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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

Fri, 02 Dec 2011 09:33:07 -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/02/t13228364595wj2l2sgcygs3b5.htm/, Retrieved Mon, 29 Apr 2024 05:54:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150252, Retrieved Mon, 29 Apr 2024 05:54:13 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

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

-       [Standard Deviation-Mean Plot] [] [2011-12-02 14:33:07] [307fb8dee51f98edb4f1db3243dd69bf] [Current]

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Dataseries X:

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Histogram

Boxplots

5.51
5.54
5.56
5.57
5.57
5.58
5.56
5.57
5.57
5.6
5.61
5.63
5.65
5.71
5.78
5.8
5.8
5.8
5.81
5.84
5.83
5.86
5.88
5.88
5.89
5.91
5.91
5.95
5.92
5.92
5.91
5.95
6.01
6.07
6.08
6.1
6.11
6.13
6.21
6.19
6.17
6.17
6.19
6.21
6.32
6.36
6.36
6.38
6.36
6.42
6.42
6.44
6.41
6.42
6.43
6.44
6.43
6.43
6.45
6.45

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	0 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 & 0 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150252&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]0 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=150252&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150252&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	0 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	5.545	0.026457513110646	0.0600000000000005
2	5.57	0.00816496580927745	0.0200000000000005
3	5.6025	0.0249999999999999	0.0599999999999996
4	5.735	0.0685565460040103	0.149999999999999
5	5.8125	0.0189296944860009	0.04
6	5.8625	0.0236290781312629	0.0499999999999998
7	5.915	0.025166114784236	0.0600000000000005
8	5.925	0.0173205080756888	0.04
9	6.065	0.0387298334620742	0.0899999999999999
10	6.16	0.0476095228569523	0.0999999999999996
11	6.185	0.0191485421551268	0.04
12	6.355	0.0251661147842357	0.0599999999999996
13	6.41	0.0346410161513775	0.0800000000000001
14	6.425	0.0129099444873581	0.0300000000000002
15	6.44	0.0115470053837928	0.0200000000000005

