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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

Thu, 16 Dec 2010 13:34:05 +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/16/t1292507877dczya3a22m5iupv.htm/, Retrieved Fri, 03 May 2024 05:07:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110932, Retrieved Fri, 03 May 2024 05:07:44 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

121

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

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Standard Deviation-Mean Plot] [] [2010-12-16 13:04:56] [64a7ae6044525e7ca71ecb546c042c9e]
-    D      [Standard Deviation-Mean Plot] [] [2010-12-16 13:34:05] [186d70462ffc26ec970915be294cb975] [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	'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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110932&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110932&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110932&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	4283.5	1960.28427901298	5377
2	4212.66666666667	1968.4428702234	5661
3	3979.91666666667	1858.55576668519	5311
4	3699.41666666667	1655.13484528017	4505
5	3680.91666666667	1650.8769822752	4685
6	3760.25	1789.63516469902	4671
7	3509.16666666667	1598.46095486953	4238
8	3369.5	1621.98629632144	5229
9	3481.41666666667	1541.65881488582	4898
10	3608	1504.04412411097	4176
11	3598.5	1581.28437440179	4234

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4283.5 & 1960.28427901298 & 5377 \tabularnewline
2 & 4212.66666666667 & 1968.4428702234 & 5661 \tabularnewline
3 & 3979.91666666667 & 1858.55576668519 & 5311 \tabularnewline
4 & 3699.41666666667 & 1655.13484528017 & 4505 \tabularnewline
5 & 3680.91666666667 & 1650.8769822752 & 4685 \tabularnewline
6 & 3760.25 & 1789.63516469902 & 4671 \tabularnewline
7 & 3509.16666666667 & 1598.46095486953 & 4238 \tabularnewline
8 & 3369.5 & 1621.98629632144 & 5229 \tabularnewline
9 & 3481.41666666667 & 1541.65881488582 & 4898 \tabularnewline
10 & 3608 & 1504.04412411097 & 4176 \tabularnewline
11 & 3598.5 & 1581.28437440179 & 4234 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110932&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]4283.5[/C][C]1960.28427901298[/C][C]5377[/C][/ROW]
[ROW][C]2[/C][C]4212.66666666667[/C][C]1968.4428702234[/C][C]5661[/C][/ROW]
[ROW][C]3[/C][C]3979.91666666667[/C][C]1858.55576668519[/C][C]5311[/C][/ROW]
[ROW][C]4[/C][C]3699.41666666667[/C][C]1655.13484528017[/C][C]4505[/C][/ROW]
[ROW][C]5[/C][C]3680.91666666667[/C][C]1650.8769822752[/C][C]4685[/C][/ROW]
[ROW][C]6[/C][C]3760.25[/C][C]1789.63516469902[/C][C]4671[/C][/ROW]
[ROW][C]7[/C][C]3509.16666666667[/C][C]1598.46095486953[/C][C]4238[/C][/ROW]
[ROW][C]8[/C][C]3369.5[/C][C]1621.98629632144[/C][C]5229[/C][/ROW]
[ROW][C]9[/C][C]3481.41666666667[/C][C]1541.65881488582[/C][C]4898[/C][/ROW]
[ROW][C]10[/C][C]3608[/C][C]1504.04412411097[/C][C]4176[/C][/ROW]
[ROW][C]11[/C][C]3598.5[/C][C]1581.28437440179[/C][C]4234[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110932&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110932&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	4283.5	1960.28427901298	5377
2	4212.66666666667	1968.4428702234	5661
3	3979.91666666667	1858.55576668519	5311
4	3699.41666666667	1655.13484528017	4505
5	3680.91666666667	1650.8769822752	4685
6	3760.25	1789.63516469902	4671
7	3509.16666666667	1598.46095486953	4238
8	3369.5	1621.98629632144	5229
9	3481.41666666667	1541.65881488582	4898
10	3608	1504.04412411097	4176
11	3598.5	1581.28437440179	4234

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-213.854351393828
beta	0.511925657593746
S.D.	0.0725751194602251
T-STAT	7.05373496318263
p-value	5.96145327527334e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -213.854351393828 \tabularnewline
beta & 0.511925657593746 \tabularnewline
S.D. & 0.0725751194602251 \tabularnewline
T-STAT & 7.05373496318263 \tabularnewline
p-value & 5.96145327527334e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110932&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-213.854351393828[/C][/ROW]
[ROW][C]beta[/C][C]0.511925657593746[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0725751194602251[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.05373496318263[/C][/ROW]
[ROW][C]p-value[/C][C]5.96145327527334e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110932&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110932&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	-213.854351393828
beta	0.511925657593746
S.D.	0.0725751194602251
T-STAT	7.05373496318263
p-value	5.96145327527334e-05

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-1.70889296976896
beta	1.11180691810503
S.D.	0.172276269920456
T-STAT	6.45362776091204
p-value	0.000117641717123537
Lambda	-0.111806918105033

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.70889296976896 \tabularnewline
beta & 1.11180691810503 \tabularnewline
S.D. & 0.172276269920456 \tabularnewline
T-STAT & 6.45362776091204 \tabularnewline
p-value & 0.000117641717123537 \tabularnewline
Lambda & -0.111806918105033 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110932&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.70889296976896[/C][/ROW]
[ROW][C]beta[/C][C]1.11180691810503[/C][/ROW]
[ROW][C]S.D.[/C][C]0.172276269920456[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.45362776091204[/C][/ROW]
[ROW][C]p-value[/C][C]0.000117641717123537[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.111806918105033[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110932&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110932&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	-1.70889296976896
beta	1.11180691810503
S.D.	0.172276269920456
T-STAT	6.45362776091204
p-value	0.000117641717123537
Lambda	-0.111806918105033

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