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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

Wed, 23 Oct 2013 09:58:44 -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/Oct/23/t13825367453hfjawuef6az981.htm/, Retrieved Sat, 27 Apr 2024 20:02:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=218953, Retrieved Sat, 27 Apr 2024 20:02:29 +0000

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Original text written by user:

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No (this computation is public)

User-defined keywords

Estimated Impact

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

-     [Maximum-likelihood Fitting - Normal Distribution] [Intrinsic Motivat...] [2010-10-12 11:57:21] [b98453cac15ba1066b407e146608df68]
- RMPD    [Standard Deviation-Mean Plot] [] [2013-10-23 13:58:44] [1ec45202e9eb14af6f043d0f580e703c] [Current]

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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=218953&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=218953&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=218953&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	19.8333333333333	3.63901418552116	12
2	19.3333333333333	4.75458311590623	16
3	21	4.84298930976989	17
4	21.5	4.50252454437811	16
5	20	4.80530010414637	13
6	21	2.66287609379578	9
7	21.4166666666667	4.05548636996473	13
8	20.5833333333333	5.24765459875922	22
9	20.9166666666667	2.46644143115812	9
10	20.3333333333333	5.4993112516409	17
11	20.5833333333333	4.42016728053122	14
12	20.1666666666667	5.0602431370499	15
13	20.6666666666667	2.57022578892606	9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 19.8333333333333 & 3.63901418552116 & 12 \tabularnewline
2 & 19.3333333333333 & 4.75458311590623 & 16 \tabularnewline
3 & 21 & 4.84298930976989 & 17 \tabularnewline
4 & 21.5 & 4.50252454437811 & 16 \tabularnewline
5 & 20 & 4.80530010414637 & 13 \tabularnewline
6 & 21 & 2.66287609379578 & 9 \tabularnewline
7 & 21.4166666666667 & 4.05548636996473 & 13 \tabularnewline
8 & 20.5833333333333 & 5.24765459875922 & 22 \tabularnewline
9 & 20.9166666666667 & 2.46644143115812 & 9 \tabularnewline
10 & 20.3333333333333 & 5.4993112516409 & 17 \tabularnewline
11 & 20.5833333333333 & 4.42016728053122 & 14 \tabularnewline
12 & 20.1666666666667 & 5.0602431370499 & 15 \tabularnewline
13 & 20.6666666666667 & 2.57022578892606 & 9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=218953&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]19.8333333333333[/C][C]3.63901418552116[/C][C]12[/C][/ROW]
[ROW][C]2[/C][C]19.3333333333333[/C][C]4.75458311590623[/C][C]16[/C][/ROW]
[ROW][C]3[/C][C]21[/C][C]4.84298930976989[/C][C]17[/C][/ROW]
[ROW][C]4[/C][C]21.5[/C][C]4.50252454437811[/C][C]16[/C][/ROW]
[ROW][C]5[/C][C]20[/C][C]4.80530010414637[/C][C]13[/C][/ROW]
[ROW][C]6[/C][C]21[/C][C]2.66287609379578[/C][C]9[/C][/ROW]
[ROW][C]7[/C][C]21.4166666666667[/C][C]4.05548636996473[/C][C]13[/C][/ROW]
[ROW][C]8[/C][C]20.5833333333333[/C][C]5.24765459875922[/C][C]22[/C][/ROW]
[ROW][C]9[/C][C]20.9166666666667[/C][C]2.46644143115812[/C][C]9[/C][/ROW]
[ROW][C]10[/C][C]20.3333333333333[/C][C]5.4993112516409[/C][C]17[/C][/ROW]
[ROW][C]11[/C][C]20.5833333333333[/C][C]4.42016728053122[/C][C]14[/C][/ROW]
[ROW][C]12[/C][C]20.1666666666667[/C][C]5.0602431370499[/C][C]15[/C][/ROW]
[ROW][C]13[/C][C]20.6666666666667[/C][C]2.57022578892606[/C][C]9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=218953&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=218953&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	19.8333333333333	3.63901418552116	12
2	19.3333333333333	4.75458311590623	16
3	21	4.84298930976989	17
4	21.5	4.50252454437811	16
5	20	4.80530010414637	13
6	21	2.66287609379578	9
7	21.4166666666667	4.05548636996473	13
8	20.5833333333333	5.24765459875922	22
9	20.9166666666667	2.46644143115812	9
10	20.3333333333333	5.4993112516409	17
11	20.5833333333333	4.42016728053122	14
12	20.1666666666667	5.0602431370499	15
13	20.6666666666667	2.57022578892606	9

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	14.0004664039862
beta	-0.476855035063366
S.D.	0.48284524839424
T-STAT	-0.987593927141677
p-value	0.344577313010773

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 14.0004664039862 \tabularnewline
beta & -0.476855035063366 \tabularnewline
S.D. & 0.48284524839424 \tabularnewline
T-STAT & -0.987593927141677 \tabularnewline
p-value & 0.344577313010773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=218953&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]14.0004664039862[/C][/ROW]
[ROW][C]beta[/C][C]-0.476855035063366[/C][/ROW]
[ROW][C]S.D.[/C][C]0.48284524839424[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.987593927141677[/C][/ROW]
[ROW][C]p-value[/C][C]0.344577313010773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=218953&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=218953&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	14.0004664039862
beta	-0.476855035063366
S.D.	0.48284524839424
T-STAT	-0.987593927141677
p-value	0.344577313010773

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	9.27005962429239
beta	-2.60331983165993
S.D.	2.66977923813659
T-STAT	-0.975106778295632
p-value	0.350463740131074
Lambda	3.60331983165993

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 9.27005962429239 \tabularnewline
beta & -2.60331983165993 \tabularnewline
S.D. & 2.66977923813659 \tabularnewline
T-STAT & -0.975106778295632 \tabularnewline
p-value & 0.350463740131074 \tabularnewline
Lambda & 3.60331983165993 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=218953&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.27005962429239[/C][/ROW]
[ROW][C]beta[/C][C]-2.60331983165993[/C][/ROW]
[ROW][C]S.D.[/C][C]2.66977923813659[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.975106778295632[/C][/ROW]
[ROW][C]p-value[/C][C]0.350463740131074[/C][/ROW]
[ROW][C]Lambda[/C][C]3.60331983165993[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=218953&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=218953&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	9.27005962429239
beta	-2.60331983165993
S.D.	2.66977923813659
T-STAT	-0.975106778295632
p-value	0.350463740131074
Lambda	3.60331983165993

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code