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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

Tue, 21 May 2013 13:08:20 -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/2013/May/21/t1369156110pepsqs5vba1qfbq.htm/, Retrieved Thu, 02 May 2024 04:36:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=209258, Retrieved Thu, 02 May 2024 04:36:40 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Standard Deviation-Mean Plot] [] [2013-05-21 17:08:20] [138d0669d5f70cc84d77479d15dc4661] [Current]

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Histogram

Boxplots

7.72
7.67
7.84
7.79
7.83
7.94
8.02
8.06
8.12
8.13
7.97
8.01
8
7.9
7.99
8.02
8.08
8.02
8.07
8.11
8.19
8.16
8.08
8.22
8.15
8.19
8.31
8.3
8.34
8.31
8.38
8.34
8.44
8.64
8.6
8.61
8.54
8.69
8.73
8.91
9.01
9.08
8.94
9.03
9.02
8.96
9.03
8.94
8.95
8.95
8.99
8.93
8.98
8.95
9.02
8.92
9.1
9.06
8.97
8.89
8.99
8.79
8.83
8.61
8.71
8.91
8.91
8.89
8.98
9
8.99
8.88

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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209258&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209258&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209258&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	'Gertrude Mary Cox' @ cox.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	7.925	0.153237783140511	0.460000000000001
2	8.07	0.0914529188360676	0.32
3	8.38416666666667	0.159741742329374	0.49
4	8.90666666666667	0.165602664302971	0.540000000000001
5	8.97583333333333	0.0597659576763369	0.209999999999999
6	8.87416666666667	0.121539992171177	0.390000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 7.925 & 0.153237783140511 & 0.460000000000001 \tabularnewline
2 & 8.07 & 0.0914529188360676 & 0.32 \tabularnewline
3 & 8.38416666666667 & 0.159741742329374 & 0.49 \tabularnewline
4 & 8.90666666666667 & 0.165602664302971 & 0.540000000000001 \tabularnewline
5 & 8.97583333333333 & 0.0597659576763369 & 0.209999999999999 \tabularnewline
6 & 8.87416666666667 & 0.121539992171177 & 0.390000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209258&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]7.925[/C][C]0.153237783140511[/C][C]0.460000000000001[/C][/ROW]
[ROW][C]2[/C][C]8.07[/C][C]0.0914529188360676[/C][C]0.32[/C][/ROW]
[ROW][C]3[/C][C]8.38416666666667[/C][C]0.159741742329374[/C][C]0.49[/C][/ROW]
[ROW][C]4[/C][C]8.90666666666667[/C][C]0.165602664302971[/C][C]0.540000000000001[/C][/ROW]
[ROW][C]5[/C][C]8.97583333333333[/C][C]0.0597659576763369[/C][C]0.209999999999999[/C][/ROW]
[ROW][C]6[/C][C]8.87416666666667[/C][C]0.121539992171177[/C][C]0.390000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209258&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209258&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	7.925	0.153237783140511	0.460000000000001
2	8.07	0.0914529188360676	0.32
3	8.38416666666667	0.159741742329374	0.49
4	8.90666666666667	0.165602664302971	0.540000000000001
5	8.97583333333333	0.0597659576763369	0.209999999999999
6	8.87416666666667	0.121539992171177	0.390000000000001

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.299997239613636
beta	-0.0205069969700056
S.D.	0.0450882605678945
T-STAT	-0.454818986399484
p-value	0.672830040478149

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.299997239613636 \tabularnewline
beta & -0.0205069969700056 \tabularnewline
S.D. & 0.0450882605678945 \tabularnewline
T-STAT & -0.454818986399484 \tabularnewline
p-value & 0.672830040478149 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209258&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.299997239613636[/C][/ROW]
[ROW][C]beta[/C][C]-0.0205069969700056[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0450882605678945[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.454818986399484[/C][/ROW]
[ROW][C]p-value[/C][C]0.672830040478149[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209258&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209258&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	0.299997239613636
beta	-0.0205069969700056
S.D.	0.0450882605678945
T-STAT	-0.454818986399484
p-value	0.672830040478149

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.08732956164269
beta	-1.97282764719651
S.D.	3.55154463281926
T-STAT	-0.555484402185437
p-value	0.608164619114767
Lambda	2.97282764719651

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.08732956164269 \tabularnewline
beta & -1.97282764719651 \tabularnewline
S.D. & 3.55154463281926 \tabularnewline
T-STAT & -0.555484402185437 \tabularnewline
p-value & 0.608164619114767 \tabularnewline
Lambda & 2.97282764719651 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209258&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.08732956164269[/C][/ROW]
[ROW][C]beta[/C][C]-1.97282764719651[/C][/ROW]
[ROW][C]S.D.[/C][C]3.55154463281926[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.555484402185437[/C][/ROW]
[ROW][C]p-value[/C][C]0.608164619114767[/C][/ROW]
[ROW][C]Lambda[/C][C]2.97282764719651[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209258&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209258&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	2.08732956164269
beta	-1.97282764719651
S.D.	3.55154463281926
T-STAT	-0.555484402185437
p-value	0.608164619114767
Lambda	2.97282764719651

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