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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

Mon, 20 Dec 2010 14:51:11 +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/20/t1292856569hdtwbgyplto10jz.htm/, Retrieved Sat, 04 May 2024 04:10:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112978, Retrieved Sat, 04 May 2024 04:10:42 +0000

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Original text written by user:

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No (this computation is public)

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Estimated Impact

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

-       [Standard Deviation-Mean Plot] [] [2010-12-20 14:51:11] [40b262140b988d7b8204c4955f8b7651] [Current]

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Histogram

Boxplots

9.4
9.4
9.5
9.5
9.4
9.4
9.3
9.4
9.4
9.2
9.1
9.1
9.1
9.0
9.0
8.9
8.8
8.7
8.5
8.3
8.1
7.9
7.8
7.6
7.4
7.2
7.0
7.0
6.8
6.8
6.7
6.8
6.7
6.7
6.7
6.5
6.3
6.3
6.3
6.5
6.6
6.5
6.3
6.3
6.5
7.0
7.1
7.3
7.3
7.4
7.4
7.3
7.4
7.5
7.7
7.7
7.7
7.7
7.7
7.8
8.0
8.1
8.1
8.2
8.2
8.2
8.1
8.1
8.2
8.3
8.3
8.4
8.5
8.5
8.4
8.0
7.9
8.1
8.5
8.8
8.8
8.6
8.3
8.3
8.3
8.4
8.4
8.5
8.6
8.6
8.6
8.6
8.6
8.5
8.4
8.4
8.4
8.5
8.5
8.6
8.6
8.4
8.2
8.0
8.0
8.0
8.0
7.9
7.9
7.8
7.8
8.0
7.8
7.4
7.2
7.0
7.0
7.2
7.2
7.2
7.0
6.9
6.8
6.8
6.8
6.9
7.2
7.2
7.2
7.1
7.2
7.3
7.5
7.6
7.7
7.7
7.7
7.8
8.0
8.1
8.1
8.0
8.1
8.2
8.3
8.4
8.4
8.4
8.5
8.5
8.6
8.6
8.5
8.5

