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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, 24 Dec 2010 14:05:02 +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/Dec/24/t12931993631ka08dk9jc3kiqh.htm/, Retrieved Tue, 30 Apr 2024 06:14:35 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 06:14:35 +0200

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

Dataseries X:

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Histogram

Boxplots

6.4
7.7
9.2
8.6
7.4
8.6
6.2
6
6.6
5.1
4.7
5
3.6
1.9
-0.1
-5.7
-5.6
-6.4
-7.7
-8
-11.9
-15.4
-15.5
-13.4
-10.9
-10.8
-7.3
-6.5
-5.1
-5.3
-6.8
-8.4
-8.4
-9.7
-8.8
-9.6
-11.5
-11
-14.9
-16.2
-14.4
-17.3
-15.7
-12.6
-9.4
-8.1
-5.4
-4.6
-4.9
-4
-3.1
-1.3
0
-0.4
3
0.4
1.2
0.6
-1.3
-3.2
-1.8
-3.6
-4.2
-6.9
-8
-7.5
-8.2
-7.6
-3.7
-1.7
-0.7
0.2
0.6
2.2
3.3
5.3
5.5
6.3
7.7
6.5
5.5
6.9
5.7
6.9
6.1
4.8
3.7
5.8
6.8
8.5
7.2
5
4.7
2.3
2.4
0.1
1.9
1.7
2
-1.9
0.5
-1.3
-3.3
-2.8
-8
-13.9
-21.9
-28.8
-27.6
-31.4
-31.8
-29.4
-27.6
-23.6
-22.8
-18.2
-17.8
-14.2
-8.8
-7.9
-7
-7
-3.6
-2.4
-4.9
-7.7
-6.5
-5.1
-3.4
-2.8
0.8

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	6.79166666666667	1.51204757821567	4.5
2	-7.01666666666667	6.41345649727386	19.1
3	-8.13333333333333	1.96160107766049	5.8
4	-11.7583333333333	4.20810005354032	12.7
5	-1.08333333333333	2.34087525718415	7.9
6	-4.475	3.06746119483494	8.4
7	5.2	2.11359237490883	7.1
8	4.78333333333333	2.36444624819556	8.4
9	-6.31666666666667	10.1005700409192	30.8
10	-21.7583333333333	8.36849702301688	23.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6.79166666666667 & 1.51204757821567 & 4.5 \tabularnewline
2 & -7.01666666666667 & 6.41345649727386 & 19.1 \tabularnewline
3 & -8.13333333333333 & 1.96160107766049 & 5.8 \tabularnewline
4 & -11.7583333333333 & 4.20810005354032 & 12.7 \tabularnewline
5 & -1.08333333333333 & 2.34087525718415 & 7.9 \tabularnewline
6 & -4.475 & 3.06746119483494 & 8.4 \tabularnewline
7 & 5.2 & 2.11359237490883 & 7.1 \tabularnewline
8 & 4.78333333333333 & 2.36444624819556 & 8.4 \tabularnewline
9 & -6.31666666666667 & 10.1005700409192 & 30.8 \tabularnewline
10 & -21.7583333333333 & 8.36849702301688 & 23.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]6.79166666666667[/C][C]1.51204757821567[/C][C]4.5[/C][/ROW]
[ROW][C]2[/C][C]-7.01666666666667[/C][C]6.41345649727386[/C][C]19.1[/C][/ROW]
[ROW][C]3[/C][C]-8.13333333333333[/C][C]1.96160107766049[/C][C]5.8[/C][/ROW]
[ROW][C]4[/C][C]-11.7583333333333[/C][C]4.20810005354032[/C][C]12.7[/C][/ROW]
[ROW][C]5[/C][C]-1.08333333333333[/C][C]2.34087525718415[/C][C]7.9[/C][/ROW]
[ROW][C]6[/C][C]-4.475[/C][C]3.06746119483494[/C][C]8.4[/C][/ROW]
[ROW][C]7[/C][C]5.2[/C][C]2.11359237490883[/C][C]7.1[/C][/ROW]
[ROW][C]8[/C][C]4.78333333333333[/C][C]2.36444624819556[/C][C]8.4[/C][/ROW]
[ROW][C]9[/C][C]-6.31666666666667[/C][C]10.1005700409192[/C][C]30.8[/C][/ROW]
[ROW][C]10[/C][C]-21.7583333333333[/C][C]8.36849702301688[/C][C]23.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	6.79166666666667	1.51204757821567	4.5
2	-7.01666666666667	6.41345649727386	19.1
3	-8.13333333333333	1.96160107766049	5.8
4	-11.7583333333333	4.20810005354032	12.7
5	-1.08333333333333	2.34087525718415	7.9
6	-4.475	3.06746119483494	8.4
7	5.2	2.11359237490883	7.1
8	4.78333333333333	2.36444624819556	8.4
9	-6.31666666666667	10.1005700409192	30.8
10	-21.7583333333333	8.36849702301688	23.9

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	3.27059104112975
beta	-0.222652024397237
S.D.	0.0925178915489023
T-STAT	-2.40658342586146
p-value	0.0427354272353758

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.27059104112975 \tabularnewline
beta & -0.222652024397237 \tabularnewline
S.D. & 0.0925178915489023 \tabularnewline
T-STAT & -2.40658342586146 \tabularnewline
p-value & 0.0427354272353758 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.27059104112975[/C][/ROW]
[ROW][C]beta[/C][C]-0.222652024397237[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0925178915489023[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.40658342586146[/C][/ROW]
[ROW][C]p-value[/C][C]0.0427354272353758[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	3.27059104112975
beta	-0.222652024397237
S.D.	0.0925178915489023
T-STAT	-2.40658342586146
p-value	0.0427354272353758

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.8459429034218
beta	-1.27019015600093
S.D.	0.0170157195672399
T-STAT	-74.6480424164019
p-value	0.00852777479035878
Lambda	2.27019015600093

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.8459429034218 \tabularnewline
beta & -1.27019015600093 \tabularnewline
S.D. & 0.0170157195672399 \tabularnewline
T-STAT & -74.6480424164019 \tabularnewline
p-value & 0.00852777479035878 \tabularnewline
Lambda & 2.27019015600093 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.8459429034218[/C][/ROW]
[ROW][C]beta[/C][C]-1.27019015600093[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0170157195672399[/C][/ROW]
[ROW][C]T-STAT[/C][C]-74.6480424164019[/C][/ROW]
[ROW][C]p-value[/C][C]0.00852777479035878[/C][/ROW]
[ROW][C]Lambda[/C][C]2.27019015600093[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	2.8459429034218
beta	-1.27019015600093
S.D.	0.0170157195672399
T-STAT	-74.6480424164019
p-value	0.00852777479035878
Lambda	2.27019015600093

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')

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Dataset

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Figures (Output of Computation)

Input Parameters & R Code