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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

Wed, 26 May 2010 21:28:29 +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/May/26/t1274909341n67vczts6f5ywp4.htm/, Retrieved Fri, 03 May 2024 13:50:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76566, Retrieved Fri, 03 May 2024 13:50:45 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

109

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

-       [Standard Deviation-Mean Plot] [] [2010-05-26 21:28:29] [589929edeb20bd59f78e9be1ffd92c80] [Current]

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Dataseries X:

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Histogram

Boxplots

2
2.4
1.5
1.2
1.5
0.6
2.7
3.7
4.9
6.6
7.4
7.2
5.3
4.7
6.1
6.6
7
7.5
6.6
7.8
4.7
5.4
4.3
4.5
5.8
4.6
5.2
3.6
4.8
6.7
6.3
4.8
8.7
6.8
7.4
9
7.9
9.1
8.7
9.8
6.4
6.1
4.7
4.8
4.2
2.8
6.1
5.8
4.9
4.6
4.1
3.6
5.9
4.5
4.8
5.7
5
7
4.6
2.6
5
4.1
3.2
0
2.3
3.8
4.5
5.9
5
4.2
4.5
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' @ 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=76566&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=76566&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76566&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	1.775	0.531507290636732	1.2
2	2.125	1.35738719604982	3.1
3	6.525	1.13541475535007	2.5
4	5.675	0.842120339777318	1.9
5	7.225	0.531507290636733	1.2
6	4.725	0.478713553878169	1.1
7	4.8	0.938083151964686	2.2
8	5.65	0.99498743710662	1.9
9	7.975	1.04682058316281	2.2
10	8.875	0.79320026895272	1.9
11	5.5	0.875595035770913	1.7
12	4.725	1.53052278650140	3.3
13	4.3	0.571547606649408	1.3
14	5.225	0.680073525436772	1.4
15	4.8	1.80369990112916	4.4
16	3.075	2.17772817403826	5
17	4.125	1.49749791318719	3.6
18	4.925	0.788986691902975	1.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.775 & 0.531507290636732 & 1.2 \tabularnewline
2 & 2.125 & 1.35738719604982 & 3.1 \tabularnewline
3 & 6.525 & 1.13541475535007 & 2.5 \tabularnewline
4 & 5.675 & 0.842120339777318 & 1.9 \tabularnewline
5 & 7.225 & 0.531507290636733 & 1.2 \tabularnewline
6 & 4.725 & 0.478713553878169 & 1.1 \tabularnewline
7 & 4.8 & 0.938083151964686 & 2.2 \tabularnewline
8 & 5.65 & 0.99498743710662 & 1.9 \tabularnewline
9 & 7.975 & 1.04682058316281 & 2.2 \tabularnewline
10 & 8.875 & 0.79320026895272 & 1.9 \tabularnewline
11 & 5.5 & 0.875595035770913 & 1.7 \tabularnewline
12 & 4.725 & 1.53052278650140 & 3.3 \tabularnewline
13 & 4.3 & 0.571547606649408 & 1.3 \tabularnewline
14 & 5.225 & 0.680073525436772 & 1.4 \tabularnewline
15 & 4.8 & 1.80369990112916 & 4.4 \tabularnewline
16 & 3.075 & 2.17772817403826 & 5 \tabularnewline
17 & 4.125 & 1.49749791318719 & 3.6 \tabularnewline
18 & 4.925 & 0.788986691902975 & 1.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76566&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]1.775[/C][C]0.531507290636732[/C][C]1.2[/C][/ROW]
[ROW][C]2[/C][C]2.125[/C][C]1.35738719604982[/C][C]3.1[/C][/ROW]
[ROW][C]3[/C][C]6.525[/C][C]1.13541475535007[/C][C]2.5[/C][/ROW]
[ROW][C]4[/C][C]5.675[/C][C]0.842120339777318[/C][C]1.9[/C][/ROW]
[ROW][C]5[/C][C]7.225[/C][C]0.531507290636733[/C][C]1.2[/C][/ROW]
[ROW][C]6[/C][C]4.725[/C][C]0.478713553878169[/C][C]1.1[/C][/ROW]
[ROW][C]7[/C][C]4.8[/C][C]0.938083151964686[/C][C]2.2[/C][/ROW]
[ROW][C]8[/C][C]5.65[/C][C]0.99498743710662[/C][C]1.9[/C][/ROW]
[ROW][C]9[/C][C]7.975[/C][C]1.04682058316281[/C][C]2.2[/C][/ROW]
[ROW][C]10[/C][C]8.875[/C][C]0.79320026895272[/C][C]1.9[/C][/ROW]
[ROW][C]11[/C][C]5.5[/C][C]0.875595035770913[/C][C]1.7[/C][/ROW]
[ROW][C]12[/C][C]4.725[/C][C]1.53052278650140[/C][C]3.3[/C][/ROW]
[ROW][C]13[/C][C]4.3[/C][C]0.571547606649408[/C][C]1.3[/C][/ROW]
[ROW][C]14[/C][C]5.225[/C][C]0.680073525436772[/C][C]1.4[/C][/ROW]
[ROW][C]15[/C][C]4.8[/C][C]1.80369990112916[/C][C]4.4[/C][/ROW]
[ROW][C]16[/C][C]3.075[/C][C]2.17772817403826[/C][C]5[/C][/ROW]
[ROW][C]17[/C][C]4.125[/C][C]1.49749791318719[/C][C]3.6[/C][/ROW]
[ROW][C]18[/C][C]4.925[/C][C]0.788986691902975[/C][C]1.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76566&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76566&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	1.775	0.531507290636732	1.2
2	2.125	1.35738719604982	3.1
3	6.525	1.13541475535007	2.5
4	5.675	0.842120339777318	1.9
5	7.225	0.531507290636733	1.2
6	4.725	0.478713553878169	1.1
7	4.8	0.938083151964686	2.2
8	5.65	0.99498743710662	1.9
9	7.975	1.04682058316281	2.2
10	8.875	0.79320026895272	1.9
11	5.5	0.875595035770913	1.7
12	4.725	1.53052278650140	3.3
13	4.3	0.571547606649408	1.3
14	5.225	0.680073525436772	1.4
15	4.8	1.80369990112916	4.4
16	3.075	2.17772817403826	5
17	4.125	1.49749791318719	3.6
18	4.925	0.788986691902975	1.8

