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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

Mon, 25 Jan 2010 09:25:42 -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/2010/Jan/25/t1264436811vm8hdi0jybke1vx.htm/, Retrieved Thu, 03 Apr 2025 07:54:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72465, Retrieved Thu, 03 Apr 2025 07:54:24 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

201

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

-     [(Partial) Autocorrelation Function] [Autocorrelation F...] [2010-01-25 13:50:04] [830dacb160eeaee72e8ff2204da365bc]
-    D  [(Partial) Autocorrelation Function] [Autocorrelation F...] [2010-01-25 14:02:55] [830dacb160eeaee72e8ff2204da365bc]
- RMP       [Standard Deviation-Mean Plot] [spreidings- en ge...] [2010-01-25 16:25:42] [3588db8f96a346e7899895ad48978494] [Current]

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Dataseries X:

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Histogram

Boxplots

8,2
8,21
8,22
8,2
8,18
8,2
8,19
8,24
8,31
8,27
8,36
8,32
8,29
8,27
8,27
8,43
8,46
8,48
8,46
8,46
8,43
8,4
8,38
8,3
8,39
8,53
8,52
8,54
8,62
8,52
8,49
8,44
8,31
8,26
8,21
8,03
7,89
7,83
7,85
7,84
7,88
8,01
8,08
8,11
8,11
8,07
8,06
7,95
7,95
8,07
8,17
8,21
8,2
8,19
8,18
8,16
8,17
8,17
8,19
8,01
8,04
8,13
8,14
8,17
8,25
8,27
8,27
8,26
8,24
8,21
8,25
8,06
8,16
8,32
8,43
8,39
8,41

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=72465&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=72465&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72465&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	8.2075	0.0095742710775641	0.0200000000000014
2	8.2025	0.0262995563967661	0.0600000000000005
3	8.315	0.0369684550213647	0.0899999999999999
4	8.315	0.0772442015083766	0.16
5	8.465	0.00999999999999979	0.0199999999999996
6	8.3775	0.0556027577253739	0.129999999999999
7	8.495	0.0704745817062193	0.149999999999999
8	8.5175	0.0758836829188812	0.180000000000000
9	8.2025	0.122031416719904	0.280000000000001
10	7.8525	0.0262995563967657	0.0599999999999996
11	8.02	0.102306728354819	0.230000000000000
12	8.0475	0.0684957419601149	0.159999999999999
13	8.1	0.116045967903528	0.260000000000001
14	8.1825	0.0170782512765990	0.0399999999999991
15	8.135	0.0838649708360608	0.180000000000000
16	8.12	0.0559761854124894	0.130000000000001
17	8.2625	0.00957427107756318	0.0199999999999996
18	8.19	0.0883176086632783	0.190000000000000
19	8.325	0.119023807142381	0.270000000000000

