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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, 28 Jul 2010 13:41:04 +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/Jul/28/t1280324549ih32g1sro6nv198.htm/, Retrieved Mon, 29 Apr 2024 14:00:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78145, Retrieved Mon, 29 Apr 2024 14:00:49 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Patrick Fieremans

Estimated Impact

216

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

-       [Standard Deviation-Mean Plot] [Tijdreeks 1 - Sta...] [2010-07-28 13:41:04] [c9c054077df6495a4b48ba74c2b1bb38] [Current]

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Boxplots

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78145&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78145&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78145&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	134.25	1.70782512765993	4
2	141.25	12.5266382827424	26
3	128	1.4142135623731	3
4	114.5	9.03696114115064	21
5	123.75	6.34428877022476	15
6	116.25	3.947573094109	9
7	100.5	11.5614301306831	25
8	116.75	3.5939764421413	8
9	120.25	0.5	1
10	106.25	10.4682058316281	22
11	129.25	6.89806736219163	15
12	130.25	3.86221007541882	9
13	110	11.1654228162962	23
14	133.75	8.30160627027485	20
15	137.25	2.62995563967658	6
16	117.75	13.1751027826478	29
17	143.5	12.369316876853	30
18	136.5	1.91485421551268	4
19	114.5	15.545631755148	33
20	141.75	13.1497781983829	32
21	130	3.55902608401044	8
22	109.75	11.5578256317239	25
23	147.25	16.4595463687997	40
24	130.5	8.10349718742881	15
25	113.75	12.5532200384337	27
26	151.25	16.8597153000874	38
27	131	8.04155872120988	18
28	115	9.76387901058454	21
29	151.25	15.5214904782584	37
30	132.25	11.9547758936195	26

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 134.25 & 1.70782512765993 & 4 \tabularnewline
2 & 141.25 & 12.5266382827424 & 26 \tabularnewline
3 & 128 & 1.4142135623731 & 3 \tabularnewline
4 & 114.5 & 9.03696114115064 & 21 \tabularnewline
5 & 123.75 & 6.34428877022476 & 15 \tabularnewline
6 & 116.25 & 3.947573094109 & 9 \tabularnewline
7 & 100.5 & 11.5614301306831 & 25 \tabularnewline
8 & 116.75 & 3.5939764421413 & 8 \tabularnewline
9 & 120.25 & 0.5 & 1 \tabularnewline
10 & 106.25 & 10.4682058316281 & 22 \tabularnewline
11 & 129.25 & 6.89806736219163 & 15 \tabularnewline
12 & 130.25 & 3.86221007541882 & 9 \tabularnewline
13 & 110 & 11.1654228162962 & 23 \tabularnewline
14 & 133.75 & 8.30160627027485 & 20 \tabularnewline
15 & 137.25 & 2.62995563967658 & 6 \tabularnewline
16 & 117.75 & 13.1751027826478 & 29 \tabularnewline
17 & 143.5 & 12.369316876853 & 30 \tabularnewline
18 & 136.5 & 1.91485421551268 & 4 \tabularnewline
19 & 114.5 & 15.545631755148 & 33 \tabularnewline
20 & 141.75 & 13.1497781983829 & 32 \tabularnewline
21 & 130 & 3.55902608401044 & 8 \tabularnewline
22 & 109.75 & 11.5578256317239 & 25 \tabularnewline
23 & 147.25 & 16.4595463687997 & 40 \tabularnewline
24 & 130.5 & 8.10349718742881 & 15 \tabularnewline
25 & 113.75 & 12.5532200384337 & 27 \tabularnewline
26 & 151.25 & 16.8597153000874 & 38 \tabularnewline
27 & 131 & 8.04155872120988 & 18 \tabularnewline
28 & 115 & 9.76387901058454 & 21 \tabularnewline
29 & 151.25 & 15.5214904782584 & 37 \tabularnewline
30 & 132.25 & 11.9547758936195 & 26 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78145&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]134.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]141.25[/C][C]12.5266382827424[/C][C]26[/C][/ROW]
[ROW][C]3[/C][C]128[/C][C]1.4142135623731[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]114.5[/C][C]9.03696114115064[/C][C]21[/C][/ROW]
[ROW][C]5[/C][C]123.75[/C][C]6.34428877022476[/C][C]15[/C][/ROW]
[ROW][C]6[/C][C]116.25[/C][C]3.947573094109[/C][C]9[/C][/ROW]
[ROW][C]7[/C][C]100.5[/C][C]11.5614301306831[/C][C]25[/C][/ROW]
[ROW][C]8[/C][C]116.75[/C][C]3.5939764421413[/C][C]8[/C][/ROW]
[ROW][C]9[/C][C]120.25[/C][C]0.5[/C][C]1[/C][/ROW]
[ROW][C]10[/C][C]106.25[/C][C]10.4682058316281[/C][C]22[/C][/ROW]
[ROW][C]11[/C][C]129.25[/C][C]6.89806736219163[/C][C]15[/C][/ROW]
[ROW][C]12[/C][C]130.25[/C][C]3.86221007541882[/C][C]9[/C][/ROW]
[ROW][C]13[/C][C]110[/C][C]11.1654228162962[/C][C]23[/C][/ROW]
[ROW][C]14[/C][C]133.75[/C][C]8.30160627027485[/C][C]20[/C][/ROW]
[ROW][C]15[/C][C]137.25[/C][C]2.62995563967658[/C][C]6[/C][/ROW]
[ROW][C]16[/C][C]117.75[/C][C]13.1751027826478[/C][C]29[/C][/ROW]
[ROW][C]17[/C][C]143.5[/C][C]12.369316876853[/C][C]30[/C][/ROW]
[ROW][C]18[/C][C]136.5[/C][C]1.91485421551268[/C][C]4[/C][/ROW]
[ROW][C]19[/C][C]114.5[/C][C]15.545631755148[/C][C]33[/C][/ROW]
[ROW][C]20[/C][C]141.75[/C][C]13.1497781983829[/C][C]32[/C][/ROW]
[ROW][C]21[/C][C]130[/C][C]3.55902608401044[/C][C]8[/C][/ROW]
[ROW][C]22[/C][C]109.75[/C][C]11.5578256317239[/C][C]25[/C][/ROW]
[ROW][C]23[/C][C]147.25[/C][C]16.4595463687997[/C][C]40[/C][/ROW]
[ROW][C]24[/C][C]130.5[/C][C]8.10349718742881[/C][C]15[/C][/ROW]
[ROW][C]25[/C][C]113.75[/C][C]12.5532200384337[/C][C]27[/C][/ROW]
[ROW][C]26[/C][C]151.25[/C][C]16.8597153000874[/C][C]38[/C][/ROW]
[ROW][C]27[/C][C]131[/C][C]8.04155872120988[/C][C]18[/C][/ROW]
[ROW][C]28[/C][C]115[/C][C]9.76387901058454[/C][C]21[/C][/ROW]
[ROW][C]29[/C][C]151.25[/C][C]15.5214904782584[/C][C]37[/C][/ROW]
[ROW][C]30[/C][C]132.25[/C][C]11.9547758936195[/C][C]26[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78145&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78145&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	134.25	1.70782512765993	4
2	141.25	12.5266382827424	26
3	128	1.4142135623731	3
4	114.5	9.03696114115064	21
5	123.75	6.34428877022476	15
6	116.25	3.947573094109	9
7	100.5	11.5614301306831	25
8	116.75	3.5939764421413	8
9	120.25	0.5	1
10	106.25	10.4682058316281	22
11	129.25	6.89806736219163	15
12	130.25	3.86221007541882	9
13	110	11.1654228162962	23
14	133.75	8.30160627027485	20
15	137.25	2.62995563967658	6
16	117.75	13.1751027826478	29
17	143.5	12.369316876853	30
18	136.5	1.91485421551268	4
19	114.5	15.545631755148	33
20	141.75	13.1497781983829	32
21	130	3.55902608401044	8
22	109.75	11.5578256317239	25
23	147.25	16.4595463687997	40
24	130.5	8.10349718742881	15
25	113.75	12.5532200384337	27
26	151.25	16.8597153000874	38
27	131	8.04155872120988	18
28	115	9.76387901058454	21
29	151.25	15.5214904782584	37
30	132.25	11.9547758936195	26

