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Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Tue, 02 Jun 2009 15:33:51 -0600

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/2009/Jun/02/t1243978490wvkiocglm14xf35.htm/, Retrieved Fri, 10 May 2024 21:07:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41403, Retrieved Fri, 10 May 2024 21:07:43 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

127

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

-     [Bootstrap Plot - Central Tendency] [Bootstrap plot (7...] [2009-05-28 12:38:57] [b92d8e33f38b56c8010fa2bf0795e6cd]
- RMPD  [Standard Deviation Plot] [Standard deviatio...] [2009-06-02 20:35:29] [b92d8e33f38b56c8010fa2bf0795e6cd]
- RM D      [Standard Deviation-Mean Plot] [standard deviatio...] [2009-06-02 21:33:51] [8c726525c89fb87c09aaacaddee1db18] [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=41403&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=41403&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41403&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	103.675	6.99160210538329	16.8
2	100.05	3.43171482886715	8.2
3	105.55	4.89387372129686	11.7
4	122.45	5.3100533581751	10.4
5	136.25	4.6278144589716	10.9000000000000
6	144.45	6.67158152164838	15.7000000000000
7	159.625	10.9466509338092	21.1
8	176.2	12.2150180788514	29.5
9	181.725	6.27023391376536	15.2
10	200.975	10.3209737912660	22.5
11	224.1	5.41541011066259	11.8000000000000
12	201.775	4.97619332421882	10.9
13	206.575	13.8879744143390	32.8
14	233.425	8.38744100823765	20.2
15	271.7	17.1815792832518	37.4
16	322.3	23.1013708106972	52.3
17	391.65	23.3095831508559	50.9
18	228	70.6660220096382	162.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 103.675 & 6.99160210538329 & 16.8 \tabularnewline
2 & 100.05 & 3.43171482886715 & 8.2 \tabularnewline
3 & 105.55 & 4.89387372129686 & 11.7 \tabularnewline
4 & 122.45 & 5.3100533581751 & 10.4 \tabularnewline
5 & 136.25 & 4.6278144589716 & 10.9000000000000 \tabularnewline
6 & 144.45 & 6.67158152164838 & 15.7000000000000 \tabularnewline
7 & 159.625 & 10.9466509338092 & 21.1 \tabularnewline
8 & 176.2 & 12.2150180788514 & 29.5 \tabularnewline
9 & 181.725 & 6.27023391376536 & 15.2 \tabularnewline
10 & 200.975 & 10.3209737912660 & 22.5 \tabularnewline
11 & 224.1 & 5.41541011066259 & 11.8000000000000 \tabularnewline
12 & 201.775 & 4.97619332421882 & 10.9 \tabularnewline
13 & 206.575 & 13.8879744143390 & 32.8 \tabularnewline
14 & 233.425 & 8.38744100823765 & 20.2 \tabularnewline
15 & 271.7 & 17.1815792832518 & 37.4 \tabularnewline
16 & 322.3 & 23.1013708106972 & 52.3 \tabularnewline
17 & 391.65 & 23.3095831508559 & 50.9 \tabularnewline
18 & 228 & 70.6660220096382 & 162.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41403&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]103.675[/C][C]6.99160210538329[/C][C]16.8[/C][/ROW]
[ROW][C]2[/C][C]100.05[/C][C]3.43171482886715[/C][C]8.2[/C][/ROW]
[ROW][C]3[/C][C]105.55[/C][C]4.89387372129686[/C][C]11.7[/C][/ROW]
[ROW][C]4[/C][C]122.45[/C][C]5.3100533581751[/C][C]10.4[/C][/ROW]
[ROW][C]5[/C][C]136.25[/C][C]4.6278144589716[/C][C]10.9000000000000[/C][/ROW]
[ROW][C]6[/C][C]144.45[/C][C]6.67158152164838[/C][C]15.7000000000000[/C][/ROW]
[ROW][C]7[/C][C]159.625[/C][C]10.9466509338092[/C][C]21.1[/C][/ROW]
[ROW][C]8[/C][C]176.2[/C][C]12.2150180788514[/C][C]29.5[/C][/ROW]
[ROW][C]9[/C][C]181.725[/C][C]6.27023391376536[/C][C]15.2[/C][/ROW]
[ROW][C]10[/C][C]200.975[/C][C]10.3209737912660[/C][C]22.5[/C][/ROW]
[ROW][C]11[/C][C]224.1[/C][C]5.41541011066259[/C][C]11.8000000000000[/C][/ROW]
[ROW][C]12[/C][C]201.775[/C][C]4.97619332421882[/C][C]10.9[/C][/ROW]
[ROW][C]13[/C][C]206.575[/C][C]13.8879744143390[/C][C]32.8[/C][/ROW]
[ROW][C]14[/C][C]233.425[/C][C]8.38744100823765[/C][C]20.2[/C][/ROW]
[ROW][C]15[/C][C]271.7[/C][C]17.1815792832518[/C][C]37.4[/C][/ROW]
[ROW][C]16[/C][C]322.3[/C][C]23.1013708106972[/C][C]52.3[/C][/ROW]
[ROW][C]17[/C][C]391.65[/C][C]23.3095831508559[/C][C]50.9[/C][/ROW]
[ROW][C]18[/C][C]228[/C][C]70.6660220096382[/C][C]162.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41403&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41403&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	103.675	6.99160210538329	16.8
2	100.05	3.43171482886715	8.2
3	105.55	4.89387372129686	11.7
4	122.45	5.3100533581751	10.4
5	136.25	4.6278144589716	10.9000000000000
6	144.45	6.67158152164838	15.7000000000000
7	159.625	10.9466509338092	21.1
8	176.2	12.2150180788514	29.5
9	181.725	6.27023391376536	15.2
10	200.975	10.3209737912660	22.5
11	224.1	5.41541011066259	11.8000000000000
12	201.775	4.97619332421882	10.9
13	206.575	13.8879744143390	32.8
14	233.425	8.38744100823765	20.2
15	271.7	17.1815792832518	37.4
16	322.3	23.1013708106972	52.3
17	391.65	23.3095831508559	50.9
18	228	70.6660220096382	162.2

