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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Wed, 10 Dec 2008 11:14:21 -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/2008/Dec/10/t1228932883rull2bkxn80iefa.htm/, Retrieved Sun, 19 May 2024 05:36:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32055, Retrieved Sun, 19 May 2024 05:36:26 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

221

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [Variance Reduction Matrix] [] [2008-11-30 18:13:06] [b745fd448f60064800b631a75a630267]
F RM D    [Standard Deviation-Mean Plot] [SMP Q1] [2008-12-07 13:12:10] [e5d91604aae608e98a8ea24759233f66]
F RM        [Variance Reduction Matrix] [VRM Q1] [2008-12-07 13:13:31] [e5d91604aae608e98a8ea24759233f66]
F RMP         [(Partial) Autocorrelation Function] [ACF Q2] [2008-12-07 13:20:49] [e5d91604aae608e98a8ea24759233f66]
F RMP           [ARIMA Backward Selection] [ARMA Q5] [2008-12-07 13:46:58] [e5d91604aae608e98a8ea24759233f66]
- RMPD              [Standard Deviation-Mean Plot] [SD mean plot] [2008-12-10 18:14:21] [55ca0ca4a201c9689dcf5fae352c92eb] [Current]

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Dataseries X:

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Histogram

Boxplots

9.4
9.4
9.5
9.5
9.4
9.4
9.3
9.4
9.4
9.2
9.1
9.1
9.1
9.1
9
8.9
8.8
8.7
8.4
8.3
8.2
7.9
7.8
7.7
7.3
7.2
7.1
6.9
6.8
6.7
6.8
6.9
6.7
6.8
6.8
6.7
6.3
6.2
6.2
6.5
6.5
6.4
6.2
6.2
6.3
7.5
7.4
7.4
7.4
7.4
7.4
7.2
7.2
7.1
7.5
7.4
7.5
8
8.1
8.1
8.1
8.1
8.1
7.9
7.9
8
8.1
8.1
8.1
8.6
8.6
8.6
8.4
8.4
8.4
7.7
7.8
7.9
8.7
8.8
8.8
8.5
8.5
8.5
8.4
8.5
8.5
8.3
8.4
8.4
8.5
8.4
8.4
8.5
8.5
8.5
8.5
8.5
8.5
8.3
8.3
8.3
8.3
8.2
8.2
8.1
8
7.8
7.9
7.8
7.7
7.8
7.7
7.6
7.3
7.3
7.1
7.1
7.1
7

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32055&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32055&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32055&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	9.34166666666667	0.137895436890245	0.4
2	8.49166666666667	0.512495380614806	1.4
3	6.89166666666667	0.202072594216369	0.6
4	6.59166666666667	0.519542339395205	1.3
5	7.525	0.349350045864394	1
6	8.18333333333333	0.262274434110301	0.699999999999999
7	8.36666666666667	0.37254245232977	1.1
8	8.44166666666667	0.0668557923421519	0.199999999999999
9	8.25	0.211057941204435	0.7
10	7.45	0.33166247903554	0.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.34166666666667 & 0.137895436890245 & 0.4 \tabularnewline
2 & 8.49166666666667 & 0.512495380614806 & 1.4 \tabularnewline
3 & 6.89166666666667 & 0.202072594216369 & 0.6 \tabularnewline
4 & 6.59166666666667 & 0.519542339395205 & 1.3 \tabularnewline
5 & 7.525 & 0.349350045864394 & 1 \tabularnewline
6 & 8.18333333333333 & 0.262274434110301 & 0.699999999999999 \tabularnewline
7 & 8.36666666666667 & 0.37254245232977 & 1.1 \tabularnewline
8 & 8.44166666666667 & 0.0668557923421519 & 0.199999999999999 \tabularnewline
9 & 8.25 & 0.211057941204435 & 0.7 \tabularnewline
10 & 7.45 & 0.33166247903554 & 0.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32055&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]9.34166666666667[/C][C]0.137895436890245[/C][C]0.4[/C][/ROW]
[ROW][C]2[/C][C]8.49166666666667[/C][C]0.512495380614806[/C][C]1.4[/C][/ROW]
[ROW][C]3[/C][C]6.89166666666667[/C][C]0.202072594216369[/C][C]0.6[/C][/ROW]
[ROW][C]4[/C][C]6.59166666666667[/C][C]0.519542339395205[/C][C]1.3[/C][/ROW]
[ROW][C]5[/C][C]7.525[/C][C]0.349350045864394[/C][C]1[/C][/ROW]
[ROW][C]6[/C][C]8.18333333333333[/C][C]0.262274434110301[/C][C]0.699999999999999[/C][/ROW]
[ROW][C]7[/C][C]8.36666666666667[/C][C]0.37254245232977[/C][C]1.1[/C][/ROW]
[ROW][C]8[/C][C]8.44166666666667[/C][C]0.0668557923421519[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]9[/C][C]8.25[/C][C]0.211057941204435[/C][C]0.7[/C][/ROW]
[ROW][C]10[/C][C]7.45[/C][C]0.33166247903554[/C][C]0.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32055&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32055&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	9.34166666666667	0.137895436890245	0.4
2	8.49166666666667	0.512495380614806	1.4
3	6.89166666666667	0.202072594216369	0.6
4	6.59166666666667	0.519542339395205	1.3
5	7.525	0.349350045864394	1
6	8.18333333333333	0.262274434110301	0.699999999999999
7	8.36666666666667	0.37254245232977	1.1
8	8.44166666666667	0.0668557923421519	0.199999999999999
9	8.25	0.211057941204435	0.7
10	7.45	0.33166247903554	0.9

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.890151327572583
beta	-0.0746324104742994
S.D.	0.0580998852696035
T-STAT	-1.28455349142222
p-value	0.234893733275607

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.890151327572583 \tabularnewline
beta & -0.0746324104742994 \tabularnewline
S.D. & 0.0580998852696035 \tabularnewline
T-STAT & -1.28455349142222 \tabularnewline
p-value & 0.234893733275607 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32055&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.890151327572583[/C][/ROW]
[ROW][C]beta[/C][C]-0.0746324104742994[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0580998852696035[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.28455349142222[/C][/ROW]
[ROW][C]p-value[/C][C]0.234893733275607[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32055&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32055&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	0.890151327572583
beta	-0.0746324104742994
S.D.	0.0580998852696035
T-STAT	-1.28455349142222
p-value	0.234893733275607

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	3.83536405880661
beta	-2.51375431719708
S.D.	1.89992350812307
T-STAT	-1.32308185379548
p-value	0.222372391816897
Lambda	3.51375431719708

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.83536405880661 \tabularnewline
beta & -2.51375431719708 \tabularnewline
S.D. & 1.89992350812307 \tabularnewline
T-STAT & -1.32308185379548 \tabularnewline
p-value & 0.222372391816897 \tabularnewline
Lambda & 3.51375431719708 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32055&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.83536405880661[/C][/ROW]
[ROW][C]beta[/C][C]-2.51375431719708[/C][/ROW]
[ROW][C]S.D.[/C][C]1.89992350812307[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.32308185379548[/C][/ROW]
[ROW][C]p-value[/C][C]0.222372391816897[/C][/ROW]
[ROW][C]Lambda[/C][C]3.51375431719708[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32055&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32055&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	3.83536405880661
beta	-2.51375431719708
S.D.	1.89992350812307
T-STAT	-1.32308185379548
p-value	0.222372391816897
Lambda	3.51375431719708

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

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