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	2.69425782176937
beta	0.0482268386886864
S.D.	0.0676496644978061
T-STAT	0.712891025353871
p-value	0.481812591310796

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.69425782176937 \tabularnewline
beta & 0.0482268386886864 \tabularnewline
S.D. & 0.0676496644978061 \tabularnewline
T-STAT & 0.712891025353871 \tabularnewline
p-value & 0.481812591310796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78145&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.69425782176937[/C][/ROW]
[ROW][C]beta[/C][C]0.0482268386886864[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0676496644978061[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.712891025353871[/C][/ROW]
[ROW][C]p-value[/C][C]0.481812591310796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78145&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78145&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	2.69425782176937
beta	0.0482268386886864
S.D.	0.0676496644978061
T-STAT	0.712891025353871
p-value	0.481812591310796

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	1.45940963577288
beta	0.095251744601347
S.D.	1.51392171629481
T-STAT	0.0629172192829542
p-value	0.950279429350192
Lambda	0.904748255398653

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.45940963577288 \tabularnewline
beta & 0.095251744601347 \tabularnewline
S.D. & 1.51392171629481 \tabularnewline
T-STAT & 0.0629172192829542 \tabularnewline
p-value & 0.950279429350192 \tabularnewline
Lambda & 0.904748255398653 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78145&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.45940963577288[/C][/ROW]
[ROW][C]beta[/C][C]0.095251744601347[/C][/ROW]
[ROW][C]S.D.[/C][C]1.51392171629481[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0629172192829542[/C][/ROW]
[ROW][C]p-value[/C][C]0.950279429350192[/C][/ROW]
[ROW][C]Lambda[/C][C]0.904748255398653[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78145&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78145&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	1.45940963577288
beta	0.095251744601347
S.D.	1.51392171629481
T-STAT	0.0629172192829542
p-value	0.950279429350192
Lambda	0.904748255398653

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