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.38470985890139
beta	-0.0689962940298096
S.D.	0.0630004875829804
T-STAT	-1.09517079433603
p-value	0.289654281631892

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.38470985890139 \tabularnewline
beta & -0.0689962940298096 \tabularnewline
S.D. & 0.0630004875829804 \tabularnewline
T-STAT & -1.09517079433603 \tabularnewline
p-value & 0.289654281631892 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76566&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.38470985890139[/C][/ROW]
[ROW][C]beta[/C][C]-0.0689962940298096[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0630004875829804[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.09517079433603[/C][/ROW]
[ROW][C]p-value[/C][C]0.289654281631892[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76566&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76566&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	1.38470985890139
beta	-0.0689962940298096
S.D.	0.0630004875829804
T-STAT	-1.09517079433603
p-value	0.289654281631892

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.153427759737002
beta	-0.137847361603651
S.D.	0.266314208619147
T-STAT	-0.517611742604333
p-value	0.611811601641243
Lambda	1.13784736160365

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.153427759737002 \tabularnewline
beta & -0.137847361603651 \tabularnewline
S.D. & 0.266314208619147 \tabularnewline
T-STAT & -0.517611742604333 \tabularnewline
p-value & 0.611811601641243 \tabularnewline
Lambda & 1.13784736160365 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76566&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.153427759737002[/C][/ROW]
[ROW][C]beta[/C][C]-0.137847361603651[/C][/ROW]
[ROW][C]S.D.[/C][C]0.266314208619147[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.517611742604333[/C][/ROW]
[ROW][C]p-value[/C][C]0.611811601641243[/C][/ROW]
[ROW][C]Lambda[/C][C]1.13784736160365[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76566&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76566&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	0.153427759737002
beta	-0.137847361603651
S.D.	0.266314208619147
T-STAT	-0.517611742604333
p-value	0.611811601641243
Lambda	1.13784736160365

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 4 ;

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