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*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Wed, 07 Dec 2011 14:31:01 -0500

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/2011/Dec/07/t1323286335ys3g04eefuei9u5.htm/, Retrieved Fri, 03 May 2024 01:06:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152640, Retrieved Fri, 03 May 2024 01:06:56 +0000

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No (this computation is public)

User-defined keywords

KDGP2W83

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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] [] [2011-12-07 19:31:01] [df3d6db53fdf346bf57a43ea3fa80561] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152640&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152640&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152640&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	'Gertrude Mary Cox' @ cox.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	14.795	0.131782649338471	0.279999999999999
2	15.0325	0.0170782512765996	0.0400000000000009
3	15.1575	0.0861684396980706	0.17
4	15.37	0.113431330181157	0.27
5	15.66	0.0535412613473637	0.130000000000001
6	15.775	0.0191485421551264	0.0399999999999991
7	16.615	0.0842614977317648	0.180000000000003
8	16.7525	0.0150000000000006	0.0300000000000011
9	16.79	0.0216024689946919	0.0499999999999972
10	17.065	0.124498995979887	0.289999999999999
11	17.2675	0.0236290781312634	0.0500000000000007
12	17.3375	0.0221735578260842	0.0500000000000007
13	17.485	0.0953939201416938	0.199999999999999
14	17.66	0.0316227766016839	0.0700000000000003
15	17.865	0.0591607978309954	0.129999999999999
16	18.015	0.0768114574786855	0.149999999999999
17	18.1075	0.0206155281280882	0.0399999999999991
18	18.1775	0.0221735578260838	0.0500000000000007
19	18.39	0.127279220613578	0.27
20	18.5075	0.0221735578260836	0.0500000000000007
21	18.6725	0.0457347424467068	0.0999999999999979

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14.795 & 0.131782649338471 & 0.279999999999999 \tabularnewline
2 & 15.0325 & 0.0170782512765996 & 0.0400000000000009 \tabularnewline
3 & 15.1575 & 0.0861684396980706 & 0.17 \tabularnewline
4 & 15.37 & 0.113431330181157 & 0.27 \tabularnewline
5 & 15.66 & 0.0535412613473637 & 0.130000000000001 \tabularnewline
6 & 15.775 & 0.0191485421551264 & 0.0399999999999991 \tabularnewline
7 & 16.615 & 0.0842614977317648 & 0.180000000000003 \tabularnewline
8 & 16.7525 & 0.0150000000000006 & 0.0300000000000011 \tabularnewline
9 & 16.79 & 0.0216024689946919 & 0.0499999999999972 \tabularnewline
10 & 17.065 & 0.124498995979887 & 0.289999999999999 \tabularnewline
11 & 17.2675 & 0.0236290781312634 & 0.0500000000000007 \tabularnewline
12 & 17.3375 & 0.0221735578260842 & 0.0500000000000007 \tabularnewline
13 & 17.485 & 0.0953939201416938 & 0.199999999999999 \tabularnewline
14 & 17.66 & 0.0316227766016839 & 0.0700000000000003 \tabularnewline
15 & 17.865 & 0.0591607978309954 & 0.129999999999999 \tabularnewline
16 & 18.015 & 0.0768114574786855 & 0.149999999999999 \tabularnewline
17 & 18.1075 & 0.0206155281280882 & 0.0399999999999991 \tabularnewline
18 & 18.1775 & 0.0221735578260838 & 0.0500000000000007 \tabularnewline
19 & 18.39 & 0.127279220613578 & 0.27 \tabularnewline
20 & 18.5075 & 0.0221735578260836 & 0.0500000000000007 \tabularnewline
21 & 18.6725 & 0.0457347424467068 & 0.0999999999999979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152640&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]14.795[/C][C]0.131782649338471[/C][C]0.279999999999999[/C][/ROW]
[ROW][C]2[/C][C]15.0325[/C][C]0.0170782512765996[/C][C]0.0400000000000009[/C][/ROW]
[ROW][C]3[/C][C]15.1575[/C][C]0.0861684396980706[/C][C]0.17[/C][/ROW]
[ROW][C]4[/C][C]15.37[/C][C]0.113431330181157[/C][C]0.27[/C][/ROW]
[ROW][C]5[/C][C]15.66[/C][C]0.0535412613473637[/C][C]0.130000000000001[/C][/ROW]
[ROW][C]6[/C][C]15.775[/C][C]0.0191485421551264[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]7[/C][C]16.615[/C][C]0.0842614977317648[/C][C]0.180000000000003[/C][/ROW]
[ROW][C]8[/C][C]16.7525[/C][C]0.0150000000000006[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]9[/C][C]16.79[/C][C]0.0216024689946919[/C][C]0.0499999999999972[/C][/ROW]
[ROW][C]10[/C][C]17.065[/C][C]0.124498995979887[/C][C]0.289999999999999[/C][/ROW]
[ROW][C]11[/C][C]17.2675[/C][C]0.0236290781312634[/C][C]0.0500000000000007[/C][/ROW]
[ROW][C]12[/C][C]17.3375[/C][C]0.0221735578260842[/C][C]0.0500000000000007[/C][/ROW]
[ROW][C]13[/C][C]17.485[/C][C]0.0953939201416938[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]14[/C][C]17.66[/C][C]0.0316227766016839[/C][C]0.0700000000000003[/C][/ROW]
[ROW][C]15[/C][C]17.865[/C][C]0.0591607978309954[/C][C]0.129999999999999[/C][/ROW]
[ROW][C]16[/C][C]18.015[/C][C]0.0768114574786855[/C][C]0.149999999999999[/C][/ROW]
[ROW][C]17[/C][C]18.1075[/C][C]0.0206155281280882[/C][C]0.0399999999999991[/C][/ROW]
[ROW][C]18[/C][C]18.1775[/C][C]0.0221735578260838[/C][C]0.0500000000000007[/C][/ROW]
[ROW][C]19[/C][C]18.39[/C][C]0.127279220613578[/C][C]0.27[/C][/ROW]
[ROW][C]20[/C][C]18.5075[/C][C]0.0221735578260836[/C][C]0.0500000000000007[/C][/ROW]
[ROW][C]21[/C][C]18.6725[/C][C]0.0457347424467068[/C][C]0.0999999999999979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152640&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152640&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	14.795	0.131782649338471	0.279999999999999
2	15.0325	0.0170782512765996	0.0400000000000009
3	15.1575	0.0861684396980706	0.17
4	15.37	0.113431330181157	0.27
5	15.66	0.0535412613473637	0.130000000000001
6	15.775	0.0191485421551264	0.0399999999999991
7	16.615	0.0842614977317648	0.180000000000003
8	16.7525	0.0150000000000006	0.0300000000000011
9	16.79	0.0216024689946919	0.0499999999999972
10	17.065	0.124498995979887	0.289999999999999
11	17.2675	0.0236290781312634	0.0500000000000007
12	17.3375	0.0221735578260842	0.0500000000000007
13	17.485	0.0953939201416938	0.199999999999999
14	17.66	0.0316227766016839	0.0700000000000003
15	17.865	0.0591607978309954	0.129999999999999
16	18.015	0.0768114574786855	0.149999999999999
17	18.1075	0.0206155281280882	0.0399999999999991
18	18.1775	0.0221735578260838	0.0500000000000007
19	18.39	0.127279220613578	0.27
20	18.5075	0.0221735578260836	0.0500000000000007
21	18.6725	0.0457347424467068	0.0999999999999979

