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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, 03 Aug 2010 17:52:27 +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/Aug/03/t1280857946fc8qs31lji85i0v.htm/, Retrieved Thu, 02 May 2024 19:22:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78285, Retrieved Thu, 02 May 2024 19:22:50 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Lisa Bruggeman

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] [TIJDREEKS B - STA...] [2010-08-03 17:52:27] [0e6aef37627b8cf9d1bd74110cef2cca] [Current]

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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=78285&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=78285&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78285&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	160.25	1.70782512765993	4
2	156.25	1.25830573921179	3
3	160	1.41421356237310	3
4	152	3.55902608401044	8
5	147.25	2.98607881119482	7
6	146.75	5.31507290636732	11
7	139.25	4.11298755975102	10
8	133.75	3.30403793359983	7
9	137	6.97614984548545	15
10	141.5	3.3166247903554	8
11	138.5	1	2
12	142	7.30296743340222	16
13	138.5	3.10912635102960	7
14	129.25	3.77491721763537	8
15	141.75	9.81070843517429	22
16	141	5.47722557505166	13
17	122.75	5.25198375219624	11
18	133.25	10.6575481858321	24
19	147	10.6770782520313	24
20	119.25	8.65544144839919	21
21	128.5	6.6583281184794	15

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 160.25 & 1.70782512765993 & 4 \tabularnewline
2 & 156.25 & 1.25830573921179 & 3 \tabularnewline
3 & 160 & 1.41421356237310 & 3 \tabularnewline
4 & 152 & 3.55902608401044 & 8 \tabularnewline
5 & 147.25 & 2.98607881119482 & 7 \tabularnewline
6 & 146.75 & 5.31507290636732 & 11 \tabularnewline
7 & 139.25 & 4.11298755975102 & 10 \tabularnewline
8 & 133.75 & 3.30403793359983 & 7 \tabularnewline
9 & 137 & 6.97614984548545 & 15 \tabularnewline
10 & 141.5 & 3.3166247903554 & 8 \tabularnewline
11 & 138.5 & 1 & 2 \tabularnewline
12 & 142 & 7.30296743340222 & 16 \tabularnewline
13 & 138.5 & 3.10912635102960 & 7 \tabularnewline
14 & 129.25 & 3.77491721763537 & 8 \tabularnewline
15 & 141.75 & 9.81070843517429 & 22 \tabularnewline
16 & 141 & 5.47722557505166 & 13 \tabularnewline
17 & 122.75 & 5.25198375219624 & 11 \tabularnewline
18 & 133.25 & 10.6575481858321 & 24 \tabularnewline
19 & 147 & 10.6770782520313 & 24 \tabularnewline
20 & 119.25 & 8.65544144839919 & 21 \tabularnewline
21 & 128.5 & 6.6583281184794 & 15 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78285&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]160.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]156.25[/C][C]1.25830573921179[/C][C]3[/C][/ROW]
[ROW][C]3[/C][C]160[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]152[/C][C]3.55902608401044[/C][C]8[/C][/ROW]
[ROW][C]5[/C][C]147.25[/C][C]2.98607881119482[/C][C]7[/C][/ROW]
[ROW][C]6[/C][C]146.75[/C][C]5.31507290636732[/C][C]11[/C][/ROW]
[ROW][C]7[/C][C]139.25[/C][C]4.11298755975102[/C][C]10[/C][/ROW]
[ROW][C]8[/C][C]133.75[/C][C]3.30403793359983[/C][C]7[/C][/ROW]
[ROW][C]9[/C][C]137[/C][C]6.97614984548545[/C][C]15[/C][/ROW]
[ROW][C]10[/C][C]141.5[/C][C]3.3166247903554[/C][C]8[/C][/ROW]
[ROW][C]11[/C][C]138.5[/C][C]1[/C][C]2[/C][/ROW]
[ROW][C]12[/C][C]142[/C][C]7.30296743340222[/C][C]16[/C][/ROW]
[ROW][C]13[/C][C]138.5[/C][C]3.10912635102960[/C][C]7[/C][/ROW]
[ROW][C]14[/C][C]129.25[/C][C]3.77491721763537[/C][C]8[/C][/ROW]
[ROW][C]15[/C][C]141.75[/C][C]9.81070843517429[/C][C]22[/C][/ROW]
[ROW][C]16[/C][C]141[/C][C]5.47722557505166[/C][C]13[/C][/ROW]
[ROW][C]17[/C][C]122.75[/C][C]5.25198375219624[/C][C]11[/C][/ROW]
[ROW][C]18[/C][C]133.25[/C][C]10.6575481858321[/C][C]24[/C][/ROW]
[ROW][C]19[/C][C]147[/C][C]10.6770782520313[/C][C]24[/C][/ROW]
[ROW][C]20[/C][C]119.25[/C][C]8.65544144839919[/C][C]21[/C][/ROW]
[ROW][C]21[/C][C]128.5[/C][C]6.6583281184794[/C][C]15[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78285&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78285&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	160.25	1.70782512765993	4
2	156.25	1.25830573921179	3
3	160	1.41421356237310	3
4	152	3.55902608401044	8
5	147.25	2.98607881119482	7
6	146.75	5.31507290636732	11
7	139.25	4.11298755975102	10
8	133.75	3.30403793359983	7
9	137	6.97614984548545	15
10	141.5	3.3166247903554	8
11	138.5	1	2
12	142	7.30296743340222	16
13	138.5	3.10912635102960	7
14	129.25	3.77491721763537	8
15	141.75	9.81070843517429	22
16	141	5.47722557505166	13
17	122.75	5.25198375219624	11
18	133.25	10.6575481858321	24
19	147	10.6770782520313	24
20	119.25	8.65544144839919	21
21	128.5	6.6583281184794	15

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	21.7647968620488
beta	-0.118661959561460
S.D.	0.0569152241896707
T-STAT	-2.08488960995773
p-value	0.0508103480988565

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 21.7647968620488 \tabularnewline
beta & -0.118661959561460 \tabularnewline
S.D. & 0.0569152241896707 \tabularnewline
T-STAT & -2.08488960995773 \tabularnewline
p-value & 0.0508103480988565 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78285&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]21.7647968620488[/C][/ROW]
[ROW][C]beta[/C][C]-0.118661959561460[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0569152241896707[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.08488960995773[/C][/ROW]
[ROW][C]p-value[/C][C]0.0508103480988565[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78285&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78285&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	21.7647968620488
beta	-0.118661959561460
S.D.	0.0569152241896707
T-STAT	-2.08488960995773
p-value	0.0508103480988565

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	23.6031051615039
beta	-4.48724296517405
S.D.	1.75529531612061
T-STAT	-2.5564034290773
p-value	0.0192950670450515
Lambda	5.48724296517405

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 23.6031051615039 \tabularnewline
beta & -4.48724296517405 \tabularnewline
S.D. & 1.75529531612061 \tabularnewline
T-STAT & -2.5564034290773 \tabularnewline
p-value & 0.0192950670450515 \tabularnewline
Lambda & 5.48724296517405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78285&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]23.6031051615039[/C][/ROW]
[ROW][C]beta[/C][C]-4.48724296517405[/C][/ROW]
[ROW][C]S.D.[/C][C]1.75529531612061[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.5564034290773[/C][/ROW]
[ROW][C]p-value[/C][C]0.0192950670450515[/C][/ROW]
[ROW][C]Lambda[/C][C]5.48724296517405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78285&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78285&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	23.6031051615039
beta	-4.48724296517405
S.D.	1.75529531612061
T-STAT	-2.5564034290773
p-value	0.0192950670450515
Lambda	5.48724296517405

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code