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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

Fri, 23 Dec 2016 13:27:27 +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/23/t1482496627nojkpfkani4iuns.htm/, Retrieved Thu, 03 Apr 2025 04:13:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302901, Retrieved Thu, 03 Apr 2025 04:13:09 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

129

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

-       [Standard Deviation-Mean Plot] [] [2016-12-23 12:27:27] [219800a2f11ddd28e3280d87dbde8c8d] [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	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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302901&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]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302901&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302901&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	Big Analytics Cloud Computing Center

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	5031.16666666667	143.631367385295	432
2	5385.91666666667	81.0313725252962	270
3	5869.83333333333	211.975484574528	638
4	6664.83333333333	332.40140939788	1036
5	7438.25	84.9161350981072	266
6	7755.16666666667	112.631202953657	298
7	7830.08333333333	58.5622564352491	209
8	8115.58333333333	100.743110148656	305
9	8599.91666666667	219.904300810947	702

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5031.16666666667 & 143.631367385295 & 432 \tabularnewline
2 & 5385.91666666667 & 81.0313725252962 & 270 \tabularnewline
3 & 5869.83333333333 & 211.975484574528 & 638 \tabularnewline
4 & 6664.83333333333 & 332.40140939788 & 1036 \tabularnewline
5 & 7438.25 & 84.9161350981072 & 266 \tabularnewline
6 & 7755.16666666667 & 112.631202953657 & 298 \tabularnewline
7 & 7830.08333333333 & 58.5622564352491 & 209 \tabularnewline
8 & 8115.58333333333 & 100.743110148656 & 305 \tabularnewline
9 & 8599.91666666667 & 219.904300810947 & 702 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302901&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]5031.16666666667[/C][C]143.631367385295[/C][C]432[/C][/ROW]
[ROW][C]2[/C][C]5385.91666666667[/C][C]81.0313725252962[/C][C]270[/C][/ROW]
[ROW][C]3[/C][C]5869.83333333333[/C][C]211.975484574528[/C][C]638[/C][/ROW]
[ROW][C]4[/C][C]6664.83333333333[/C][C]332.40140939788[/C][C]1036[/C][/ROW]
[ROW][C]5[/C][C]7438.25[/C][C]84.9161350981072[/C][C]266[/C][/ROW]
[ROW][C]6[/C][C]7755.16666666667[/C][C]112.631202953657[/C][C]298[/C][/ROW]
[ROW][C]7[/C][C]7830.08333333333[/C][C]58.5622564352491[/C][C]209[/C][/ROW]
[ROW][C]8[/C][C]8115.58333333333[/C][C]100.743110148656[/C][C]305[/C][/ROW]
[ROW][C]9[/C][C]8599.91666666667[/C][C]219.904300810947[/C][C]702[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302901&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302901&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	5031.16666666667	143.631367385295	432
2	5385.91666666667	81.0313725252962	270
3	5869.83333333333	211.975484574528	638
4	6664.83333333333	332.40140939788	1036
5	7438.25	84.9161350981072	266
6	7755.16666666667	112.631202953657	298
7	7830.08333333333	58.5622564352491	209
8	8115.58333333333	100.743110148656	305
9	8599.91666666667	219.904300810947	702

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	193.725965650223
beta	-0.00634442962514239
S.D.	0.0261292830268447
T-STAT	-0.242809173853881
p-value	0.815114384863737

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 193.725965650223 \tabularnewline
beta & -0.00634442962514239 \tabularnewline
S.D. & 0.0261292830268447 \tabularnewline
T-STAT & -0.242809173853881 \tabularnewline
p-value & 0.815114384863737 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302901&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]193.725965650223[/C][/ROW]
[ROW][C]beta[/C][C]-0.00634442962514239[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0261292830268447[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.242809173853881[/C][/ROW]
[ROW][C]p-value[/C][C]0.815114384863737[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302901&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302901&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	193.725965650223
beta	-0.00634442962514239
S.D.	0.0261292830268447
T-STAT	-0.242809173853881
p-value	0.815114384863737

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	7.86818166900929
beta	-0.340238935318969
S.D.	1.09396061193763
T-STAT	-0.311015708980908
p-value	0.764845872831083
Lambda	1.34023893531897

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.86818166900929 \tabularnewline
beta & -0.340238935318969 \tabularnewline
S.D. & 1.09396061193763 \tabularnewline
T-STAT & -0.311015708980908 \tabularnewline
p-value & 0.764845872831083 \tabularnewline
Lambda & 1.34023893531897 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302901&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.86818166900929[/C][/ROW]
[ROW][C]beta[/C][C]-0.340238935318969[/C][/ROW]
[ROW][C]S.D.[/C][C]1.09396061193763[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.311015708980908[/C][/ROW]
[ROW][C]p-value[/C][C]0.764845872831083[/C][/ROW]
[ROW][C]Lambda[/C][C]1.34023893531897[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302901&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302901&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	7.86818166900929
beta	-0.340238935318969
S.D.	1.09396061193763
T-STAT	-0.311015708980908
p-value	0.764845872831083
Lambda	1.34023893531897

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