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Free Statistics

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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

Sun, 25 Nov 2007 12:57:53 -0700

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/2007/Nov/25/t11960201670cnpm9wcgc9shsb.htm/, Retrieved Sat, 04 May 2024 18:14:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6541, Retrieved Sat, 04 May 2024 18:14:46 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

196

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

-       [Standard Deviation-Mean Plot] [Stdev mean plot w...] [2007-11-25 19:57:53] [4a507cbea0acb4f2b617b46f2010fec1] [Current]

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Dataseries X:

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Histogram

Boxplots

8.1
8.2
8
8.1
8.3
8.2
8.1
7.7
7.6
7.7
8.2
8.4
8.4
8.6
8.4
8.5
8.7
8.7
8.6
7.4
7.3
7.4
9
9.2
9.2
8.5
8.3
8.3
8.6
8.6
8.5
8.1
8.1
8
8.6
8.7
8.7
8.6
8.4
8.4
8.7
8.7
8.5
8.3
8.3
8.3
8.1
8.2
8.1
8.1
7.9
7.7
8.1
8
7.7
7.8
7.6
7.4
7.7
7.9
7.6

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6541&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6541&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6541&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	8.05	0.254057974772402	0.300000000000001
2	8.35	0.636038878171338	1.1
3	8.45833333333333	0.328794860978788	1.3
4	8.43333333333333	0.205971460217775	1
5	7.83333333333333	0.222928171609085	0

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.05 & 0.254057974772402 & 0.300000000000001 \tabularnewline
2 & 8.35 & 0.636038878171338 & 1.1 \tabularnewline
3 & 8.45833333333333 & 0.328794860978788 & 1.3 \tabularnewline
4 & 8.43333333333333 & 0.205971460217775 & 1 \tabularnewline
5 & 7.83333333333333 & 0.222928171609085 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6541&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]8.05[/C][C]0.254057974772402[/C][C]0.300000000000001[/C][/ROW]
[ROW][C]2[/C][C]8.35[/C][C]0.636038878171338[/C][C]1.1[/C][/ROW]
[ROW][C]3[/C][C]8.45833333333333[/C][C]0.328794860978788[/C][C]1.3[/C][/ROW]
[ROW][C]4[/C][C]8.43333333333333[/C][C]0.205971460217775[/C][C]1[/C][/ROW]
[ROW][C]5[/C][C]7.83333333333333[/C][C]0.222928171609085[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6541&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6541&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	8.05	0.254057974772402	0.300000000000001
2	8.35	0.636038878171338	1.1
3	8.45833333333333	0.328794860978788	1.3
4	8.43333333333333	0.205971460217775	1
5	7.83333333333333	0.222928171609085	0

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-1.53276702364391
beta	0.226422527999245
S.D.	0.352697389023887
T-STAT	0.641973927354222
p-value	0.566575190750175

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.53276702364391 \tabularnewline
beta & 0.226422527999245 \tabularnewline
S.D. & 0.352697389023887 \tabularnewline
T-STAT & 0.641973927354222 \tabularnewline
p-value & 0.566575190750175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6541&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.53276702364391[/C][/ROW]
[ROW][C]beta[/C][C]0.226422527999245[/C][/ROW]
[ROW][C]S.D.[/C][C]0.352697389023887[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.641973927354222[/C][/ROW]
[ROW][C]p-value[/C][C]0.566575190750175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6541&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6541&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	-1.53276702364391
beta	0.226422527999245
S.D.	0.352697389023887
T-STAT	0.641973927354222
p-value	0.566575190750175

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-11.8156456942745
beta	5.03740060023144
S.D.	7.30429457896266
T-STAT	0.689649157187585
p-value	0.539972661395469
Lambda	-4.03740060023144

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.8156456942745 \tabularnewline
beta & 5.03740060023144 \tabularnewline
S.D. & 7.30429457896266 \tabularnewline
T-STAT & 0.689649157187585 \tabularnewline
p-value & 0.539972661395469 \tabularnewline
Lambda & -4.03740060023144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6541&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.8156456942745[/C][/ROW]
[ROW][C]beta[/C][C]5.03740060023144[/C][/ROW]
[ROW][C]S.D.[/C][C]7.30429457896266[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.689649157187585[/C][/ROW]
[ROW][C]p-value[/C][C]0.539972661395469[/C][/ROW]
[ROW][C]Lambda[/C][C]-4.03740060023144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6541&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6541&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	-11.8156456942745
beta	5.03740060023144
S.D.	7.30429457896266
T-STAT	0.689649157187585
p-value	0.539972661395469
Lambda	-4.03740060023144

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