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Free Statistics

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Author's title

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Tue, 06 Dec 2011 08:15:19 -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/06/t13231775032wb1s5v3ihlp8m0.htm/, Retrieved Mon, 29 Apr 2024 03:48:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151543, Retrieved Mon, 29 Apr 2024 03:48:27 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

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

-       [Standard Deviation-Mean Plot] [opgave 8] [2011-12-06 13:15:19] [824ef6e68de890e55183bcf963376e73] [Current]

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Histogram

Boxplots

6.3
6.2
6.3
6.5
6.6
6.4
6.2
6.3
6.6
7.1
7.2
7.3
7.3
7.3
7.4
7.3
7.4
7.4
7.6
7.6
7.7
7.7
7.8
7.8
8
8.1
8.1
8.2
8.1
8.1
8.1
8.1
8.2
8.4
8.4
8.5
8.6
8.5
8.3
7.8
7.8
8
8.6
8.9
8.9
8.6
8.3
8.3
8.3
8.4
8.5
8.4
8.6
8.5
8.5
8.5
8.5
8.5
8.5
8.5
8.5
8.6
8.6
8.6
8.6
8.4
8.1
7.9
7.9
8
8
7.9
7.9
7.9
7.9
8
7.9
7.5
7.2
7
6.9
7.1
7.1
7.2
7.1
6.9
6.8
6.8
6.7
6.9
7.3
7.4
7.3
7.1
7
7.1
7.5
7.7
7.8
7.7
7.7
7.8
8
8.1
8.1
8
8.1
8.2
8.3
8.4
8.5
8.5
8.5
8.5
8.5
8.3
8.2
8.1
7.9
7.6

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' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151543&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151543&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151543&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' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	6.58333333333333	0.397339637940626	1.1
2	7.525	0.195982373975546	0.5
3	8.19166666666667	0.156427928995103	0.5
4	8.38333333333333	0.373760578040234	1.1
5	8.475	0.0753778361444406	0.299999999999999
6	8.25833333333333	0.314666730867995	0.699999999999999
7	7.46666666666667	0.424977717775957	1.1
8	7.03333333333333	0.222928171609085	0.7
9	7.89166666666667	0.219330938551907	0.699999999999999
10	8.275	0.286435777348876	0.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6.58333333333333 & 0.397339637940626 & 1.1 \tabularnewline
2 & 7.525 & 0.195982373975546 & 0.5 \tabularnewline
3 & 8.19166666666667 & 0.156427928995103 & 0.5 \tabularnewline
4 & 8.38333333333333 & 0.373760578040234 & 1.1 \tabularnewline
5 & 8.475 & 0.0753778361444406 & 0.299999999999999 \tabularnewline
6 & 8.25833333333333 & 0.314666730867995 & 0.699999999999999 \tabularnewline
7 & 7.46666666666667 & 0.424977717775957 & 1.1 \tabularnewline
8 & 7.03333333333333 & 0.222928171609085 & 0.7 \tabularnewline
9 & 7.89166666666667 & 0.219330938551907 & 0.699999999999999 \tabularnewline
10 & 8.275 & 0.286435777348876 & 0.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151543&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]6.58333333333333[/C][C]0.397339637940626[/C][C]1.1[/C][/ROW]
[ROW][C]2[/C][C]7.525[/C][C]0.195982373975546[/C][C]0.5[/C][/ROW]
[ROW][C]3[/C][C]8.19166666666667[/C][C]0.156427928995103[/C][C]0.5[/C][/ROW]
[ROW][C]4[/C][C]8.38333333333333[/C][C]0.373760578040234[/C][C]1.1[/C][/ROW]
[ROW][C]5[/C][C]8.475[/C][C]0.0753778361444406[/C][C]0.299999999999999[/C][/ROW]
[ROW][C]6[/C][C]8.25833333333333[/C][C]0.314666730867995[/C][C]0.699999999999999[/C][/ROW]
[ROW][C]7[/C][C]7.46666666666667[/C][C]0.424977717775957[/C][C]1.1[/C][/ROW]
[ROW][C]8[/C][C]7.03333333333333[/C][C]0.222928171609085[/C][C]0.7[/C][/ROW]
[ROW][C]9[/C][C]7.89166666666667[/C][C]0.219330938551907[/C][C]0.699999999999999[/C][/ROW]
[ROW][C]10[/C][C]8.275[/C][C]0.286435777348876[/C][C]0.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151543&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151543&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	6.58333333333333	0.397339637940626	1.1
2	7.525	0.195982373975546	0.5
3	8.19166666666667	0.156427928995103	0.5
4	8.38333333333333	0.373760578040234	1.1
5	8.475	0.0753778361444406	0.299999999999999
6	8.25833333333333	0.314666730867995	0.699999999999999
7	7.46666666666667	0.424977717775957	1.1
8	7.03333333333333	0.222928171609085	0.7
9	7.89166666666667	0.219330938551907	0.699999999999999
10	8.275	0.286435777348876	0.9

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.783846475424825
beta	-0.0662271555560105
S.D.	0.0580106694453197
T-STAT	-1.14163749857146
p-value	0.28662249997908

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.783846475424825 \tabularnewline
beta & -0.0662271555560105 \tabularnewline
S.D. & 0.0580106694453197 \tabularnewline
T-STAT & -1.14163749857146 \tabularnewline
p-value & 0.28662249997908 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151543&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.783846475424825[/C][/ROW]
[ROW][C]beta[/C][C]-0.0662271555560105[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0580106694453197[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.14163749857146[/C][/ROW]
[ROW][C]p-value[/C][C]0.28662249997908[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151543&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151543&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	0.783846475424825
beta	-0.0662271555560105
S.D.	0.0580106694453197
T-STAT	-1.14163749857146
p-value	0.28662249997908

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	3.56956450671459
beta	-2.43428934819544
S.D.	2.01626379739262
T-STAT	-1.20732681474686
p-value	0.261787765720295
Lambda	3.43428934819544

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.56956450671459 \tabularnewline
beta & -2.43428934819544 \tabularnewline
S.D. & 2.01626379739262 \tabularnewline
T-STAT & -1.20732681474686 \tabularnewline
p-value & 0.261787765720295 \tabularnewline
Lambda & 3.43428934819544 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151543&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.56956450671459[/C][/ROW]
[ROW][C]beta[/C][C]-2.43428934819544[/C][/ROW]
[ROW][C]S.D.[/C][C]2.01626379739262[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.20732681474686[/C][/ROW]
[ROW][C]p-value[/C][C]0.261787765720295[/C][/ROW]
[ROW][C]Lambda[/C][C]3.43428934819544[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151543&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151543&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	3.56956450671459
beta	-2.43428934819544
S.D.	2.01626379739262
T-STAT	-1.20732681474686
p-value	0.261787765720295
Lambda	3.43428934819544

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