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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

Mon, 14 Dec 2009 01:42:56 -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/14/t1260780267haf7pw1efmei0n2.htm/, Retrieved Sun, 05 May 2024 14:10:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67438, Retrieved Sun, 05 May 2024 14:10:38 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

164

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]
-   PD        [Standard Deviation-Mean Plot] [smp] [2009-11-26 18:37:16] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   PD          [Standard Deviation-Mean Plot] [smp lambda] [2009-12-12 16:32:15] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D              [Standard Deviation-Mean Plot] [lambda] [2009-12-14 08:42:56] [307139c5e328127f586f26d5bcc435d8] [Current]

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Dataseries X:

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Histogram

Boxplots

2.7
2.5
2.2
2.9
3.1
3
2.8
2.5
1.9
1.9
1.8
2
2.6
2.5
2.5
1.6
1.4
0.8
1.1
1.3
1.2
1.3
1.1
1.3
1.2
1.6
1.7
1.5
0.9
1.5
1.4
1.6
1.7
1.4
1.8
1.7
1.4
1.2
1
1.7
2.4
2
2.1
2
1.8
2.7
2.3
1.9
2
2.3
2.8
2.4
2.3
2.7
2.7
2.9
3
2.2
2.3
2.8
2.8

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=67438&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=67438&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67438&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	2.44166666666667	0.467990546395065	1.3
2	1.55833333333333	0.618588324454572	1.8
3	1.5	0.252262489554756	0.9
4	1.875	0.495663008688179	1.7
5	2.53333333333333	0.320037876546265	1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2.44166666666667 & 0.467990546395065 & 1.3 \tabularnewline
2 & 1.55833333333333 & 0.618588324454572 & 1.8 \tabularnewline
3 & 1.5 & 0.252262489554756 & 0.9 \tabularnewline
4 & 1.875 & 0.495663008688179 & 1.7 \tabularnewline
5 & 2.53333333333333 & 0.320037876546265 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67438&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]2.44166666666667[/C][C]0.467990546395065[/C][C]1.3[/C][/ROW]
[ROW][C]2[/C][C]1.55833333333333[/C][C]0.618588324454572[/C][C]1.8[/C][/ROW]
[ROW][C]3[/C][C]1.5[/C][C]0.252262489554756[/C][C]0.9[/C][/ROW]
[ROW][C]4[/C][C]1.875[/C][C]0.495663008688179[/C][C]1.7[/C][/ROW]
[ROW][C]5[/C][C]2.53333333333333[/C][C]0.320037876546265[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67438&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67438&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	2.44166666666667	0.467990546395065	1.3
2	1.55833333333333	0.618588324454572	1.8
3	1.5	0.252262489554756	0.9
4	1.875	0.495663008688179	1.7
5	2.53333333333333	0.320037876546265	1

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.524691887801804
beta	-0.0473255367572932
S.D.	0.171586921896146
T-STAT	-0.275810861540702
p-value	0.800601076745577

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.524691887801804 \tabularnewline
beta & -0.0473255367572932 \tabularnewline
S.D. & 0.171586921896146 \tabularnewline
T-STAT & -0.275810861540702 \tabularnewline
p-value & 0.800601076745577 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67438&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.524691887801804[/C][/ROW]
[ROW][C]beta[/C][C]-0.0473255367572932[/C][/ROW]
[ROW][C]S.D.[/C][C]0.171586921896146[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.275810861540702[/C][/ROW]
[ROW][C]p-value[/C][C]0.800601076745577[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67438&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67438&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	0.524691887801804
beta	-0.0473255367572932
S.D.	0.171586921896146
T-STAT	-0.275810861540702
p-value	0.800601076745577

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.871452365679
beta	-0.0305525789586005
S.D.	0.850671951365779
T-STAT	-0.0359158179713666
p-value	0.973605660967624
Lambda	1.0305525789586

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.871452365679 \tabularnewline
beta & -0.0305525789586005 \tabularnewline
S.D. & 0.850671951365779 \tabularnewline
T-STAT & -0.0359158179713666 \tabularnewline
p-value & 0.973605660967624 \tabularnewline
Lambda & 1.0305525789586 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67438&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.871452365679[/C][/ROW]
[ROW][C]beta[/C][C]-0.0305525789586005[/C][/ROW]
[ROW][C]S.D.[/C][C]0.850671951365779[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0359158179713666[/C][/ROW]
[ROW][C]p-value[/C][C]0.973605660967624[/C][/ROW]
[ROW][C]Lambda[/C][C]1.0305525789586[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67438&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67438&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	-0.871452365679
beta	-0.0305525789586005
S.D.	0.850671951365779
T-STAT	-0.0359158179713666
p-value	0.973605660967624
Lambda	1.0305525789586

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