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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, 04 Dec 2009 07:16:27 -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/04/t12599362239vwmkdcclukyw63.htm/, Retrieved Sun, 28 Apr 2024 17:27:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63579, Retrieved Sun, 28 Apr 2024 17:27:40 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
-    D        [Standard Deviation-Mean Plot] [mean plot ] [2009-11-27 17:04:24] [ba905ddf7cdf9ecb063c35348c4dab2e]
-    D            [Standard Deviation-Mean Plot] [removing ] [2009-12-04 14:16:27] [244731fa3e7e6c85774b8c0902c58f85] [Current]

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Dataseries X:

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Histogram

Boxplots

5,4
5,4
5,6
5,7
5,8
5,8
5,8
5,9
6,1
6,4
6,4
6,3
6,2
6,2
6,3
6,4
6,5
6,6
6,6
6,6
6,8
7
7,2
7,3
7,5
7,6
7,6
7,7
7,7
7,7
7,7
7,6
7,7
7,9
7,9
7,9
7,8
7,6
7,4
7
7
7,2
7,5
7,8
7,8
7,7
7,6
7,5
7,5
7,5
7,5
7,6
7,9
7,6
7,5
7,5
7,6
7,7
7,9
7,9

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=63579&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=63579&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63579&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	5.88333333333333	0.351188458428425	1
2	6.64166666666667	0.367938565359474	1.1
3	7.70833333333333	0.131137217055151	0.4
4	7.49166666666667	0.290636709604442	0.8
5	7.64166666666667	0.167648622440092	0.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5.88333333333333 & 0.351188458428425 & 1 \tabularnewline
2 & 6.64166666666667 & 0.367938565359474 & 1.1 \tabularnewline
3 & 7.70833333333333 & 0.131137217055151 & 0.4 \tabularnewline
4 & 7.49166666666667 & 0.290636709604442 & 0.8 \tabularnewline
5 & 7.64166666666667 & 0.167648622440092 & 0.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63579&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]5.88333333333333[/C][C]0.351188458428425[/C][C]1[/C][/ROW]
[ROW][C]2[/C][C]6.64166666666667[/C][C]0.367938565359474[/C][C]1.1[/C][/ROW]
[ROW][C]3[/C][C]7.70833333333333[/C][C]0.131137217055151[/C][C]0.4[/C][/ROW]
[ROW][C]4[/C][C]7.49166666666667[/C][C]0.290636709604442[/C][C]0.8[/C][/ROW]
[ROW][C]5[/C][C]7.64166666666667[/C][C]0.167648622440092[/C][C]0.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63579&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63579&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	5.88333333333333	0.351188458428425	1
2	6.64166666666667	0.367938565359474	1.1
3	7.70833333333333	0.131137217055151	0.4
4	7.49166666666667	0.290636709604442	0.8
5	7.64166666666667	0.167648622440092	0.4

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.04317327711245
beta	-0.110480211479963
S.D.	0.0453759922604229
T-STAT	-2.43477235375685
p-value	0.0929328936862875

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.04317327711245 \tabularnewline
beta & -0.110480211479963 \tabularnewline
S.D. & 0.0453759922604229 \tabularnewline
T-STAT & -2.43477235375685 \tabularnewline
p-value & 0.0929328936862875 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63579&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.04317327711245[/C][/ROW]
[ROW][C]beta[/C][C]-0.110480211479963[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0453759922604229[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.43477235375685[/C][/ROW]
[ROW][C]p-value[/C][C]0.0929328936862875[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63579&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63579&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	1.04317327711245
beta	-0.110480211479963
S.D.	0.0453759922604229
T-STAT	-2.43477235375685
p-value	0.0929328936862875

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	4.51415286717719
beta	-3.04146783699437
S.D.	1.47339103468811
T-STAT	-2.06426384129465
p-value	0.130959600165074
Lambda	4.04146783699437

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 4.51415286717719 \tabularnewline
beta & -3.04146783699437 \tabularnewline
S.D. & 1.47339103468811 \tabularnewline
T-STAT & -2.06426384129465 \tabularnewline
p-value & 0.130959600165074 \tabularnewline
Lambda & 4.04146783699437 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63579&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.51415286717719[/C][/ROW]
[ROW][C]beta[/C][C]-3.04146783699437[/C][/ROW]
[ROW][C]S.D.[/C][C]1.47339103468811[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.06426384129465[/C][/ROW]
[ROW][C]p-value[/C][C]0.130959600165074[/C][/ROW]
[ROW][C]Lambda[/C][C]4.04146783699437[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63579&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63579&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	4.51415286717719
beta	-3.04146783699437
S.D.	1.47339103468811
T-STAT	-2.06426384129465
p-value	0.130959600165074
Lambda	4.04146783699437

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