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5.545 & 0.026457513110646 & 0.0600000000000005 \tabularnewline
2 & 5.57 & 0.00816496580927745 & 0.0200000000000005 \tabularnewline
3 & 5.6025 & 0.0249999999999999 & 0.0599999999999996 \tabularnewline
4 & 5.735 & 0.0685565460040103 & 0.149999999999999 \tabularnewline
5 & 5.8125 & 0.0189296944860009 & 0.04 \tabularnewline
6 & 5.8625 & 0.0236290781312629 & 0.0499999999999998 \tabularnewline
7 & 5.915 & 0.025166114784236 & 0.0600000000000005 \tabularnewline
8 & 5.925 & 0.0173205080756888 & 0.04 \tabularnewline
9 & 6.065 & 0.0387298334620742 & 0.0899999999999999 \tabularnewline
10 & 6.16 & 0.0476095228569523 & 0.0999999999999996 \tabularnewline
11 & 6.185 & 0.0191485421551268 & 0.04 \tabularnewline
12 & 6.355 & 0.0251661147842357 & 0.0599999999999996 \tabularnewline
13 & 6.41 & 0.0346410161513775 & 0.0800000000000001 \tabularnewline
14 & 6.425 & 0.0129099444873581 & 0.0300000000000002 \tabularnewline
15 & 6.44 & 0.0115470053837928 & 0.0200000000000005 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150252&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]5.545[/C][C]0.026457513110646[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]2[/C][C]5.57[/C][C]0.00816496580927745[/C][C]0.0200000000000005[/C][/ROW]
[ROW][C]3[/C][C]5.6025[/C][C]0.0249999999999999[/C][C]0.0599999999999996[/C][/ROW]
[ROW][C]4[/C][C]5.735[/C][C]0.0685565460040103[/C][C]0.149999999999999[/C][/ROW]
[ROW][C]5[/C][C]5.8125[/C][C]0.0189296944860009[/C][C]0.04[/C][/ROW]
[ROW][C]6[/C][C]5.8625[/C][C]0.0236290781312629[/C][C]0.0499999999999998[/C][/ROW]
[ROW][C]7[/C][C]5.915[/C][C]0.025166114784236[/C][C]0.0600000000000005[/C][/ROW]
[ROW][C]8[/C][C]5.925[/C][C]0.0173205080756888[/C][C]0.04[/C][/ROW]
[ROW][C]9[/C][C]6.065[/C][C]0.0387298334620742[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]10[/C][C]6.16[/C][C]0.0476095228569523[/C][C]0.0999999999999996[/C][/ROW]
[ROW][C]11[/C][C]6.185[/C][C]0.0191485421551268[/C][C]0.04[/C][/ROW]
[ROW][C]12[/C][C]6.355[/C][C]0.0251661147842357[/C][C]0.0599999999999996[/C][/ROW]
[ROW][C]13[/C][C]6.41[/C][C]0.0346410161513775[/C][C]0.0800000000000001[/C][/ROW]
[ROW][C]14[/C][C]6.425[/C][C]0.0129099444873581[/C][C]0.0300000000000002[/C][/ROW]
[ROW][C]15[/C][C]6.44[/C][C]0.0115470053837928[/C][C]0.0200000000000005[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150252&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150252&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	5.545	0.026457513110646	0.0600000000000005
2	5.57	0.00816496580927745	0.0200000000000005
3	5.6025	0.0249999999999999	0.0599999999999996
4	5.735	0.0685565460040103	0.149999999999999
5	5.8125	0.0189296944860009	0.04
6	5.8625	0.0236290781312629	0.0499999999999998
7	5.915	0.025166114784236	0.0600000000000005
8	5.925	0.0173205080756888	0.04
9	6.065	0.0387298334620742	0.0899999999999999
10	6.16	0.0476095228569523	0.0999999999999996
11	6.185	0.0191485421551268	0.04
12	6.355	0.0251661147842357	0.0599999999999996
13	6.41	0.0346410161513775	0.0800000000000001
14	6.425	0.0129099444873581	0.0300000000000002
15	6.44	0.0115470053837928	0.0200000000000005

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.0552319937966308
beta	-0.00472742279551618
S.D.	0.0134749771236697
T-STAT	-0.350829745544589
p-value	0.731336006560368

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0552319937966308 \tabularnewline
beta & -0.00472742279551618 \tabularnewline
S.D. & 0.0134749771236697 \tabularnewline
T-STAT & -0.350829745544589 \tabularnewline
p-value & 0.731336006560368 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150252&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0552319937966308[/C][/ROW]
[ROW][C]beta[/C][C]-0.00472742279551618[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0134749771236697[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.350829745544589[/C][/ROW]
[ROW][C]p-value[/C][C]0.731336006560368[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150252&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150252&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	0.0552319937966308
beta	-0.00472742279551618
S.D.	0.0134749771236697
T-STAT	-0.350829745544589
p-value	0.731336006560368

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-2.94949777932169
beta	-0.451431338497608
S.D.	2.87006983170279
T-STAT	-0.157289322200839
p-value	0.877433524829948
Lambda	1.45143133849761

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.94949777932169 \tabularnewline
beta & -0.451431338497608 \tabularnewline
S.D. & 2.87006983170279 \tabularnewline
T-STAT & -0.157289322200839 \tabularnewline
p-value & 0.877433524829948 \tabularnewline
Lambda & 1.45143133849761 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150252&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.94949777932169[/C][/ROW]
[ROW][C]beta[/C][C]-0.451431338497608[/C][/ROW]
[ROW][C]S.D.[/C][C]2.87006983170279[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.157289322200839[/C][/ROW]
[ROW][C]p-value[/C][C]0.877433524829948[/C][/ROW]
[ROW][C]Lambda[/C][C]1.45143133849761[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150252&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150252&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	-2.94949777932169
beta	-0.451431338497608
S.D.	2.87006983170279
T-STAT	-0.157289322200839
p-value	0.877433524829948
Lambda	1.45143133849761

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