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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

Thu, 22 Dec 2011 20:41:32 -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/22/t13246045447empkdvv4zngsmh.htm/, Retrieved Fri, 03 May 2024 04:41:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160148, Retrieved Fri, 03 May 2024 04:41:32 +0000

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Estimated Impact

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       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Spectral Analysis] [Births] [2010-11-29 09:38:20] [b98453cac15ba1066b407e146608df68]
- R  D          [Spectral Analysis] [WS9 3.2 CP d=0, D=0] [2010-12-07 10:39:32] [afe9379cca749d06b3d6872e02cc47ed]
- RMPD              [Standard Deviation-Mean Plot] [PAPER: aantal fai...] [2011-12-23 01:41:32] [6baf48ba14bcb50d9e72b77bece8a45b] [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	'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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160148&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160148&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160148&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	'AstonUniversity' @ aston.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	598.75	124.563328179977	447
2	630.5	121.916886741449	466
3	659.333333333333	150.060795760393	487
4	661.5	143.894847971452	487
5	631.916666666667	136.441434877808	409
6	642.5	145.286237851666	508
7	682.333333333333	157.491894933349	560
8	776	176.961731867245	619
9	807.75	162.32130034427	585
10	836.333333333333	203.630830552535	712

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 598.75 & 124.563328179977 & 447 \tabularnewline
2 & 630.5 & 121.916886741449 & 466 \tabularnewline
3 & 659.333333333333 & 150.060795760393 & 487 \tabularnewline
4 & 661.5 & 143.894847971452 & 487 \tabularnewline
5 & 631.916666666667 & 136.441434877808 & 409 \tabularnewline
6 & 642.5 & 145.286237851666 & 508 \tabularnewline
7 & 682.333333333333 & 157.491894933349 & 560 \tabularnewline
8 & 776 & 176.961731867245 & 619 \tabularnewline
9 & 807.75 & 162.32130034427 & 585 \tabularnewline
10 & 836.333333333333 & 203.630830552535 & 712 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160148&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]598.75[/C][C]124.563328179977[/C][C]447[/C][/ROW]
[ROW][C]2[/C][C]630.5[/C][C]121.916886741449[/C][C]466[/C][/ROW]
[ROW][C]3[/C][C]659.333333333333[/C][C]150.060795760393[/C][C]487[/C][/ROW]
[ROW][C]4[/C][C]661.5[/C][C]143.894847971452[/C][C]487[/C][/ROW]
[ROW][C]5[/C][C]631.916666666667[/C][C]136.441434877808[/C][C]409[/C][/ROW]
[ROW][C]6[/C][C]642.5[/C][C]145.286237851666[/C][C]508[/C][/ROW]
[ROW][C]7[/C][C]682.333333333333[/C][C]157.491894933349[/C][C]560[/C][/ROW]
[ROW][C]8[/C][C]776[/C][C]176.961731867245[/C][C]619[/C][/ROW]
[ROW][C]9[/C][C]807.75[/C][C]162.32130034427[/C][C]585[/C][/ROW]
[ROW][C]10[/C][C]836.333333333333[/C][C]203.630830552535[/C][C]712[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160148&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160148&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	598.75	124.563328179977	447
2	630.5	121.916886741449	466
3	659.333333333333	150.060795760393	487
4	661.5	143.894847971452	487
5	631.916666666667	136.441434877808	409
6	642.5	145.286237851666	508
7	682.333333333333	157.491894933349	560
8	776	176.961731867245	619
9	807.75	162.32130034427	585
10	836.333333333333	203.630830552535	712

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-34.3129474090145
beta	0.269340437159913
S.D.	0.0437497005127001
T-STAT	6.15639499250347
p-value	0.000272083497777367

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -34.3129474090145 \tabularnewline
beta & 0.269340437159913 \tabularnewline
S.D. & 0.0437497005127001 \tabularnewline
T-STAT & 6.15639499250347 \tabularnewline
p-value & 0.000272083497777367 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160148&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-34.3129474090145[/C][/ROW]
[ROW][C]beta[/C][C]0.269340437159913[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0437497005127001[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.15639499250347[/C][/ROW]
[ROW][C]p-value[/C][C]0.000272083497777367[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160148&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160148&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	-34.3129474090145
beta	0.269340437159913
S.D.	0.0437497005127001
T-STAT	6.15639499250347
p-value	0.000272083497777367

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-2.98147441799868
beta	1.22365644346115
S.D.	0.198083584455355
T-STAT	6.17747526543244
p-value	0.000265882432005747
Lambda	-0.223656443461151

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.98147441799868 \tabularnewline
beta & 1.22365644346115 \tabularnewline
S.D. & 0.198083584455355 \tabularnewline
T-STAT & 6.17747526543244 \tabularnewline
p-value & 0.000265882432005747 \tabularnewline
Lambda & -0.223656443461151 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160148&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.98147441799868[/C][/ROW]
[ROW][C]beta[/C][C]1.22365644346115[/C][/ROW]
[ROW][C]S.D.[/C][C]0.198083584455355[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.17747526543244[/C][/ROW]
[ROW][C]p-value[/C][C]0.000265882432005747[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.223656443461151[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160148&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160148&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	-2.98147441799868
beta	1.22365644346115
S.D.	0.198083584455355
T-STAT	6.17747526543244
p-value	0.000265882432005747
Lambda	-0.223656443461151

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = multiplicative ; par2 = 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