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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, 18 Dec 2009 06:56:42 -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/2009/Dec/18/t126114463644cvk03o40dkynt.htm/, Retrieved Sat, 27 Apr 2024 12:59:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69334, Retrieved Sat, 27 Apr 2024 12:59:02 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

104

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [] [2009-11-27 14:40:44] [b98453cac15ba1066b407e146608df68]
-   PD    [Standard Deviation-Mean Plot] [] [2009-12-04 14:55:35] [ac45432a6622e5ac7affd14a540160b0]
-             [Standard Deviation-Mean Plot] [] [2009-12-18 13:56:42] [612b7913d2a3b4fa79d126829bd148db] [Current]

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Dataseries X:

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Histogram

Boxplots

8
8.1
7.7
7.5
7.6
7.8
7.8
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.2
7.9
7.3
6.9
6.6
6.7
6.9
7
7.1
7.2
7.1
6.9
7
6.8
6.4
6.7
6.6
6.4
6.3
6.2
6.5
6.8
6.8
6.4
6.1
5.8
6.1
7.2
7.3
6.9
6.1
5.8
6.2
7.1
7.7
7.9
7.7
7.4
7.5
8
8.1

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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69334&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69334&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69334&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	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	7.825	0.275378527364305	0.6
2	7.75	0.1	0.2
3	7.4	0.2	0.4
4	7.625	0.095742710775634	0.2
5	8.1	0.141421356237309	0.299999999999999
6	7.575	0.585234995535981	1.3
7	6.8	0.182574185835056	0.4
8	7.075	0.125830573921179	0.3
9	6.725	0.25	0.6
10	6.375	0.170782512765993	0.399999999999999
11	6.625	0.206155281280883	0.399999999999999
12	6.3	0.616441400296898	1.4
13	6.525	0.69462219947249	1.5
14	7.225	0.763216876123687	1.7
15	7.65	0.264575131106459	0.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 7.825 & 0.275378527364305 & 0.6 \tabularnewline
2 & 7.75 & 0.1 & 0.2 \tabularnewline
3 & 7.4 & 0.2 & 0.4 \tabularnewline
4 & 7.625 & 0.095742710775634 & 0.2 \tabularnewline
5 & 8.1 & 0.141421356237309 & 0.299999999999999 \tabularnewline
6 & 7.575 & 0.585234995535981 & 1.3 \tabularnewline
7 & 6.8 & 0.182574185835056 & 0.4 \tabularnewline
8 & 7.075 & 0.125830573921179 & 0.3 \tabularnewline
9 & 6.725 & 0.25 & 0.6 \tabularnewline
10 & 6.375 & 0.170782512765993 & 0.399999999999999 \tabularnewline
11 & 6.625 & 0.206155281280883 & 0.399999999999999 \tabularnewline
12 & 6.3 & 0.616441400296898 & 1.4 \tabularnewline
13 & 6.525 & 0.69462219947249 & 1.5 \tabularnewline
14 & 7.225 & 0.763216876123687 & 1.7 \tabularnewline
15 & 7.65 & 0.264575131106459 & 0.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69334&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]7.825[/C][C]0.275378527364305[/C][C]0.6[/C][/ROW]
[ROW][C]2[/C][C]7.75[/C][C]0.1[/C][C]0.2[/C][/ROW]
[ROW][C]3[/C][C]7.4[/C][C]0.2[/C][C]0.4[/C][/ROW]
[ROW][C]4[/C][C]7.625[/C][C]0.095742710775634[/C][C]0.2[/C][/ROW]
[ROW][C]5[/C][C]8.1[/C][C]0.141421356237309[/C][C]0.299999999999999[/C][/ROW]
[ROW][C]6[/C][C]7.575[/C][C]0.585234995535981[/C][C]1.3[/C][/ROW]
[ROW][C]7[/C][C]6.8[/C][C]0.182574185835056[/C][C]0.4[/C][/ROW]
[ROW][C]8[/C][C]7.075[/C][C]0.125830573921179[/C][C]0.3[/C][/ROW]
[ROW][C]9[/C][C]6.725[/C][C]0.25[/C][C]0.6[/C][/ROW]
[ROW][C]10[/C][C]6.375[/C][C]0.170782512765993[/C][C]0.399999999999999[/C][/ROW]
[ROW][C]11[/C][C]6.625[/C][C]0.206155281280883[/C][C]0.399999999999999[/C][/ROW]
[ROW][C]12[/C][C]6.3[/C][C]0.616441400296898[/C][C]1.4[/C][/ROW]
[ROW][C]13[/C][C]6.525[/C][C]0.69462219947249[/C][C]1.5[/C][/ROW]
[ROW][C]14[/C][C]7.225[/C][C]0.763216876123687[/C][C]1.7[/C][/ROW]
[ROW][C]15[/C][C]7.65[/C][C]0.264575131106459[/C][C]0.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69334&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69334&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	7.825	0.275378527364305	0.6
2	7.75	0.1	0.2
3	7.4	0.2	0.4
4	7.625	0.095742710775634	0.2
5	8.1	0.141421356237309	0.299999999999999
6	7.575	0.585234995535981	1.3
7	6.8	0.182574185835056	0.4
8	7.075	0.125830573921179	0.3
9	6.725	0.25	0.6
10	6.375	0.170782512765993	0.399999999999999
11	6.625	0.206155281280883	0.399999999999999
12	6.3	0.616441400296898	1.4
13	6.525	0.69462219947249	1.5
14	7.225	0.763216876123687	1.7
15	7.65	0.264575131106459	0.6

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.16831398361614
beta	-0.119476960293063
S.D.	0.104586318062130
T-STAT	-1.14237657952627
p-value	0.273901751921961

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.16831398361614 \tabularnewline
beta & -0.119476960293063 \tabularnewline
S.D. & 0.104586318062130 \tabularnewline
T-STAT & -1.14237657952627 \tabularnewline
p-value & 0.273901751921961 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69334&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.16831398361614[/C][/ROW]
[ROW][C]beta[/C][C]-0.119476960293063[/C][/ROW]
[ROW][C]S.D.[/C][C]0.104586318062130[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.14237657952627[/C][/ROW]
[ROW][C]p-value[/C][C]0.273901751921961[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69334&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69334&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	1.16831398361614
beta	-0.119476960293063
S.D.	0.104586318062130
T-STAT	-1.14237657952627
p-value	0.273901751921961

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.23696911533956
beta	-2.86549347428927
S.D.	2.21696041278523
T-STAT	-1.29253254039357
p-value	0.218674623910829
Lambda	3.86549347428927

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.23696911533956 \tabularnewline
beta & -2.86549347428927 \tabularnewline
S.D. & 2.21696041278523 \tabularnewline
T-STAT & -1.29253254039357 \tabularnewline
p-value & 0.218674623910829 \tabularnewline
Lambda & 3.86549347428927 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69334&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.23696911533956[/C][/ROW]
[ROW][C]beta[/C][C]-2.86549347428927[/C][/ROW]
[ROW][C]S.D.[/C][C]2.21696041278523[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.29253254039357[/C][/ROW]
[ROW][C]p-value[/C][C]0.218674623910829[/C][/ROW]
[ROW][C]Lambda[/C][C]3.86549347428927[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69334&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69334&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	4.23696911533956
beta	-2.86549347428927
S.D.	2.21696041278523
T-STAT	-1.29253254039357
p-value	0.218674623910829
Lambda	3.86549347428927

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 4 ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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