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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, 23 Dec 2009 04:52:37 -0700

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/2009/Dec/23/t1261569232tpu9vzrymc10a8h.htm/, Retrieved Mon, 29 Apr 2024 11:49:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70508, Retrieved Mon, 29 Apr 2024 11:49:31 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

paper, TRA,levensm4

Estimated Impact

154

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

-     [(Partial) Autocorrelation Function] [] [2009-12-22 10:45:15] [0750c128064677e728c9436fc3f45ae7]
- RMPD    [Standard Deviation-Mean Plot] [] [2009-12-23 11:52:37] [30f5b608e5a1bbbae86b1702c0071566] [Current]
- RMPD      [(Partial) Autocorrelation Function] [] [2009-12-23 11:57:09] [0750c128064677e728c9436fc3f45ae7] 
- RMPD      [(Partial) Autocorrelation Function] [] [2009-12-23 11:59:58] [0750c128064677e728c9436fc3f45ae7] 
- RM D      [Variance Reduction Matrix] [] [2009-12-23 12:01:40] [0750c128064677e728c9436fc3f45ae7] 
- RMPD      [Spectral Analysis] [] [2009-12-23 12:07:28] [0750c128064677e728c9436fc3f45ae7] 
- RMPD      [Spectral Analysis] [] [2009-12-23 12:08:52] [0750c128064677e728c9436fc3f45ae7] 
-    D      [Standard Deviation-Mean Plot] [] [2009-12-23 12:10:30] [0750c128064677e728c9436fc3f45ae7] 
- RMPD      [ARIMA Backward Selection] [] [2009-12-23 12:14:39] [0750c128064677e728c9436fc3f45ae7] 
- RMPD      [Univariate Explorative Data Analysis] [] [2009-12-23 12:18:50] [0750c128064677e728c9436fc3f45ae7] 
- RMPD      [ARIMA Backward Selection] [] [2009-12-23 12:24:26] [0750c128064677e728c9436fc3f45ae7] 
- RMPD      [Univariate Explorative Data Analysis] [] [2009-12-23 12:27:59] [0750c128064677e728c9436fc3f45ae7] 
- RMPD      [ARIMA Backward Selection] [] [2009-12-23 12:32:33] [0750c128064677e728c9436fc3f45ae7] 
- RMPD      [Univariate Explorative Data Analysis] [] [2009-12-23 12:34:54] [0750c128064677e728c9436fc3f45ae7] 
- RMPD      [ARIMA Forecasting] [] [2009-12-23 12:40:08] [0750c128064677e728c9436fc3f45ae7] 
- RMPD      [ARIMA Forecasting] [] [2009-12-23 12:43:23] [0750c128064677e728c9436fc3f45ae7] 
- RMPD      [ARIMA Forecasting] [] [2009-12-23 12:45:30] [0750c128064677e728c9436fc3f45ae7] 

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Dataseries X:

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Histogram

Boxplots

1.1
1.2
1.1
1.2
1.4
1.5
1.5
1.8
1.6
1.5
1.4
1.4
1.4
1.4
1.5
1.4
1.1
1.1
0.9
0.9
0.9
0.9
1.1
1.3
1
1.1
1.4
1.4
1.3
1.4
1
1.8
1.5
1.5
1.4
1.6
1.6
1.6
1.4
1.7
1.8
1.9
2.2
2.1
2.4
2.6
2.8
2.7
2.6
2.9
2.8
2.2
2.2
2.2
2
2
1.7
1.4
1.3
1.4
1.3
2.5
2.4
2.4
2.1
1.7
1.4
1.2
1.1
0.8
0.5
0.6
0.4
0.4
0.3
0.6
0.7
0.8
0.9
0.7
0.6
0.6
0.6
0.5
0.8
0.9
1
1
1.2
1.3
1.3
1.3
1.3
1.4
1.7
1.8
1.4
1.5
1.7
1.6
1.7
1.8
1.7
2.2
2.7
3
2.8
2.7
2.7
2.5
2
1.8
1.4
1.5
1.6
1.3
1.1
0.8
1.1
1.3
1.5
1.8

