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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, 27 Nov 2009 05:30:10 -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/Nov/27/t125932511766qkc4tw34170uu.htm/, Retrieved Sun, 28 Apr 2024 22:09:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60645, Retrieved Sun, 28 Apr 2024 22:09:19 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

132

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       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
- RMPD          [Standard Deviation-Mean Plot] [] [2009-11-27 12:30:10] [2f6049721194fa571920c3539d7b729e] [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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60645&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60645&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60645&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	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	15.5	1.29099444873581	3
2	14	1.82574185835055	4
3	12	1.41421356237310	3
4	14.75	0.957427107756338	2
5	14.75	1.25830573921179	3
6	14.5	1	2
7	15.5	1	2
8	14.75	0.5	1
9	13	0.816496580927726	2
10	9.75	1.70782512765993	4
11	8.75	1.5	3
12	7	2.58198889747161	6
13	6.25	1.89296944860009	4
14	8.5	2.08166599946613	5
15	10.25	1.5	3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 15.5 & 1.29099444873581 & 3 \tabularnewline
2 & 14 & 1.82574185835055 & 4 \tabularnewline
3 & 12 & 1.41421356237310 & 3 \tabularnewline
4 & 14.75 & 0.957427107756338 & 2 \tabularnewline
5 & 14.75 & 1.25830573921179 & 3 \tabularnewline
6 & 14.5 & 1 & 2 \tabularnewline
7 & 15.5 & 1 & 2 \tabularnewline
8 & 14.75 & 0.5 & 1 \tabularnewline
9 & 13 & 0.816496580927726 & 2 \tabularnewline
10 & 9.75 & 1.70782512765993 & 4 \tabularnewline
11 & 8.75 & 1.5 & 3 \tabularnewline
12 & 7 & 2.58198889747161 & 6 \tabularnewline
13 & 6.25 & 1.89296944860009 & 4 \tabularnewline
14 & 8.5 & 2.08166599946613 & 5 \tabularnewline
15 & 10.25 & 1.5 & 3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60645&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]15.5[/C][C]1.29099444873581[/C][C]3[/C][/ROW]
[ROW][C]2[/C][C]14[/C][C]1.82574185835055[/C][C]4[/C][/ROW]
[ROW][C]3[/C][C]12[/C][C]1.41421356237310[/C][C]3[/C][/ROW]
[ROW][C]4[/C][C]14.75[/C][C]0.957427107756338[/C][C]2[/C][/ROW]
[ROW][C]5[/C][C]14.75[/C][C]1.25830573921179[/C][C]3[/C][/ROW]
[ROW][C]6[/C][C]14.5[/C][C]1[/C][C]2[/C][/ROW]
[ROW][C]7[/C][C]15.5[/C][C]1[/C][C]2[/C][/ROW]
[ROW][C]8[/C][C]14.75[/C][C]0.5[/C][C]1[/C][/ROW]
[ROW][C]9[/C][C]13[/C][C]0.816496580927726[/C][C]2[/C][/ROW]
[ROW][C]10[/C][C]9.75[/C][C]1.70782512765993[/C][C]4[/C][/ROW]
[ROW][C]11[/C][C]8.75[/C][C]1.5[/C][C]3[/C][/ROW]
[ROW][C]12[/C][C]7[/C][C]2.58198889747161[/C][C]6[/C][/ROW]
[ROW][C]13[/C][C]6.25[/C][C]1.89296944860009[/C][C]4[/C][/ROW]
[ROW][C]14[/C][C]8.5[/C][C]2.08166599946613[/C][C]5[/C][/ROW]
[ROW][C]15[/C][C]10.25[/C][C]1.5[/C][C]3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60645&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60645&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	15.5	1.29099444873581	3
2	14	1.82574185835055	4
3	12	1.41421356237310	3
4	14.75	0.957427107756338	2
5	14.75	1.25830573921179	3
6	14.5	1	2
7	15.5	1	2
8	14.75	0.5	1
9	13	0.816496580927726	2
10	9.75	1.70782512765993	4
11	8.75	1.5	3
12	7	2.58198889747161	6
13	6.25	1.89296944860009	4
14	8.5	2.08166599946613	5
15	10.25	1.5	3

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	2.95425095575434
beta	-0.128235065917780
S.D.	0.0295061662418572
T-STAT	-4.34604295477285
p-value	0.000792771451933434

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.95425095575434 \tabularnewline
beta & -0.128235065917780 \tabularnewline
S.D. & 0.0295061662418572 \tabularnewline
T-STAT & -4.34604295477285 \tabularnewline
p-value & 0.000792771451933434 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60645&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.95425095575434[/C][/ROW]
[ROW][C]beta[/C][C]-0.128235065917780[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0295061662418572[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.34604295477285[/C][/ROW]
[ROW][C]p-value[/C][C]0.000792771451933434[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60645&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60645&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	2.95425095575434
beta	-0.128235065917780
S.D.	0.0295061662418572
T-STAT	-4.34604295477285
p-value	0.000792771451933434

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.65069351629168
beta	-0.9723958643905
S.D.	0.266936173189080
T-STAT	-3.64280289468943
p-value	0.0029779838786225
Lambda	1.9723958643905

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.65069351629168 \tabularnewline
beta & -0.9723958643905 \tabularnewline
S.D. & 0.266936173189080 \tabularnewline
T-STAT & -3.64280289468943 \tabularnewline
p-value & 0.0029779838786225 \tabularnewline
Lambda & 1.9723958643905 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60645&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.65069351629168[/C][/ROW]
[ROW][C]beta[/C][C]-0.9723958643905[/C][/ROW]
[ROW][C]S.D.[/C][C]0.266936173189080[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.64280289468943[/C][/ROW]
[ROW][C]p-value[/C][C]0.0029779838786225[/C][/ROW]
[ROW][C]Lambda[/C][C]1.9723958643905[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60645&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60645&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	2.65069351629168
beta	-0.9723958643905
S.D.	0.266936173189080
T-STAT	-3.64280289468943
p-value	0.0029779838786225
Lambda	1.9723958643905

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 ;

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