547722557505166[/C][C]1.3[/C][/ROW]
[ROW][C]3[/C][C]1.35[/C][C]0.881286937760152[/C][C]1.7[/C][/ROW]
[ROW][C]4[/C][C]3.975[/C][C]1.35492927244684[/C][C]2.9[/C][/ROW]
[ROW][C]5[/C][C]5.575[/C][C]0.330403793359983[/C][C]0.7[/C][/ROW]
[ROW][C]6[/C][C]3.925[/C][C]0.442530601578392[/C][C]0.9[/C][/ROW]
[ROW][C]7[/C][C]2.425[/C][C]0.727438428093173[/C][C]1.6[/C][/ROW]
[ROW][C]8[/C][C]1.275[/C][C]0.125830573921179[/C][C]0.3[/C][/ROW]
[ROW][C]9[/C][C]1.775[/C][C]0.05[/C][C]0.1[/C][/ROW]
[ROW][C]10[/C][C]1.375[/C][C]0.206155281280883[/C][C]0.4[/C][/ROW]
[ROW][C]11[/C][C]1.825[/C][C]0.287228132326901[/C][C]0.6[/C][/ROW]
[ROW][C]12[/C][C]2.175[/C][C]0.403112887414928[/C][C]0.9[/C][/ROW]
[ROW][C]13[/C][C]2.8[/C][C]0.316227766016838[/C][C]0.7[/C][/ROW]
[ROW][C]14[/C][C]2.9[/C][C]0.282842712474619[/C][C]0.6[/C][/ROW]
[ROW][C]15[/C][C]2.7[/C][C]0.336650164612069[/C][C]0.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116998&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116998&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	-0.5	0.716472842006823	1.5
2	-1	0.547722557505166	1.3
3	1.35	0.881286937760152	1.7
4	3.975	1.35492927244684	2.9
5	5.575	0.330403793359983	0.7
6	3.925	0.442530601578392	0.9
7	2.425	0.727438428093173	1.6
8	1.275	0.125830573921179	0.3
9	1.775	0.05	0.1
10	1.375	0.206155281280883	0.4
11	1.825	0.287228132326901	0.6
12	2.175	0.403112887414928	0.9
13	2.8	0.316227766016838	0.7
14	2.9	0.282842712474619	0.6
15	2.7	0.336650164612069	0.8

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.448209087225037
beta	0.00877039577658906
S.D.	0.0560151295587556
T-STAT	0.156571909155179
p-value	0.87798765530487

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.448209087225037 \tabularnewline
beta & 0.00877039577658906 \tabularnewline
S.D. & 0.0560151295587556 \tabularnewline
T-STAT & 0.156571909155179 \tabularnewline
p-value & 0.87798765530487 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116998&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.448209087225037[/C][/ROW]
[ROW][C]beta[/C][C]0.00877039577658906[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0560151295587556[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.156571909155179[/C][/ROW]
[ROW][C]p-value[/C][C]0.87798765530487[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116998&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116998&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	0.448209087225037
beta	0.00877039577658906
S.D.	0.0560151295587556
T-STAT	0.156571909155179
p-value	0.87798765530487

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.70443233782684
beta	0.692039215709545
S.D.	0.514626789736827
T-STAT	1.34473997372629
p-value	0.205780725838339
Lambda	0.307960784290455

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.70443233782684 \tabularnewline
beta & 0.692039215709545 \tabularnewline
S.D. & 0.514626789736827 \tabularnewline
T-STAT & 1.34473997372629 \tabularnewline
p-value & 0.205780725838339 \tabularnewline
Lambda & 0.307960784290455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116998&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.70443233782684[/C][/ROW]
[ROW][C]beta[/C][C]0.692039215709545[/C][/ROW]
[ROW][C]S.D.[/C][C]0.514626789736827[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.34473997372629[/C][/ROW]
[ROW][C]p-value[/C][C]0.205780725838339[/C][/ROW]
[ROW][C]Lambda[/C][C]0.307960784290455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116998&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116998&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	-1.70443233782684
beta	0.692039215709545
S.D.	0.514626789736827
T-STAT	1.34473997372629
p-value	0.205780725838339
Lambda	0.307960784290455

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