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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 15:45:02 +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/t12930333085uzdpq76h0dzenc.htm/, Retrieved Sun, 05 May 2024 23:43:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114334, Retrieved Sun, 05 May 2024 23:43:21 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

161

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

-     [Univariate Data Series] [] [2008-12-14 11:54:22] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [(Partial) Autocorrelation Function] [] [2010-12-07 13:42:19] [dd4fe494cff2ee46c12b15bdc7b848ca]
-   P     [(Partial) Autocorrelation Function] [] [2010-12-07 13:48:04] [dd4fe494cff2ee46c12b15bdc7b848ca]
- RM        [Spectral Analysis] [] [2010-12-07 14:05:43] [dd4fe494cff2ee46c12b15bdc7b848ca]
-             [Spectral Analysis] [] [2010-12-07 14:08:00] [dd4fe494cff2ee46c12b15bdc7b848ca]
- RM            [Standard Deviation-Mean Plot] [] [2010-12-07 14:26:40] [dd4fe494cff2ee46c12b15bdc7b848ca]
-   PD              [Standard Deviation-Mean Plot] [] [2010-12-22 15:45:02] [6c31f786e793d35ef3a03978bc5de774] [Current]

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Boxplots

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=114334&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=114334&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114334&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	307.833333333333	59.404366740828	185
2	335.083333333333	73.5186535801794	261
3	347.333333333333	64.4096736570374	247
4	360.75	85.3539422320109	278
5	346.166666666667	77.645854930439	263
6	324.416666666667	61.2007996580754	199
7	332.666666666667	62.8509540440113	207
8	356.083333333333	72.7879339817619	230
9	415.25	92.4535509913442	333

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 307.833333333333 & 59.404366740828 & 185 \tabularnewline
2 & 335.083333333333 & 73.5186535801794 & 261 \tabularnewline
3 & 347.333333333333 & 64.4096736570374 & 247 \tabularnewline
4 & 360.75 & 85.3539422320109 & 278 \tabularnewline
5 & 346.166666666667 & 77.645854930439 & 263 \tabularnewline
6 & 324.416666666667 & 61.2007996580754 & 199 \tabularnewline
7 & 332.666666666667 & 62.8509540440113 & 207 \tabularnewline
8 & 356.083333333333 & 72.7879339817619 & 230 \tabularnewline
9 & 415.25 & 92.4535509913442 & 333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114334&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]307.833333333333[/C][C]59.404366740828[/C][C]185[/C][/ROW]
[ROW][C]2[/C][C]335.083333333333[/C][C]73.5186535801794[/C][C]261[/C][/ROW]
[ROW][C]3[/C][C]347.333333333333[/C][C]64.4096736570374[/C][C]247[/C][/ROW]
[ROW][C]4[/C][C]360.75[/C][C]85.3539422320109[/C][C]278[/C][/ROW]
[ROW][C]5[/C][C]346.166666666667[/C][C]77.645854930439[/C][C]263[/C][/ROW]
[ROW][C]6[/C][C]324.416666666667[/C][C]61.2007996580754[/C][C]199[/C][/ROW]
[ROW][C]7[/C][C]332.666666666667[/C][C]62.8509540440113[/C][C]207[/C][/ROW]
[ROW][C]8[/C][C]356.083333333333[/C][C]72.7879339817619[/C][C]230[/C][/ROW]
[ROW][C]9[/C][C]415.25[/C][C]92.4535509913442[/C][C]333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114334&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114334&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	307.833333333333	59.404366740828	185
2	335.083333333333	73.5186535801794	261
3	347.333333333333	64.4096736570374	247
4	360.75	85.3539422320109	278
5	346.166666666667	77.645854930439	263
6	324.416666666667	61.2007996580754	199
7	332.666666666667	62.8509540440113	207
8	356.083333333333	72.7879339817619	230
9	415.25	92.4535509913442	333

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-43.0543595790847
beta	0.331814850356717
S.D.	0.0686757605688846
T-STAT	4.831615225053
p-value	0.00189594254783973

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -43.0543595790847 \tabularnewline
beta & 0.331814850356717 \tabularnewline
S.D. & 0.0686757605688846 \tabularnewline
T-STAT & 4.831615225053 \tabularnewline
p-value & 0.00189594254783973 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114334&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-43.0543595790847[/C][/ROW]
[ROW][C]beta[/C][C]0.331814850356717[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0686757605688846[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.831615225053[/C][/ROW]
[ROW][C]p-value[/C][C]0.00189594254783973[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114334&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114334&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	-43.0543595790847
beta	0.331814850356717
S.D.	0.0686757605688846
T-STAT	4.831615225053
p-value	0.00189594254783973

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-5.11768309373146
beta	1.60529044671113
S.D.	0.34336266825302
T-STAT	4.67520378635981
p-value	0.00227357381686876
Lambda	-0.605290446711129

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.11768309373146 \tabularnewline
beta & 1.60529044671113 \tabularnewline
S.D. & 0.34336266825302 \tabularnewline
T-STAT & 4.67520378635981 \tabularnewline
p-value & 0.00227357381686876 \tabularnewline
Lambda & -0.605290446711129 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114334&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.11768309373146[/C][/ROW]
[ROW][C]beta[/C][C]1.60529044671113[/C][/ROW]
[ROW][C]S.D.[/C][C]0.34336266825302[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.67520378635981[/C][/ROW]
[ROW][C]p-value[/C][C]0.00227357381686876[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.605290446711129[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114334&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114334&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	-5.11768309373146
beta	1.60529044671113
S.D.	0.34336266825302
T-STAT	4.67520378635981
p-value	0.00227357381686876
Lambda	-0.605290446711129

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