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-3.45404858362612
beta	0.0856801331242085
S.D.	0.045193463153264
T-STAT	1.89585234558464
p-value	0.0761891072167998

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -3.45404858362612 \tabularnewline
beta & 0.0856801331242085 \tabularnewline
S.D. & 0.045193463153264 \tabularnewline
T-STAT & 1.89585234558464 \tabularnewline
p-value & 0.0761891072167998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41403&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.45404858362612[/C][/ROW]
[ROW][C]beta[/C][C]0.0856801331242085[/C][/ROW]
[ROW][C]S.D.[/C][C]0.045193463153264[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.89585234558464[/C][/ROW]
[ROW][C]p-value[/C][C]0.0761891072167998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41403&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41403&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	-3.45404858362612
beta	0.0856801331242085
S.D.	0.045193463153264
T-STAT	1.89585234558464
p-value	0.0761891072167998

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-4.61714771337925
beta	1.31877137296134
S.D.	0.358415072554981
T-STAT	3.67945288561782
p-value	0.00202851101513453
Lambda	-0.318771372961344

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.61714771337925 \tabularnewline
beta & 1.31877137296134 \tabularnewline
S.D. & 0.358415072554981 \tabularnewline
T-STAT & 3.67945288561782 \tabularnewline
p-value & 0.00202851101513453 \tabularnewline
Lambda & -0.318771372961344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41403&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.61714771337925[/C][/ROW]
[ROW][C]beta[/C][C]1.31877137296134[/C][/ROW]
[ROW][C]S.D.[/C][C]0.358415072554981[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.67945288561782[/C][/ROW]
[ROW][C]p-value[/C][C]0.00202851101513453[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.318771372961344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41403&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41403&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	-4.61714771337925
beta	1.31877137296134
S.D.	0.358415072554981
T-STAT	3.67945288561782
p-value	0.00202851101513453
Lambda	-0.318771372961344

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 50 ; par2 = 12 ;

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code