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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

Mon, 19 Dec 2016 14:29:42 +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/2016/Dec/19/t1482154293xzemhqtw41juupx.htm/, Retrieved Sat, 26 Apr 2025 04:32:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301345, Retrieved Sat, 26 Apr 2025 04:32:39 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

143

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

-       [Standard Deviation-Mean Plot] [Standard Deviatio...] [2016-12-19 13:29:42] [2e2b863c9581eba851d0277c64dc678f] [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	0 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301345&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

0 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301345&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301345&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	0 seconds
R Server	Big Analytics Cloud Computing Center

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	6127.5	1249.26978671542	4630
2	5850	525.512736633125	1800
3	5240	807.99414939376	2690
4	5152.5	474.727194387376	1700
5	4715.83333333333	527.127004419124	1610
6	5448.33333333333	1209.94239782752	3510
7	6492.5	898.889466356833	3200
8	5601.66666666667	1172.58714220334	3750
9	6716.66666666667	1027.10832688257	3510
10	5785	969.62504468105	3520
11	7250	NA	0
12	NaN	NA	-Inf

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6127.5 & 1249.26978671542 & 4630 \tabularnewline
2 & 5850 & 525.512736633125 & 1800 \tabularnewline
3 & 5240 & 807.99414939376 & 2690 \tabularnewline
4 & 5152.5 & 474.727194387376 & 1700 \tabularnewline
5 & 4715.83333333333 & 527.127004419124 & 1610 \tabularnewline
6 & 5448.33333333333 & 1209.94239782752 & 3510 \tabularnewline
7 & 6492.5 & 898.889466356833 & 3200 \tabularnewline
8 & 5601.66666666667 & 1172.58714220334 & 3750 \tabularnewline
9 & 6716.66666666667 & 1027.10832688257 & 3510 \tabularnewline
10 & 5785 & 969.62504468105 & 3520 \tabularnewline
11 & 7250 & NA & 0 \tabularnewline
12 & NaN & NA & -Inf \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301345&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]6127.5[/C][C]1249.26978671542[/C][C]4630[/C][/ROW]
[ROW][C]2[/C][C]5850[/C][C]525.512736633125[/C][C]1800[/C][/ROW]
[ROW][C]3[/C][C]5240[/C][C]807.99414939376[/C][C]2690[/C][/ROW]
[ROW][C]4[/C][C]5152.5[/C][C]474.727194387376[/C][C]1700[/C][/ROW]
[ROW][C]5[/C][C]4715.83333333333[/C][C]527.127004419124[/C][C]1610[/C][/ROW]
[ROW][C]6[/C][C]5448.33333333333[/C][C]1209.94239782752[/C][C]3510[/C][/ROW]
[ROW][C]7[/C][C]6492.5[/C][C]898.889466356833[/C][C]3200[/C][/ROW]
[ROW][C]8[/C][C]5601.66666666667[/C][C]1172.58714220334[/C][C]3750[/C][/ROW]
[ROW][C]9[/C][C]6716.66666666667[/C][C]1027.10832688257[/C][C]3510[/C][/ROW]
[ROW][C]10[/C][C]5785[/C][C]969.62504468105[/C][C]3520[/C][/ROW]
[ROW][C]11[/C][C]7250[/C][C]NA[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]NaN[/C][C]NA[/C][C]-Inf[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301345&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301345&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	6127.5	1249.26978671542	4630
2	5850	525.512736633125	1800
3	5240	807.99414939376	2690
4	5152.5	474.727194387376	1700
5	4715.83333333333	527.127004419124	1610
6	5448.33333333333	1209.94239782752	3510
7	6492.5	898.889466356833	3200
8	5601.66666666667	1172.58714220334	3750
9	6716.66666666667	1027.10832688257	3510
10	5785	969.62504468105	3520
11	7250	NA	0
12	NaN	NA	-Inf

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-392.132681612742
beta	0.223772274910337
S.D.	0.149021301408867
T-STAT	1.50161267412621
p-value	0.171594844679979

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -392.132681612742 \tabularnewline
beta & 0.223772274910337 \tabularnewline
S.D. & 0.149021301408867 \tabularnewline
T-STAT & 1.50161267412621 \tabularnewline
p-value & 0.171594844679979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301345&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-392.132681612742[/C][/ROW]
[ROW][C]beta[/C][C]0.223772274910337[/C][/ROW]
[ROW][C]S.D.[/C][C]0.149021301408867[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.50161267412621[/C][/ROW]
[ROW][C]p-value[/C][C]0.171594844679979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301345&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301345&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	-392.132681612742
beta	0.223772274910337
S.D.	0.149021301408867
T-STAT	1.50161267412621
p-value	0.171594844679979

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-8.62324424511226
beta	1.77588765083569
S.D.	1.03230977193306
T-STAT	1.72030498898623
p-value	0.123688364332204
Lambda	-0.775887650835687

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -8.62324424511226 \tabularnewline
beta & 1.77588765083569 \tabularnewline
S.D. & 1.03230977193306 \tabularnewline
T-STAT & 1.72030498898623 \tabularnewline
p-value & 0.123688364332204 \tabularnewline
Lambda & -0.775887650835687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301345&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-8.62324424511226[/C][/ROW]
[ROW][C]beta[/C][C]1.77588765083569[/C][/ROW]
[ROW][C]S.D.[/C][C]1.03230977193306[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.72030498898623[/C][/ROW]
[ROW][C]p-value[/C][C]0.123688364332204[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.775887650835687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301345&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301345&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	-8.62324424511226
beta	1.77588765083569
S.D.	1.03230977193306
T-STAT	1.72030498898623
p-value	0.123688364332204
Lambda	-0.775887650835687

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