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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

Fri, 06 Aug 2010 07:40:39 +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/06/t1281080417pwpj6tpkzpl0lvo.htm/, Retrieved Mon, 06 May 2024 11:55:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78443, Retrieved Mon, 06 May 2024 11:55:58 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Van de Walle Mathias

Estimated Impact

193

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

-     [Variability] [Spreidingsmaten -...] [2010-05-21 12:27:10] [251b004ef89b028696de15eeefcf9b4b]
- RMPD    [Standard Deviation-Mean Plot] [tijdreeks 2 - sta...] [2010-08-06 07:40:39] [589929edeb20bd59f78e9be1ffd92c80] [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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78443&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78443&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78443&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	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	237.25	1.70782512765993	4
2	233.25	1.25830573921179	3
3	237	1.41421356237310	3
4	237.25	5.7373048260195	14
5	240	2.94392028877595	7
6	229.25	1.5	3
7	226	9.83192080250175	24
8	225.25	6.60176744011279	15
9	205.5	3	6
10	195.75	10.4363148029688	25
11	182.5	6.557438524302	15
12	152.75	4.5	11
13	152.25	12.2848144742469	26
14	143.5	7.32575365861197	17
15	110	4.16333199893227	10
16	110.5	12.8711563842052	31
17	117	7.61577310586391	18
18	83.75	3.59397644214130	8
19	88.5	11.9582607431014	29
20	88.75	11.5866302262565	24
21	51.5	4.20317340430616	9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 237.25 & 1.70782512765993 & 4 \tabularnewline
2 & 233.25 & 1.25830573921179 & 3 \tabularnewline
3 & 237 & 1.41421356237310 & 3 \tabularnewline
4 & 237.25 & 5.7373048260195 & 14 \tabularnewline
5 & 240 & 2.94392028877595 & 7 \tabularnewline
6 & 229.25 & 1.5 & 3 \tabularnewline
7 & 226 & 9.83192080250175 & 24 \tabularnewline
8 & 225.25 & 6.60176744011279 & 15 \tabularnewline
9 & 205.5 & 3 & 6 \tabularnewline
10 & 195.75 & 10.4363148029688 & 25 \tabularnewline
11 & 182.5 & 6.557438524302 & 15 \tabularnewline
12 & 152.75 & 4.5 & 11 \tabularnewline
13 & 152.25 & 12.2848144742469 & 26 \tabularnewline
14 & 143.5 & 7.32575365861197 & 17 \tabularnewline
15 & 110 & 4.16333199893227 & 10 \tabularnewline
16 & 110.5 & 12.8711563842052 & 31 \tabularnewline
17 & 117 & 7.61577310586391 & 18 \tabularnewline
18 & 83.75 & 3.59397644214130 & 8 \tabularnewline
19 & 88.5 & 11.9582607431014 & 29 \tabularnewline
20 & 88.75 & 11.5866302262565 & 24 \tabularnewline
21 & 51.5 & 4.20317340430616 & 9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78443&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]237.25[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]2[/C][C]233.25[/C][C]1.25830573921179[/C][C]3[/C][/ROW]
[ROW][C]3[/C][C]237[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]237.25[/C][C]5.7373048260195[/C][C]14[/C][/ROW]
[ROW][C]5[/C][C]240[/C][C]2.94392028877595[/C][C]7[/C][/ROW]
[ROW][C]6[/C][C]229.25[/C][C]1.5[/C][C]3[/C][/ROW]
[ROW][C]7[/C][C]226[/C][C]9.83192080250175[/C][C]24[/C][/ROW]
[ROW][C]8[/C][C]225.25[/C][C]6.60176744011279[/C][C]15[/C][/ROW]
[ROW][C]9[/C][C]205.5[/C][C]3[/C][C]6[/C][/ROW]
[ROW][C]10[/C][C]195.75[/C][C]10.4363148029688[/C][C]25[/C][/ROW]
[ROW][C]11[/C][C]182.5[/C][C]6.557438524302[/C][C]15[/C][/ROW]
[ROW][C]12[/C][C]152.75[/C][C]4.5[/C][C]11[/C][/ROW]
[ROW][C]13[/C][C]152.25[/C][C]12.2848144742469[/C][C]26[/C][/ROW]
[ROW][C]14[/C][C]143.5[/C][C]7.32575365861197[/C][C]17[/C][/ROW]
[ROW][C]15[/C][C]110[/C][C]4.16333199893227[/C][C]10[/C][/ROW]
[ROW][C]16[/C][C]110.5[/C][C]12.8711563842052[/C][C]31[/C][/ROW]
[ROW][C]17[/C][C]117[/C][C]7.61577310586391[/C][C]18[/C][/ROW]
[ROW][C]18[/C][C]83.75[/C][C]3.59397644214130[/C][C]8[/C][/ROW]
[ROW][C]19[/C][C]88.5[/C][C]11.9582607431014[/C][C]29[/C][/ROW]
[ROW][C]20[/C][C]88.75[/C][C]11.5866302262565[/C][C]24[/C][/ROW]
[ROW][C]21[/C][C]51.5[/C][C]4.20317340430616[/C][C]9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78443&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78443&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	237.25	1.70782512765993	4
2	233.25	1.25830573921179	3
3	237	1.41421356237310	3
4	237.25	5.7373048260195	14
5	240	2.94392028877595	7
6	229.25	1.5	3
7	226	9.83192080250175	24
8	225.25	6.60176744011279	15
9	205.5	3	6
10	195.75	10.4363148029688	25
11	182.5	6.557438524302	15
12	152.75	4.5	11
13	152.25	12.2848144742469	26
14	143.5	7.32575365861197	17
15	110	4.16333199893227	10
16	110.5	12.8711563842052	31
17	117	7.61577310586391	18
18	83.75	3.59397644214130	8
19	88.5	11.9582607431014	29
20	88.75	11.5866302262565	24
21	51.5	4.20317340430616	9