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=70508&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=70508&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70508&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	1.39166666666667	0.210878393795327	0.7
2	1.15833333333333	0.231431644466797	0.6
3	1.36666666666667	0.238683256575942	0.8
4	2.06666666666667	0.473542420742244	1.4
5	2.05833333333333	0.538446136975875	1.6
6	1.5	0.714779050412847	2
7	0.591666666666667	0.172986249234563	0.6
8	1.25	0.3	1
9	2.06666666666667	0.57892271949848	1.6
10	1.59166666666667	0.571216140167519	1.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.39166666666667 & 0.210878393795327 & 0.7 \tabularnewline
2 & 1.15833333333333 & 0.231431644466797 & 0.6 \tabularnewline
3 & 1.36666666666667 & 0.238683256575942 & 0.8 \tabularnewline
4 & 2.06666666666667 & 0.473542420742244 & 1.4 \tabularnewline
5 & 2.05833333333333 & 0.538446136975875 & 1.6 \tabularnewline
6 & 1.5 & 0.714779050412847 & 2 \tabularnewline
7 & 0.591666666666667 & 0.172986249234563 & 0.6 \tabularnewline
8 & 1.25 & 0.3 & 1 \tabularnewline
9 & 2.06666666666667 & 0.57892271949848 & 1.6 \tabularnewline
10 & 1.59166666666667 & 0.571216140167519 & 1.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70508&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]1.39166666666667[/C][C]0.210878393795327[/C][C]0.7[/C][/ROW]
[ROW][C]2[/C][C]1.15833333333333[/C][C]0.231431644466797[/C][C]0.6[/C][/ROW]
[ROW][C]3[/C][C]1.36666666666667[/C][C]0.238683256575942[/C][C]0.8[/C][/ROW]
[ROW][C]4[/C][C]2.06666666666667[/C][C]0.473542420742244[/C][C]1.4[/C][/ROW]
[ROW][C]5[/C][C]2.05833333333333[/C][C]0.538446136975875[/C][C]1.6[/C][/ROW]
[ROW][C]6[/C][C]1.5[/C][C]0.714779050412847[/C][C]2[/C][/ROW]
[ROW][C]7[/C][C]0.591666666666667[/C][C]0.172986249234563[/C][C]0.6[/C][/ROW]
[ROW][C]8[/C][C]1.25[/C][C]0.3[/C][C]1[/C][/ROW]
[ROW][C]9[/C][C]2.06666666666667[/C][C]0.57892271949848[/C][C]1.6[/C][/ROW]
[ROW][C]10[/C][C]1.59166666666667[/C][C]0.571216140167519[/C][C]1.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70508&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70508&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	1.39166666666667	0.210878393795327	0.7
2	1.15833333333333	0.231431644466797	0.6
3	1.36666666666667	0.238683256575942	0.8
4	2.06666666666667	0.473542420742244	1.4
5	2.05833333333333	0.538446136975875	1.6
6	1.5	0.714779050412847	2
7	0.591666666666667	0.172986249234563	0.6
8	1.25	0.3	1
9	2.06666666666667	0.57892271949848	1.6
10	1.59166666666667	0.571216140167519	1.9

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-0.0239879033303845
beta	0.283928978072472
S.D.	0.104903916381124
T-STAT	2.70656223206136
p-value	0.0268003424038313

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0239879033303845 \tabularnewline
beta & 0.283928978072472 \tabularnewline
S.D. & 0.104903916381124 \tabularnewline
T-STAT & 2.70656223206136 \tabularnewline
p-value & 0.0268003424038313 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70508&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0239879033303845[/C][/ROW]
[ROW][C]beta[/C][C]0.283928978072472[/C][/ROW]
[ROW][C]S.D.[/C][C]0.104903916381124[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.70656223206136[/C][/ROW]
[ROW][C]p-value[/C][C]0.0268003424038313[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70508&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70508&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	-0.0239879033303845
beta	0.283928978072472
S.D.	0.104903916381124
T-STAT	2.70656223206136
p-value	0.0268003424038313

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.38663586546594
beta	1.03231267920778
S.D.	0.318320289457114
T-STAT	3.24299993873579
p-value	0.0118243742852956
Lambda	-0.032312679207779

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.38663586546594 \tabularnewline
beta & 1.03231267920778 \tabularnewline
S.D. & 0.318320289457114 \tabularnewline
T-STAT & 3.24299993873579 \tabularnewline
p-value & 0.0118243742852956 \tabularnewline
Lambda & -0.032312679207779 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70508&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.38663586546594[/C][/ROW]
[ROW][C]beta[/C][C]1.03231267920778[/C][/ROW]
[ROW][C]S.D.[/C][C]0.318320289457114[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.24299993873579[/C][/ROW]
[ROW][C]p-value[/C][C]0.0118243742852956[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.032312679207779[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70508&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70508&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	-1.38663586546594
beta	1.03231267920778
S.D.	0.318320289457114
T-STAT	3.24299993873579
p-value	0.0118243742852956
Lambda	-0.032312679207779

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code