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Free Statistics

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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

Mon, 29 Apr 2013 04:47:56 -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/Apr/29/t1367225342web9tlr9p0aa8vz.htm/, Retrieved Fri, 03 May 2024 04:23:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208485, Retrieved Fri, 03 May 2024 04:23:47 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

101

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

-       [Standard Deviation-Mean Plot] [standaarddeviatie...] [2013-04-29 08:47:56] [2ad6cfb061f4abd47c32d0a7b72d8383] [Current]

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Dataseries X:

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Histogram

Boxplots

4.69
4.69
4.69
4.69
4.69
4.69
4.69
4.73
4.78
4.79
4.79
4.8
4.8
4.81
5.16
5.26
5.29
5.29
5.29
5.3
5.3
5.3
5.3
5.3
5.3
5.3
5.3
5.35
5.44
5.47
5.47
5.48
5.48
5.48
5.48
5.48
5.48
5.48
5.5
5.55
5.57
5.58
5.58
5.58
5.59
5.59
5.59
5.55
5.61
5.61
5.61
5.63
5.69
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.7
5.71
5.74
5.77
5.79
5.79
5.8
5.8
5.8
5.8

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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208485&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208485&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208485&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	4.72666666666667	0.0483045891539646	0.109999999999999
2	5.2	0.188679622641132	0.5
3	5.41916666666667	0.0806178790606802	0.180000000000001
4	5.55333333333333	0.0427111510526515	0.109999999999999
5	5.67083333333333	0.0416606056197706	0.0899999999999999
6	5.75833333333333	0.044687466889159	0.0999999999999996

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4.72666666666667 & 0.0483045891539646 & 0.109999999999999 \tabularnewline
2 & 5.2 & 0.188679622641132 & 0.5 \tabularnewline
3 & 5.41916666666667 & 0.0806178790606802 & 0.180000000000001 \tabularnewline
4 & 5.55333333333333 & 0.0427111510526515 & 0.109999999999999 \tabularnewline
5 & 5.67083333333333 & 0.0416606056197706 & 0.0899999999999999 \tabularnewline
6 & 5.75833333333333 & 0.044687466889159 & 0.0999999999999996 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208485&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]4.72666666666667[/C][C]0.0483045891539646[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]2[/C][C]5.2[/C][C]0.188679622641132[/C][C]0.5[/C][/ROW]
[ROW][C]3[/C][C]5.41916666666667[/C][C]0.0806178790606802[/C][C]0.180000000000001[/C][/ROW]
[ROW][C]4[/C][C]5.55333333333333[/C][C]0.0427111510526515[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]5[/C][C]5.67083333333333[/C][C]0.0416606056197706[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]6[/C][C]5.75833333333333[/C][C]0.044687466889159[/C][C]0.0999999999999996[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208485&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208485&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	4.72666666666667	0.0483045891539646	0.109999999999999
2	5.2	0.188679622641132	0.5
3	5.41916666666667	0.0806178790606802	0.180000000000001
4	5.55333333333333	0.0427111510526515	0.109999999999999
5	5.67083333333333	0.0416606056197706	0.0899999999999999
6	5.75833333333333	0.044687466889159	0.0999999999999996

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.296038691666199
beta	-0.0411271073541219
S.D.	0.0735119401682599
T-STAT	-0.55946159576236
p-value	0.605690622337855

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.296038691666199 \tabularnewline
beta & -0.0411271073541219 \tabularnewline
S.D. & 0.0735119401682599 \tabularnewline
T-STAT & -0.55946159576236 \tabularnewline
p-value & 0.605690622337855 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208485&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.296038691666199[/C][/ROW]
[ROW][C]beta[/C][C]-0.0411271073541219[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0735119401682599[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.55946159576236[/C][/ROW]
[ROW][C]p-value[/C][C]0.605690622337855[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208485&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208485&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	0.296038691666199
beta	-0.0411271073541219
S.D.	0.0735119401682599
T-STAT	-0.55946159576236
p-value	0.605690622337855

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	0.964729505265585
beta	-2.22388523198388
S.D.	3.94758118894009
T-STAT	-0.563353893319414
p-value	0.603275605473816
Lambda	3.22388523198388

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.964729505265585 \tabularnewline
beta & -2.22388523198388 \tabularnewline
S.D. & 3.94758118894009 \tabularnewline
T-STAT & -0.563353893319414 \tabularnewline
p-value & 0.603275605473816 \tabularnewline
Lambda & 3.22388523198388 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208485&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.964729505265585[/C][/ROW]
[ROW][C]beta[/C][C]-2.22388523198388[/C][/ROW]
[ROW][C]S.D.[/C][C]3.94758118894009[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.563353893319414[/C][/ROW]
[ROW][C]p-value[/C][C]0.603275605473816[/C][/ROW]
[ROW][C]Lambda[/C][C]3.22388523198388[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208485&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208485&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	0.964729505265585
beta	-2.22388523198388
S.D.	3.94758118894009
T-STAT	-0.563353893319414
p-value	0.603275605473816
Lambda	3.22388523198388

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