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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

Mon, 18 Aug 2014 13:02:43 +0100

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/2014/Aug/18/t1408363387a9we4t7i4047tko.htm/, Retrieved Sat, 26 Apr 2025 05:17:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235711, Retrieved Sat, 26 Apr 2025 05:17:36 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Van Reusel Raphael

Estimated Impact

145

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

-       [Standard Deviation-Mean Plot] [Tijdreeks 2] [2014-08-18 12:02:43] [bf566d88435d8cc6ce5d208f6f8dd684] [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	'Sir Maurice George Kendall' @ kendall.wessa.net

\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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235711&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235711&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235711&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	804.166666666667	56.1585957693734	180
2	817.5	49.012985292397	170
3	809.166666666667	64.0253264282379	240
4	810.833333333333	74.034185387972	250
5	815.833333333333	97.6504278567486	350
6	807.5	111.283830402673	390
7	790	127.920429813366	450
8	784.166666666667	149.14656204451	540
9	777.5	140.008116647831	480

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 804.166666666667 & 56.1585957693734 & 180 \tabularnewline
2 & 817.5 & 49.012985292397 & 170 \tabularnewline
3 & 809.166666666667 & 64.0253264282379 & 240 \tabularnewline
4 & 810.833333333333 & 74.034185387972 & 250 \tabularnewline
5 & 815.833333333333 & 97.6504278567486 & 350 \tabularnewline
6 & 807.5 & 111.283830402673 & 390 \tabularnewline
7 & 790 & 127.920429813366 & 450 \tabularnewline
8 & 784.166666666667 & 149.14656204451 & 540 \tabularnewline
9 & 777.5 & 140.008116647831 & 480 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235711&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]804.166666666667[/C][C]56.1585957693734[/C][C]180[/C][/ROW]
[ROW][C]2[/C][C]817.5[/C][C]49.012985292397[/C][C]170[/C][/ROW]
[ROW][C]3[/C][C]809.166666666667[/C][C]64.0253264282379[/C][C]240[/C][/ROW]
[ROW][C]4[/C][C]810.833333333333[/C][C]74.034185387972[/C][C]250[/C][/ROW]
[ROW][C]5[/C][C]815.833333333333[/C][C]97.6504278567486[/C][C]350[/C][/ROW]
[ROW][C]6[/C][C]807.5[/C][C]111.283830402673[/C][C]390[/C][/ROW]
[ROW][C]7[/C][C]790[/C][C]127.920429813366[/C][C]450[/C][/ROW]
[ROW][C]8[/C][C]784.166666666667[/C][C]149.14656204451[/C][C]540[/C][/ROW]
[ROW][C]9[/C][C]777.5[/C][C]140.008116647831[/C][C]480[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235711&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235711&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	804.166666666667	56.1585957693734	180
2	817.5	49.012985292397	170
3	809.166666666667	64.0253264282379	240
4	810.833333333333	74.034185387972	250
5	815.833333333333	97.6504278567486	350
6	807.5	111.283830402673	390
7	790	127.920429813366	450
8	784.166666666667	149.14656204451	540
9	777.5	140.008116647831	480

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1808.18693283923
beta	-2.13456470243557
S.D.	0.569094845149826
T-STAT	-3.7508066021466
p-value	0.00716058223048944

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1808.18693283923 \tabularnewline
beta & -2.13456470243557 \tabularnewline
S.D. & 0.569094845149826 \tabularnewline
T-STAT & -3.7508066021466 \tabularnewline
p-value & 0.00716058223048944 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235711&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1808.18693283923[/C][/ROW]
[ROW][C]beta[/C][C]-2.13456470243557[/C][/ROW]
[ROW][C]S.D.[/C][C]0.569094845149826[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.7508066021466[/C][/ROW]
[ROW][C]p-value[/C][C]0.00716058223048944[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235711&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235711&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	1808.18693283923
beta	-2.13456470243557
S.D.	0.569094845149826
T-STAT	-3.7508066021466
p-value	0.00716058223048944

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	121.491315566703
beta	-17.4963189330074
S.D.	5.60712907037403
T-STAT	-3.12037028458136
p-value	0.0168349781953997
Lambda	18.4963189330074

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 121.491315566703 \tabularnewline
beta & -17.4963189330074 \tabularnewline
S.D. & 5.60712907037403 \tabularnewline
T-STAT & -3.12037028458136 \tabularnewline
p-value & 0.0168349781953997 \tabularnewline
Lambda & 18.4963189330074 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235711&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]121.491315566703[/C][/ROW]
[ROW][C]beta[/C][C]-17.4963189330074[/C][/ROW]
[ROW][C]S.D.[/C][C]5.60712907037403[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.12037028458136[/C][/ROW]
[ROW][C]p-value[/C][C]0.0168349781953997[/C][/ROW]
[ROW][C]Lambda[/C][C]18.4963189330074[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235711&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235711&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	121.491315566703
beta	-17.4963189330074
S.D.	5.60712907037403
T-STAT	-3.12037028458136
p-value	0.0168349781953997
Lambda	18.4963189330074

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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