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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

Sun, 05 Dec 2010 12:08:11 +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/05/t1291551001ycsar456roauevm.htm/, Retrieved Wed, 01 May 2024 15:55:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105350, Retrieved Wed, 01 May 2024 15:55:39 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

138

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Standard Deviation-Mean Plot] [Births] [2010-11-29 10:52:49] [b98453cac15ba1066b407e146608df68]
-   PD            [Standard Deviation-Mean Plot] [workshop 9] [2010-12-05 12:08:11] [3f56c8f677e988de577e4e00a8180a48] [Current]

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Boxplots

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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105350&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105350&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105350&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	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	2847.5	223.558208812096	744
2	2905.91666666667	268.117158358171	1094
3	2811.66666666667	327.377550552967	898
4	2704.91666666667	253.131463628661	934
5	2797.58333333333	242.094443754849	796
6	2887.5	241.486495011061	770
7	3092	294.262097148413	1142
8	2764.91666666667	269.304646124500	1123
9	2623.25	195.129385979476	687
10	2591.5	169.862243651089	659
11	2658.75	141.730297652715	456
12	2644.5	217.336981750377	638
13	2665.25	251.726086703927	892
14	2685.83333333333	156.676756606097	492
15	2564.91666666667	175.469478482122	699

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2847.5 & 223.558208812096 & 744 \tabularnewline
2 & 2905.91666666667 & 268.117158358171 & 1094 \tabularnewline
3 & 2811.66666666667 & 327.377550552967 & 898 \tabularnewline
4 & 2704.91666666667 & 253.131463628661 & 934 \tabularnewline
5 & 2797.58333333333 & 242.094443754849 & 796 \tabularnewline
6 & 2887.5 & 241.486495011061 & 770 \tabularnewline
7 & 3092 & 294.262097148413 & 1142 \tabularnewline
8 & 2764.91666666667 & 269.304646124500 & 1123 \tabularnewline
9 & 2623.25 & 195.129385979476 & 687 \tabularnewline
10 & 2591.5 & 169.862243651089 & 659 \tabularnewline
11 & 2658.75 & 141.730297652715 & 456 \tabularnewline
12 & 2644.5 & 217.336981750377 & 638 \tabularnewline
13 & 2665.25 & 251.726086703927 & 892 \tabularnewline
14 & 2685.83333333333 & 156.676756606097 & 492 \tabularnewline
15 & 2564.91666666667 & 175.469478482122 & 699 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105350&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]2847.5[/C][C]223.558208812096[/C][C]744[/C][/ROW]
[ROW][C]2[/C][C]2905.91666666667[/C][C]268.117158358171[/C][C]1094[/C][/ROW]
[ROW][C]3[/C][C]2811.66666666667[/C][C]327.377550552967[/C][C]898[/C][/ROW]
[ROW][C]4[/C][C]2704.91666666667[/C][C]253.131463628661[/C][C]934[/C][/ROW]
[ROW][C]5[/C][C]2797.58333333333[/C][C]242.094443754849[/C][C]796[/C][/ROW]
[ROW][C]6[/C][C]2887.5[/C][C]241.486495011061[/C][C]770[/C][/ROW]
[ROW][C]7[/C][C]3092[/C][C]294.262097148413[/C][C]1142[/C][/ROW]
[ROW][C]8[/C][C]2764.91666666667[/C][C]269.304646124500[/C][C]1123[/C][/ROW]
[ROW][C]9[/C][C]2623.25[/C][C]195.129385979476[/C][C]687[/C][/ROW]
[ROW][C]10[/C][C]2591.5[/C][C]169.862243651089[/C][C]659[/C][/ROW]
[ROW][C]11[/C][C]2658.75[/C][C]141.730297652715[/C][C]456[/C][/ROW]
[ROW][C]12[/C][C]2644.5[/C][C]217.336981750377[/C][C]638[/C][/ROW]
[ROW][C]13[/C][C]2665.25[/C][C]251.726086703927[/C][C]892[/C][/ROW]
[ROW][C]14[/C][C]2685.83333333333[/C][C]156.676756606097[/C][C]492[/C][/ROW]
[ROW][C]15[/C][C]2564.91666666667[/C][C]175.469478482122[/C][C]699[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105350&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105350&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	2847.5	223.558208812096	744
2	2905.91666666667	268.117158358171	1094
3	2811.66666666667	327.377550552967	898
4	2704.91666666667	253.131463628661	934
5	2797.58333333333	242.094443754849	796
6	2887.5	241.486495011061	770
7	3092	294.262097148413	1142
8	2764.91666666667	269.304646124500	1123
9	2623.25	195.129385979476	687
10	2591.5	169.862243651089	659
11	2658.75	141.730297652715	456
12	2644.5	217.336981750377	638
13	2665.25	251.726086703927	892
14	2685.83333333333	156.676756606097	492
15	2564.91666666667	175.469478482122	699

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-461.237215548352
beta	0.250832117719095
S.D.	0.0756687273327918
T-STAT	3.3148716327147
p-value	0.00558560766372271

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -461.237215548352 \tabularnewline
beta & 0.250832117719095 \tabularnewline
S.D. & 0.0756687273327918 \tabularnewline
T-STAT & 3.3148716327147 \tabularnewline
p-value & 0.00558560766372271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105350&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-461.237215548352[/C][/ROW]
[ROW][C]beta[/C][C]0.250832117719095[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0756687273327918[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.3148716327147[/C][/ROW]
[ROW][C]p-value[/C][C]0.00558560766372271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105350&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105350&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	-461.237215548352
beta	0.250832117719095
S.D.	0.0756687273327918
T-STAT	3.3148716327147
p-value	0.00558560766372271

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-19.8123725098232
beta	3.18481464552895
S.D.	0.977211738708195
T-STAT	3.25908349170984
p-value	0.00621856041871413
Lambda	-2.18481464552895

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -19.8123725098232 \tabularnewline
beta & 3.18481464552895 \tabularnewline
S.D. & 0.977211738708195 \tabularnewline
T-STAT & 3.25908349170984 \tabularnewline
p-value & 0.00621856041871413 \tabularnewline
Lambda & -2.18481464552895 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105350&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-19.8123725098232[/C][/ROW]
[ROW][C]beta[/C][C]3.18481464552895[/C][/ROW]
[ROW][C]S.D.[/C][C]0.977211738708195[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.25908349170984[/C][/ROW]
[ROW][C]p-value[/C][C]0.00621856041871413[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.18481464552895[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105350&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105350&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	-19.8123725098232
beta	3.18481464552895
S.D.	0.977211738708195
T-STAT	3.25908349170984
p-value	0.00621856041871413
Lambda	-2.18481464552895

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code