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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

Thu, 22 Dec 2011 09:51:14 -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/t132456552665bl5gfu1butqxr.htm/, Retrieved Fri, 03 May 2024 14:14:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159537, Retrieved Fri, 03 May 2024 14:14:28 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

115

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

-     [Testing Mean with unknown Variance - Critical Value] [] [2010-10-25 13:12:27] [b98453cac15ba1066b407e146608df68]
- RMPD  [Multiple Regression] [] [2011-12-22 13:45:12] [5a05da414fd67612c3b80d44effe0727]
- RM D      [Standard Deviation-Mean Plot] [] [2011-12-22 14:51:14] [95610e892c4b5c84ff80f4c898567a9d] [Current]

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Dataseries X:

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Histogram

Boxplots

7.9
7.9
8.0
8.0
7.9
8.0
7.7
7.2
7.5
7.3
7.0
7.0
7.0
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8.0
8.0
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6
8.7
8.5
8.3
8.0
8.0
8.8
8.7
8.5
8.1
7.8
7.6
7.4
7.1
6.9
6.7
6.6
6.5
7.1
7.2
6.9
6.7

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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159537&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159537&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159537&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	7.61666666666667	0.397339637940626	1
2	7.03333333333333	0.534846338737217	1.8
3	7.66666666666667	0.521071157823144	1.7
4	8.36666666666667	0.311399577664609	0.9
5	7.04166666666667	0.405548636996473	1.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 7.61666666666667 & 0.397339637940626 & 1 \tabularnewline
2 & 7.03333333333333 & 0.534846338737217 & 1.8 \tabularnewline
3 & 7.66666666666667 & 0.521071157823144 & 1.7 \tabularnewline
4 & 8.36666666666667 & 0.311399577664609 & 0.9 \tabularnewline
5 & 7.04166666666667 & 0.405548636996473 & 1.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159537&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]7.61666666666667[/C][C]0.397339637940626[/C][C]1[/C][/ROW]
[ROW][C]2[/C][C]7.03333333333333[/C][C]0.534846338737217[/C][C]1.8[/C][/ROW]
[ROW][C]3[/C][C]7.66666666666667[/C][C]0.521071157823144[/C][C]1.7[/C][/ROW]
[ROW][C]4[/C][C]8.36666666666667[/C][C]0.311399577664609[/C][C]0.9[/C][/ROW]
[ROW][C]5[/C][C]7.04166666666667[/C][C]0.405548636996473[/C][C]1.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159537&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159537&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	7.61666666666667	0.397339637940626	1
2	7.03333333333333	0.534846338737217	1.8
3	7.66666666666667	0.521071157823144	1.7
4	8.36666666666667	0.311399577664609	0.9
5	7.04166666666667	0.405548636996473	1.3

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.24482090559759
beta	-0.107459222765431
S.D.	0.0759817591692902
T-STAT	-1.41427658348905
p-value	0.252198819176179

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.24482090559759 \tabularnewline
beta & -0.107459222765431 \tabularnewline
S.D. & 0.0759817591692902 \tabularnewline
T-STAT & -1.41427658348905 \tabularnewline
p-value & 0.252198819176179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159537&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.24482090559759[/C][/ROW]
[ROW][C]beta[/C][C]-0.107459222765431[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0759817591692902[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.41427658348905[/C][/ROW]
[ROW][C]p-value[/C][C]0.252198819176179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159537&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159537&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	1.24482090559759
beta	-0.107459222765431
S.D.	0.0759817591692902
T-STAT	-1.41427658348905
p-value	0.252198819176179

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	3.28145824588981
beta	-2.0484574361458
S.D.	1.33631189952081
T-STAT	-1.5329186523598
p-value	0.222829190541395
Lambda	3.0484574361458

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.28145824588981 \tabularnewline
beta & -2.0484574361458 \tabularnewline
S.D. & 1.33631189952081 \tabularnewline
T-STAT & -1.5329186523598 \tabularnewline
p-value & 0.222829190541395 \tabularnewline
Lambda & 3.0484574361458 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159537&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.28145824588981[/C][/ROW]
[ROW][C]beta[/C][C]-2.0484574361458[/C][/ROW]
[ROW][C]S.D.[/C][C]1.33631189952081[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.5329186523598[/C][/ROW]
[ROW][C]p-value[/C][C]0.222829190541395[/C][/ROW]
[ROW][C]Lambda[/C][C]3.0484574361458[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159537&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159537&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	3.28145824588981
beta	-2.0484574361458
S.D.	1.33631189952081
T-STAT	-1.5329186523598
p-value	0.222829190541395
Lambda	3.0484574361458

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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