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	10.7727025091691
beta	-0.0268174407726457
S.D.	0.0127890858355143
T-STAT	-2.09690052264532
p-value	0.0496179594905318

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 10.7727025091691 \tabularnewline
beta & -0.0268174407726457 \tabularnewline
S.D. & 0.0127890858355143 \tabularnewline
T-STAT & -2.09690052264532 \tabularnewline
p-value & 0.0496179594905318 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78443&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]10.7727025091691[/C][/ROW]
[ROW][C]beta[/C][C]-0.0268174407726457[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0127890858355143[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.09690052264532[/C][/ROW]
[ROW][C]p-value[/C][C]0.0496179594905318[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78443&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78443&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	10.7727025091691
beta	-0.0268174407726457
S.D.	0.0127890858355143
T-STAT	-2.09690052264532
p-value	0.0496179594905318

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	5.03927258126066
beta	-0.682620677810388
S.D.	0.354055955920745
T-STAT	-1.92800224482932
p-value	0.0689362526260258
Lambda	1.68262067781039

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.03927258126066 \tabularnewline
beta & -0.682620677810388 \tabularnewline
S.D. & 0.354055955920745 \tabularnewline
T-STAT & -1.92800224482932 \tabularnewline
p-value & 0.0689362526260258 \tabularnewline
Lambda & 1.68262067781039 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78443&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.03927258126066[/C][/ROW]
[ROW][C]beta[/C][C]-0.682620677810388[/C][/ROW]
[ROW][C]S.D.[/C][C]0.354055955920745[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.92800224482932[/C][/ROW]
[ROW][C]p-value[/C][C]0.0689362526260258[/C][/ROW]
[ROW][C]Lambda[/C][C]1.68262067781039[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78443&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78443&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	5.03927258126066
beta	-0.682620677810388
S.D.	0.354055955920745
T-STAT	-1.92800224482932
p-value	0.0689362526260258
Lambda	1.68262067781039

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