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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 14:46:12 -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/t1259358450x91z0hvxfvql9yf.htm/, Retrieved Sun, 28 Apr 2024 20:33:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61300, Retrieved Sun, 28 Apr 2024 20:33:57 +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       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
-    D          [Standard Deviation-Mean Plot] [WS8 Identifying I...] [2009-11-27 21:46:12] [c6e373ff11c42d4585d53e9e88ed5606] [Current]

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Dataseries X:

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Histogram

Boxplots

7.1
6.9
6.8
7.5
7.6
7.8
8.0
8.1
8.2
8.3
8.2
8.0
7.9
7.6
7.6
8.3
8.4
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.0
8.2
8.1
8.1
8.0
7.9
7.9
8.0
8.0
7.9
8.0
7.7
7.2
7.5
7.3
7.0
7.0
7.0
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8.0
8.0
7.7
7.3
7.4
8.1
8.3
8.2

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=61300&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=61300&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61300&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	7.70833333333333	0.528218848125615	1.5
2	8.3	0.41341152730553	1.3
3	8.35833333333333	0.68815739919048	2.1
4	8.46666666666667	0.267423169368608	0.799999999999999
5	8.075	0.181533868615599	0.6
6	7.25833333333333	0.336987545853858	1.2
7	7.18333333333333	0.68997145307658	1.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 7.70833333333333 & 0.528218848125615 & 1.5 \tabularnewline
2 & 8.3 & 0.41341152730553 & 1.3 \tabularnewline
3 & 8.35833333333333 & 0.68815739919048 & 2.1 \tabularnewline
4 & 8.46666666666667 & 0.267423169368608 & 0.799999999999999 \tabularnewline
5 & 8.075 & 0.181533868615599 & 0.6 \tabularnewline
6 & 7.25833333333333 & 0.336987545853858 & 1.2 \tabularnewline
7 & 7.18333333333333 & 0.68997145307658 & 1.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61300&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]7.70833333333333[/C][C]0.528218848125615[/C][C]1.5[/C][/ROW]
[ROW][C]2[/C][C]8.3[/C][C]0.41341152730553[/C][C]1.3[/C][/ROW]
[ROW][C]3[/C][C]8.35833333333333[/C][C]0.68815739919048[/C][C]2.1[/C][/ROW]
[ROW][C]4[/C][C]8.46666666666667[/C][C]0.267423169368608[/C][C]0.799999999999999[/C][/ROW]
[ROW][C]5[/C][C]8.075[/C][C]0.181533868615599[/C][C]0.6[/C][/ROW]
[ROW][C]6[/C][C]7.25833333333333[/C][C]0.336987545853858[/C][C]1.2[/C][/ROW]
[ROW][C]7[/C][C]7.18333333333333[/C][C]0.68997145307658[/C][C]1.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61300&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61300&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	7.70833333333333	0.528218848125615	1.5
2	8.3	0.41341152730553	1.3
3	8.35833333333333	0.68815739919048	2.1
4	8.46666666666667	0.267423169368608	0.799999999999999
5	8.075	0.181533868615599	0.6
6	7.25833333333333	0.336987545853858	1.2
7	7.18333333333333	0.68997145307658	1.9

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	1.24240493224281
beta	-0.101014105043602
S.D.	0.162574812447674
T-STAT	-0.621339206995023
p-value	0.561604064169746

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.24240493224281 \tabularnewline
beta & -0.101014105043602 \tabularnewline
S.D. & 0.162574812447674 \tabularnewline
T-STAT & -0.621339206995023 \tabularnewline
p-value & 0.561604064169746 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61300&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.24240493224281[/C][/ROW]
[ROW][C]beta[/C][C]-0.101014105043602[/C][/ROW]
[ROW][C]S.D.[/C][C]0.162574812447674[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.621339206995023[/C][/ROW]
[ROW][C]p-value[/C][C]0.561604064169746[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61300&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61300&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	1.24240493224281
beta	-0.101014105043602
S.D.	0.162574812447674
T-STAT	-0.621339206995023
p-value	0.561604064169746

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	3.34424224876176
beta	-2.06000840889206
S.D.	3.14179480307168
T-STAT	-0.655678851743605
p-value	0.540996626527415
Lambda	3.06000840889206

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.34424224876176 \tabularnewline
beta & -2.06000840889206 \tabularnewline
S.D. & 3.14179480307168 \tabularnewline
T-STAT & -0.655678851743605 \tabularnewline
p-value & 0.540996626527415 \tabularnewline
Lambda & 3.06000840889206 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61300&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.34424224876176[/C][/ROW]
[ROW][C]beta[/C][C]-2.06000840889206[/C][/ROW]
[ROW][C]S.D.[/C][C]3.14179480307168[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.655678851743605[/C][/ROW]
[ROW][C]p-value[/C][C]0.540996626527415[/C][/ROW]
[ROW][C]Lambda[/C][C]3.06000840889206[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61300&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61300&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	3.34424224876176
beta	-2.06000840889206
S.D.	3.14179480307168
T-STAT	-0.655678851743605
p-value	0.540996626527415
Lambda	3.06000840889206

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