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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

Thu, 05 Aug 2010 13:39:12 +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/05/t1281015556z92s4okisa0mwqh.htm/, Retrieved Sun, 05 May 2024 15:02:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78408, Retrieved Sun, 05 May 2024 15:02:08 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

117

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

-       [Standard Deviation-Mean Plot] [] [2010-08-05 13:39:12] [d41d8cd98f00b204e9800998ecf8427e] [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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78408&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78408&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78408&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	388.5	8.72301032275608	26
2	382.666666666667	10.9406110294156	31
3	378.166666666667	14.6587444168588	50
4	356	20.0272541575451	56
5	323.5	26.4557950345305	71
6	271	33.061925368782	86
7	212.666666666667	35.5331684571762	92
8	160	29.1672294318002	76
9	115.916666666667	32.4526461544239	82
10	60.8333333333333	36.5359930462932	90

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 388.5 & 8.72301032275608 & 26 \tabularnewline
2 & 382.666666666667 & 10.9406110294156 & 31 \tabularnewline
3 & 378.166666666667 & 14.6587444168588 & 50 \tabularnewline
4 & 356 & 20.0272541575451 & 56 \tabularnewline
5 & 323.5 & 26.4557950345305 & 71 \tabularnewline
6 & 271 & 33.061925368782 & 86 \tabularnewline
7 & 212.666666666667 & 35.5331684571762 & 92 \tabularnewline
8 & 160 & 29.1672294318002 & 76 \tabularnewline
9 & 115.916666666667 & 32.4526461544239 & 82 \tabularnewline
10 & 60.8333333333333 & 36.5359930462932 & 90 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78408&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]388.5[/C][C]8.72301032275608[/C][C]26[/C][/ROW]
[ROW][C]2[/C][C]382.666666666667[/C][C]10.9406110294156[/C][C]31[/C][/ROW]
[ROW][C]3[/C][C]378.166666666667[/C][C]14.6587444168588[/C][C]50[/C][/ROW]
[ROW][C]4[/C][C]356[/C][C]20.0272541575451[/C][C]56[/C][/ROW]
[ROW][C]5[/C][C]323.5[/C][C]26.4557950345305[/C][C]71[/C][/ROW]
[ROW][C]6[/C][C]271[/C][C]33.061925368782[/C][C]86[/C][/ROW]
[ROW][C]7[/C][C]212.666666666667[/C][C]35.5331684571762[/C][C]92[/C][/ROW]
[ROW][C]8[/C][C]160[/C][C]29.1672294318002[/C][C]76[/C][/ROW]
[ROW][C]9[/C][C]115.916666666667[/C][C]32.4526461544239[/C][C]82[/C][/ROW]
[ROW][C]10[/C][C]60.8333333333333[/C][C]36.5359930462932[/C][C]90[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78408&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78408&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	388.5	8.72301032275608	26
2	382.666666666667	10.9406110294156	31
3	378.166666666667	14.6587444168588	50
4	356	20.0272541575451	56
5	323.5	26.4557950345305	71
6	271	33.061925368782	86
7	212.666666666667	35.5331684571762	92
8	160	29.1672294318002	76
9	115.916666666667	32.4526461544239	82
10	60.8333333333333	36.5359930462932	90

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	44.1414640057359
beta	-0.0731747712136557
S.D.	0.0161670763166611
T-STAT	-4.52615981890585
p-value	0.00193413308919233

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 44.1414640057359 \tabularnewline
beta & -0.0731747712136557 \tabularnewline
S.D. & 0.0161670763166611 \tabularnewline
T-STAT & -4.52615981890585 \tabularnewline
p-value & 0.00193413308919233 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78408&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]44.1414640057359[/C][/ROW]
[ROW][C]beta[/C][C]-0.0731747712136557[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0161670763166611[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.52615981890585[/C][/ROW]
[ROW][C]p-value[/C][C]0.00193413308919233[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78408&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78408&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	44.1414640057359
beta	-0.0731747712136557
S.D.	0.0161670763166611
T-STAT	-4.52615981890585
p-value	0.00193413308919233

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	6.27395683556674
beta	-0.582818359836589
S.D.	0.211348091802586
T-STAT	-2.75762300414324
p-value	0.0247655331385933
Lambda	1.58281835983659

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 6.27395683556674 \tabularnewline
beta & -0.582818359836589 \tabularnewline
S.D. & 0.211348091802586 \tabularnewline
T-STAT & -2.75762300414324 \tabularnewline
p-value & 0.0247655331385933 \tabularnewline
Lambda & 1.58281835983659 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78408&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.27395683556674[/C][/ROW]
[ROW][C]beta[/C][C]-0.582818359836589[/C][/ROW]
[ROW][C]S.D.[/C][C]0.211348091802586[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.75762300414324[/C][/ROW]
[ROW][C]p-value[/C][C]0.0247655331385933[/C][/ROW]
[ROW][C]Lambda[/C][C]1.58281835983659[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78408&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78408&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	6.27395683556674
beta	-0.582818359836589
S.D.	0.211348091802586
T-STAT	-2.75762300414324
p-value	0.0247655331385933
Lambda	1.58281835983659

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code