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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

Sat, 13 Dec 2008 03:17:49 -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/2008/Dec/13/t1229163713plx6q07193dcw9y.htm/, Retrieved Fri, 17 May 2024 03:41:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32938, Retrieved Fri, 17 May 2024 03:41:47 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

220

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

-     [(Partial) Autocorrelation Function] [ACF d=0 D=0 voor Xt] [2008-12-13 09:26:24] [b1bd16d1f47bfe13feacf1c27a0abba5]
-   PD  [(Partial) Autocorrelation Function] [ACF d=0 D=1] [2008-12-13 09:29:39] [b1bd16d1f47bfe13feacf1c27a0abba5]
- RMPD    [Spectral Analysis] [Spectral Analysis Xt] [2008-12-13 09:45:55] [b1bd16d1f47bfe13feacf1c27a0abba5]
-   PD      [Spectral Analysis] [Spectral analysis...] [2008-12-13 09:51:22] [b1bd16d1f47bfe13feacf1c27a0abba5]
-   P         [Spectral Analysis] [Spectral analysis...] [2008-12-13 10:03:15] [b1bd16d1f47bfe13feacf1c27a0abba5]
- RM D            [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-12-13 10:17:49] [e7b1048c2c3a353441b9143db4404b91] [Current]

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Dataseries X:

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Histogram

Boxplots

6,4
6,8
7,5
7,5
7,6
7,6
7,4
7,3
7,1
6,9
6,8
7,5
7,6
7,8
8
8,1
8,2
8,3
8,2
8
7,9
7,6
7,6
8,2
8,3
8,4
8,4
8,4
8,6
8,9
8,8
8,3
7,5
7,2
7,5
8,8
9,3
9,3
8,7
8,2
8,3
8,5
8,6
8,6
8,2
8,1
8
8,6
8,7
8,8
8,5
8,4
8,5
8,7
8,7
8,6
8,5
8,3
8,1
8,2
8,1
8,1
7,9
7,9
7,9
8
8
7,9
8
7,7
7,2
7,5
7,3
7
7
7
7,2
7,3
7,1
6,8
6,6
6,2
6,2
6,8

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=32938&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=32938&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32938&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	7.2	0.393122696553448	1.2
2	7.95833333333333	0.257464325272219	0.700000000000001
3	8.25833333333333	0.559964825735158	1.7
4	8.53333333333333	0.422833157152888	1.3
5	8.5	0.217422922601844	0.700000000000001
6	7.85	0.264575131106459	0.9
7	6.875	0.376889180722204	1.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 7.2 & 0.393122696553448 & 1.2 \tabularnewline
2 & 7.95833333333333 & 0.257464325272219 & 0.700000000000001 \tabularnewline
3 & 8.25833333333333 & 0.559964825735158 & 1.7 \tabularnewline
4 & 8.53333333333333 & 0.422833157152888 & 1.3 \tabularnewline
5 & 8.5 & 0.217422922601844 & 0.700000000000001 \tabularnewline
6 & 7.85 & 0.264575131106459 & 0.9 \tabularnewline
7 & 6.875 & 0.376889180722204 & 1.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32938&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]7.2[/C][C]0.393122696553448[/C][C]1.2[/C][/ROW]
[ROW][C]2[/C][C]7.95833333333333[/C][C]0.257464325272219[/C][C]0.700000000000001[/C][/ROW]
[ROW][C]3[/C][C]8.25833333333333[/C][C]0.559964825735158[/C][C]1.7[/C][/ROW]
[ROW][C]4[/C][C]8.53333333333333[/C][C]0.422833157152888[/C][C]1.3[/C][/ROW]
[ROW][C]5[/C][C]8.5[/C][C]0.217422922601844[/C][C]0.700000000000001[/C][/ROW]
[ROW][C]6[/C][C]7.85[/C][C]0.264575131106459[/C][C]0.9[/C][/ROW]
[ROW][C]7[/C][C]6.875[/C][C]0.376889180722204[/C][C]1.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32938&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32938&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	7.2	0.393122696553448	1.2
2	7.95833333333333	0.257464325272219	0.700000000000001
3	8.25833333333333	0.559964825735158	1.7
4	8.53333333333333	0.422833157152888	1.3
5	8.5	0.217422922601844	0.700000000000001
6	7.85	0.264575131106459	0.9
7	6.875	0.376889180722204	1.1

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.408829065063688
beta	-0.00669743935299675
S.D.	0.0835980330085934
T-STAT	-0.0801147959104288
p-value	0.939253733551808

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.408829065063688 \tabularnewline
beta & -0.00669743935299675 \tabularnewline
S.D. & 0.0835980330085934 \tabularnewline
T-STAT & -0.0801147959104288 \tabularnewline
p-value & 0.939253733551808 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32938&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.408829065063688[/C][/ROW]
[ROW][C]beta[/C][C]-0.00669743935299675[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0835980330085934[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0801147959104288[/C][/ROW]
[ROW][C]p-value[/C][C]0.939253733551808[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32938&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32938&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	0.408829065063688
beta	-0.00669743935299675
S.D.	0.0835980330085934
T-STAT	-0.0801147959104288
p-value	0.939253733551808

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.0269632097927351
beta	-0.537088934549505
S.D.	1.78715532528891
T-STAT	-0.300527283191055
p-value	0.775869619018909
Lambda	1.53708893454950

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.0269632097927351 \tabularnewline
beta & -0.537088934549505 \tabularnewline
S.D. & 1.78715532528891 \tabularnewline
T-STAT & -0.300527283191055 \tabularnewline
p-value & 0.775869619018909 \tabularnewline
Lambda & 1.53708893454950 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32938&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0269632097927351[/C][/ROW]
[ROW][C]beta[/C][C]-0.537088934549505[/C][/ROW]
[ROW][C]S.D.[/C][C]1.78715532528891[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.300527283191055[/C][/ROW]
[ROW][C]p-value[/C][C]0.775869619018909[/C][/ROW]
[ROW][C]Lambda[/C][C]1.53708893454950[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32938&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32938&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	0.0269632097927351
beta	-0.537088934549505
S.D.	1.78715532528891
T-STAT	-0.300527283191055
p-value	0.775869619018909
Lambda	1.53708893454950

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 2 ; par4 = 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