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Author's title

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Sun, 27 Apr 2014 10:14:41 -0400

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/2014/Apr/27/t1398608094dwc680mbhpowtc5.htm/, Retrieved Fri, 17 May 2024 04:19:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234617, Retrieved Fri, 17 May 2024 04:19:40 +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)

-       [Standard Deviation-Mean Plot] [] [2014-04-27 14:14:41] [45a206086251edfa7ba367c121fe1722] [Current]

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Dataseries X:

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Histogram

Boxplots

6
6.7
-0.6
5.8
16.4
1.5
5.1
14.7
4.3
1.5
9.1
4.3
5.7
13
14.5
9.7
-4.7
7.3
5.2
-2.5
11.5
4.9
-2.4
-0.3
4.4
7.9
-9.7
-4.1
16.4
-4.9
3.5
3.8
-0.2
3.1
0.7
-2.8
5.9
-5.3
-2.9
6.6
-8.1
1.3
6.9
-7.2
-1.9
4
-5.7
3.9
-7.6
-0.9
7.3
-3.7
-2.5
9.3
1.3
9.5
11.3
-1.7
8
-4.8
1.6
1.9
-0.9
5.5
1.7
-5.4
1.9
0.2
-13.3
-8.2
0.2
5.7
-1.2
-2.8
5.5
-17.3
1.4
-2.2
-8.6
-5
4.1
0.7
-4.2
-2.3

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' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234617&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234617&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234617&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' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	6.23333333333333	5.08104021800356	17
2	5.15833333333333	6.44775624586263	19.2
3	1.50833333333333	6.76225598898815	26.1
4	-0.208333333333333	5.62792684796636	15
5	2.125	6.56202920389168	18.9
6	-0.758333333333333	5.58153747690192	19
7	-2.65833333333333	6.03029598750921	22.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 6.23333333333333 & 5.08104021800356 & 17 \tabularnewline
2 & 5.15833333333333 & 6.44775624586263 & 19.2 \tabularnewline
3 & 1.50833333333333 & 6.76225598898815 & 26.1 \tabularnewline
4 & -0.208333333333333 & 5.62792684796636 & 15 \tabularnewline
5 & 2.125 & 6.56202920389168 & 18.9 \tabularnewline
6 & -0.758333333333333 & 5.58153747690192 & 19 \tabularnewline
7 & -2.65833333333333 & 6.03029598750921 & 22.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234617&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]6.23333333333333[/C][C]5.08104021800356[/C][C]17[/C][/ROW]
[ROW][C]2[/C][C]5.15833333333333[/C][C]6.44775624586263[/C][C]19.2[/C][/ROW]
[ROW][C]3[/C][C]1.50833333333333[/C][C]6.76225598898815[/C][C]26.1[/C][/ROW]
[ROW][C]4[/C][C]-0.208333333333333[/C][C]5.62792684796636[/C][C]15[/C][/ROW]
[ROW][C]5[/C][C]2.125[/C][C]6.56202920389168[/C][C]18.9[/C][/ROW]
[ROW][C]6[/C][C]-0.758333333333333[/C][C]5.58153747690192[/C][C]19[/C][/ROW]
[ROW][C]7[/C][C]-2.65833333333333[/C][C]6.03029598750921[/C][C]22.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234617&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234617&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	6.23333333333333	5.08104021800356	17
2	5.15833333333333	6.44775624586263	19.2
3	1.50833333333333	6.76225598898815	26.1
4	-0.208333333333333	5.62792684796636	15
5	2.125	6.56202920389168	18.9
6	-0.758333333333333	5.58153747690192	19
7	-2.65833333333333	6.03029598750921	22.8

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	6.03744626214575
beta	-0.0148492864821702
S.D.	0.085468083610703
T-STAT	-0.173740721153957
p-value	0.868884332241601

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 6.03744626214575 \tabularnewline
beta & -0.0148492864821702 \tabularnewline
S.D. & 0.085468083610703 \tabularnewline
T-STAT & -0.173740721153957 \tabularnewline
p-value & 0.868884332241601 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234617&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.03744626214575[/C][/ROW]
[ROW][C]beta[/C][C]-0.0148492864821702[/C][/ROW]
[ROW][C]S.D.[/C][C]0.085468083610703[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.173740721153957[/C][/ROW]
[ROW][C]p-value[/C][C]0.868884332241601[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234617&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234617&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	6.03744626214575
beta	-0.0148492864821702
S.D.	0.085468083610703
T-STAT	-0.173740721153957
p-value	0.868884332241601

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	1.98748022952558
beta	-0.144114943089645
S.D.	0.0897405729139731
T-STAT	-1.60590620730487
p-value	0.24952202775628
Lambda	1.14411494308965

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.98748022952558 \tabularnewline
beta & -0.144114943089645 \tabularnewline
S.D. & 0.0897405729139731 \tabularnewline
T-STAT & -1.60590620730487 \tabularnewline
p-value & 0.24952202775628 \tabularnewline
Lambda & 1.14411494308965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234617&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.98748022952558[/C][/ROW]
[ROW][C]beta[/C][C]-0.144114943089645[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0897405729139731[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.60590620730487[/C][/ROW]
[ROW][C]p-value[/C][C]0.24952202775628[/C][/ROW]
[ROW][C]Lambda[/C][C]1.14411494308965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234617&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234617&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	1.98748022952558
beta	-0.144114943089645
S.D.	0.0897405729139731
T-STAT	-1.60590620730487
p-value	0.24952202775628
Lambda	1.14411494308965

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