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.180336625004042
beta	-0.00721965089104635
S.D.	0.00754061368998305
T-STAT	-0.957435453912317
p-value	0.350372759963955

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.180336625004042 \tabularnewline
beta & -0.00721965089104635 \tabularnewline
S.D. & 0.00754061368998305 \tabularnewline
T-STAT & -0.957435453912317 \tabularnewline
p-value & 0.350372759963955 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152640&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.180336625004042[/C][/ROW]
[ROW][C]beta[/C][C]-0.00721965089104635[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00754061368998305[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.957435453912317[/C][/ROW]
[ROW][C]p-value[/C][C]0.350372759963955[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152640&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152640&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	0.180336625004042
beta	-0.00721965089104635
S.D.	0.00754061368998305
T-STAT	-0.957435453912317
p-value	0.350372759963955

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	1.51995833854539
beta	-1.6413054371585
S.D.	2.36130027834696
T-STAT	-0.69508543754863
p-value	0.495415443800764
Lambda	2.6413054371585

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.51995833854539 \tabularnewline
beta & -1.6413054371585 \tabularnewline
S.D. & 2.36130027834696 \tabularnewline
T-STAT & -0.69508543754863 \tabularnewline
p-value & 0.495415443800764 \tabularnewline
Lambda & 2.6413054371585 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152640&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.51995833854539[/C][/ROW]
[ROW][C]beta[/C][C]-1.6413054371585[/C][/ROW]
[ROW][C]S.D.[/C][C]2.36130027834696[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.69508543754863[/C][/ROW]
[ROW][C]p-value[/C][C]0.495415443800764[/C][/ROW]
[ROW][C]Lambda[/C][C]2.6413054371585[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152640&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152640&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	1.51995833854539
beta	-1.6413054371585
S.D.	2.36130027834696
T-STAT	-0.69508543754863
p-value	0.495415443800764
Lambda	2.6413054371585

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 4 ;

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