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112978&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112978&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112978&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	9.34166666666667	0.137895436890245	0.4
2	8.475	0.522450519623194	1.5
3	6.85833333333333	0.250302846870576	0.9
4	6.58333333333333	0.353767600483022	1
5	7.55	0.183402190925746	0.5
6	8.18333333333333	0.111464085804543	0.4
7	8.39166666666667	0.287491765362967	0.9
8	8.49166666666667	0.108362466945083	0.299999999999999
9	8.25833333333333	0.267847763183537	0.699999999999999
10	7.45833333333333	0.372847356856866	1
11	7.03333333333333	0.187487373312218	0.5
12	7.875	0.234035739306473	0.699999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.34166666666667 & 0.137895436890245 & 0.4 \tabularnewline
2 & 8.475 & 0.522450519623194 & 1.5 \tabularnewline
3 & 6.85833333333333 & 0.250302846870576 & 0.9 \tabularnewline
4 & 6.58333333333333 & 0.353767600483022 & 1 \tabularnewline
5 & 7.55 & 0.183402190925746 & 0.5 \tabularnewline
6 & 8.18333333333333 & 0.111464085804543 & 0.4 \tabularnewline
7 & 8.39166666666667 & 0.287491765362967 & 0.9 \tabularnewline
8 & 8.49166666666667 & 0.108362466945083 & 0.299999999999999 \tabularnewline
9 & 8.25833333333333 & 0.267847763183537 & 0.699999999999999 \tabularnewline
10 & 7.45833333333333 & 0.372847356856866 & 1 \tabularnewline
11 & 7.03333333333333 & 0.187487373312218 & 0.5 \tabularnewline
12 & 7.875 & 0.234035739306473 & 0.699999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112978&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]9.34166666666667[/C][C]0.137895436890245[/C][C]0.4[/C][/ROW]
[ROW][C]2[/C][C]8.475[/C][C]0.522450519623194[/C][C]1.5[/C][/ROW]
[ROW][C]3[/C][C]6.85833333333333[/C][C]0.250302846870576[/C][C]0.9[/C][/ROW]
[ROW][C]4[/C][C]6.58333333333333[/C][C]0.353767600483022[/C][C]1[/C][/ROW]
[ROW][C]5[/C][C]7.55[/C][C]0.183402190925746[/C][C]0.5[/C][/ROW]
[ROW][C]6[/C][C]8.18333333333333[/C][C]0.111464085804543[/C][C]0.4[/C][/ROW]
[ROW][C]7[/C][C]8.39166666666667[/C][C]0.287491765362967[/C][C]0.9[/C][/ROW]
[ROW][C]8[/C][C]8.49166666666667[/C][C]0.108362466945083[/C][C]0.299999999999999[/C][/ROW]
[ROW][C]9[/C][C]8.25833333333333[/C][C]0.267847763183537[/C][C]0.699999999999999[/C][/ROW]
[ROW][C]10[/C][C]7.45833333333333[/C][C]0.372847356856866[/C][C]1[/C][/ROW]
[ROW][C]11[/C][C]7.03333333333333[/C][C]0.187487373312218[/C][C]0.5[/C][/ROW]
[ROW][C]12[/C][C]7.875[/C][C]0.234035739306473[/C][C]0.699999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112978&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112978&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	9.34166666666667	0.137895436890245	0.4
2	8.475	0.522450519623194	1.5
3	6.85833333333333	0.250302846870576	0.9
4	6.58333333333333	0.353767600483022	1
5	7.55	0.183402190925746	0.5
6	8.18333333333333	0.111464085804543	0.4
7	8.39166666666667	0.287491765362967	0.9
8	8.49166666666667	0.108362466945083	0.299999999999999
9	8.25833333333333	0.267847763183537	0.699999999999999
10	7.45833333333333	0.372847356856866	1
11	7.03333333333333	0.187487373312218	0.5
12	7.875	0.234035739306473	0.699999999999999

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.491432803324167
beta	-0.0304744814214342
S.D.	0.0468502968682665
T-STAT	-0.650465065506889
p-value	0.53005200724859

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.491432803324167 \tabularnewline
beta & -0.0304744814214342 \tabularnewline
S.D. & 0.0468502968682665 \tabularnewline
T-STAT & -0.650465065506889 \tabularnewline
p-value & 0.53005200724859 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112978&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.491432803324167[/C][/ROW]
[ROW][C]beta[/C][C]-0.0304744814214342[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0468502968682665[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.650465065506889[/C][/ROW]
[ROW][C]p-value[/C][C]0.53005200724859[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112978&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112978&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	0.491432803324167
beta	-0.0304744814214342
S.D.	0.0468502968682665
T-STAT	-0.650465065506889
p-value	0.53005200724859

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	1.5844942560941
beta	-1.49182751675944
S.D.	1.42222577028332
T-STAT	-1.04893860590239
p-value	0.318895811724262
Lambda	2.49182751675944

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.5844942560941 \tabularnewline
beta & -1.49182751675944 \tabularnewline
S.D. & 1.42222577028332 \tabularnewline
T-STAT & -1.04893860590239 \tabularnewline
p-value & 0.318895811724262 \tabularnewline
Lambda & 2.49182751675944 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112978&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.5844942560941[/C][/ROW]
[ROW][C]beta[/C][C]-1.49182751675944[/C][/ROW]
[ROW][C]S.D.[/C][C]1.42222577028332[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.04893860590239[/C][/ROW]
[ROW][C]p-value[/C][C]0.318895811724262[/C][/ROW]
[ROW][C]Lambda[/C][C]2.49182751675944[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112978&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112978&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	1.5844942560941
beta	-1.49182751675944
S.D.	1.42222577028332
T-STAT	-1.04893860590239
p-value	0.318895811724262
Lambda	2.49182751675944

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 2 ; 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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code