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.2075 & 0.0095742710775641 & 0.0200000000000014 \tabularnewline
2 & 8.2025 & 0.0262995563967661 & 0.0600000000000005 \tabularnewline
3 & 8.315 & 0.0369684550213647 & 0.0899999999999999 \tabularnewline
4 & 8.315 & 0.0772442015083766 & 0.16 \tabularnewline
5 & 8.465 & 0.00999999999999979 & 0.0199999999999996 \tabularnewline
6 & 8.3775 & 0.0556027577253739 & 0.129999999999999 \tabularnewline
7 & 8.495 & 0.0704745817062193 & 0.149999999999999 \tabularnewline
8 & 8.5175 & 0.0758836829188812 & 0.180000000000000 \tabularnewline
9 & 8.2025 & 0.122031416719904 & 0.280000000000001 \tabularnewline
10 & 7.8525 & 0.0262995563967657 & 0.0599999999999996 \tabularnewline
11 & 8.02 & 0.102306728354819 & 0.230000000000000 \tabularnewline
12 & 8.0475 & 0.0684957419601149 & 0.159999999999999 \tabularnewline
13 & 8.1 & 0.116045967903528 & 0.260000000000001 \tabularnewline
14 & 8.1825 & 0.0170782512765990 & 0.0399999999999991 \tabularnewline
15 & 8.135 & 0.0838649708360608 & 0.180000000000000 \tabularnewline
16 & 8.12 & 0.0559761854124894 & 0.130000000000001 \tabularnewline
17 & 8.2625 & 0.00957427107756318 & 0.0199999999999996 \tabularnewline
18 & 8.19 & 0.0883176086632783 & 0.190000000000000 \tabularnewline
19 & 8.325 & 0.119023807142381 & 0.270000000000000 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72465&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]8.2075[/C][C]0.0095742710775641[/C][C]0.0200000000000014[/C][/ROW]
[ROW][C]2[/C][C]8.2025[/C][C]0.0262995563967661[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]3[/C][C]8.315[/C][C]0.0369684550213647[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]4[/C][C]8.315[/C][C]0.0772442015083766[/C][C]0.16[/C][/ROW]
[ROW][C]5[/C][C]8.465[/C][C]0.00999999999999979[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]6[/C][C]8.3775[/C][C]0.0556027577253739[/C][C]0.129999999999999[/C][/ROW]
[ROW][C]7[/C][C]8.495[/C][C]0.0704745817062193[/C][C]0.149999999999999[/C][/ROW]
[ROW][C]8[/C][C]8.5175[/C][C]0.0758836829188812[/C][C]0.180000000000000[/C][/ROW]
[ROW][C]9[/C][C]8.2025[/C][C]0.122031416719904[/C][C]0.280000000000001[/C][/ROW]
[ROW][C]10[/C][C]7.8525[/C][C]0.0262995563967657[/C][C]0.0599999999999996[/C][/ROW]
[ROW][C]11[/C][C]8.02[/C][C]0.102306728354819[/C][C]0.230000000000000[/C][/ROW]
[ROW][C]12[/C][C]8.0475[/C][C]0.0684957419601149[/C][C]0.159999999999999[/C][/ROW]
[ROW][C]13[/C][C]8.1[/C][C]0.116045967903528[/C][C]0.260000000000001[/C][/ROW]
[ROW][C]14[/C][C]8.1825[/C][C]0.0170782512765990[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]15[/C][C]8.135[/C][C]0.0838649708360608[/C][C]0.180000000000000[/C][/ROW]
[ROW][C]16[/C][C]8.12[/C][C]0.0559761854124894[/C][C]0.130000000000001[/C][/ROW]
[ROW][C]17[/C][C]8.2625[/C][C]0.00957427107756318[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]18[/C][C]8.19[/C][C]0.0883176086632783[/C][C]0.190000000000000[/C][/ROW]
[ROW][C]19[/C][C]8.325[/C][C]0.119023807142381[/C][C]0.270000000000000[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72465&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72465&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	8.2075	0.0095742710775641	0.0200000000000014
2	8.2025	0.0262995563967661	0.0600000000000005
3	8.315	0.0369684550213647	0.0899999999999999
4	8.315	0.0772442015083766	0.16
5	8.465	0.00999999999999979	0.0199999999999996
6	8.3775	0.0556027577253739	0.129999999999999
7	8.495	0.0704745817062193	0.149999999999999
8	8.5175	0.0758836829188812	0.180000000000000
9	8.2025	0.122031416719904	0.280000000000001
10	7.8525	0.0262995563967657	0.0599999999999996
11	8.02	0.102306728354819	0.230000000000000
12	8.0475	0.0684957419601149	0.159999999999999
13	8.1	0.116045967903528	0.260000000000001
14	8.1825	0.0170782512765990	0.0399999999999991
15	8.135	0.0838649708360608	0.180000000000000
16	8.12	0.0559761854124894	0.130000000000001
17	8.2625	0.00957427107756318	0.0199999999999996
18	8.19	0.0883176086632783	0.190000000000000
19	8.325	0.119023807142381	0.270000000000000

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.174072828452625
beta	-0.0136652438136781
S.D.	0.0548329653423773
T-STAT	-0.249215845401617
p-value	0.80617997071626

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.174072828452625 \tabularnewline
beta & -0.0136652438136781 \tabularnewline
S.D. & 0.0548329653423773 \tabularnewline
T-STAT & -0.249215845401617 \tabularnewline
p-value & 0.80617997071626 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72465&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.174072828452625[/C][/ROW]
[ROW][C]beta[/C][C]-0.0136652438136781[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0548329653423773[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.249215845401617[/C][/ROW]
[ROW][C]p-value[/C][C]0.80617997071626[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72465&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72465&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	0.174072828452625
beta	-0.0136652438136781
S.D.	0.0548329653423773
T-STAT	-0.249215845401617
p-value	0.80617997071626

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	3.30828457974671
beta	-3.02750639407862
S.D.	10.3230794416440
T-STAT	-0.29327551058703
p-value	0.772861529958183
Lambda	4.02750639407862

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.30828457974671 \tabularnewline
beta & -3.02750639407862 \tabularnewline
S.D. & 10.3230794416440 \tabularnewline
T-STAT & -0.29327551058703 \tabularnewline
p-value & 0.772861529958183 \tabularnewline
Lambda & 4.02750639407862 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72465&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.30828457974671[/C][/ROW]
[ROW][C]beta[/C][C]-3.02750639407862[/C][/ROW]
[ROW][C]S.D.[/C][C]10.3230794416440[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.29327551058703[/C][/ROW]
[ROW][C]p-value[/C][C]0.772861529958183[/C][/ROW]
[ROW][C]Lambda[/C][C]4.02750639407862[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72465&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72465&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	3.30828457974671
beta	-3.02750639407862
S.D.	10.3230794416440
T-STAT	-0.29327551058703
p-value	0.772861529958183
Lambda	4.02750639407862

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code