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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, 21 Dec 2009 08:51:38 -0700

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/2009/Dec/21/t1261410755v3fk8zfah3onq3a.htm/, Retrieved Sun, 05 May 2024 12:56:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70297, Retrieved Sun, 05 May 2024 12:56:05 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W83

Estimated Impact

149

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

-     [Standard Deviation-Mean Plot] [] [2009-12-21 15:37:35] [e5e09c53da17fb7444fa9ceb236a5291]
-    D    [Standard Deviation-Mean Plot] [] [2009-12-21 15:51:38] [ab2b68d5442f7c9b7e2e9d790849a234] [Current]
-   P       [Standard Deviation-Mean Plot] [] [2010-01-12 09:03:27] [74be16979710d4c4e7c6647856088456] 
- RMPD      [Classical Decomposition] [] [2010-01-12 09:15:15] [e5e09c53da17fb7444fa9ceb236a5291] 
-    D        [Classical Decomposition] [] [2010-01-16 10:43:37] [74be16979710d4c4e7c6647856088456] 
- RMPD        [Exponential Smoothing] [] [2010-01-16 11:07:46] [74be16979710d4c4e7c6647856088456] 
-   PD          [Exponential Smoothing] [] [2010-01-16 11:41:42] [74be16979710d4c4e7c6647856088456] 
- RMPD      [Classical Decomposition] [] [2010-01-12 09:35:07] [e5e09c53da17fb7444fa9ceb236a5291] 

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Dataseries X:

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Histogram

Boxplots

2.14
2.45
2.52
2.3
2.25
2.06
1.99
2.25
2.26
2.36
2.3
2.19
2.31
2.21
2.21
2.26
2.18
2.21
2.33
2.12
2.08
1.97
2.09
2.11
2.24
2.45
2.68
2.73
2.76
2.83
3.16
3.22
3.22
3.34
3.35
3.42
3.58
3.71
3.68
3.83
3.94
3.88
4.03
4.15
4.32
4.4
4.37
4.14
4.11
4.16
3.98
4.13
3.76
3.66
3.85
4.03
4.31
4.58
4.46
4.41
3.84
2.84
2.66
2.17
1.43
1.47
1.29
1.23
1.09
0.94
0.76
0.67

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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70297&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70297&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70297&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	'Gwilym Jenkins' @ 72.249.127.135

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	2.3525	0.168794747153656	0.38
2	2.1375	0.133010024684858	0.26
3	2.2775	0.0713559154286921	0.17
4	2.2475	0.0478713553878169	0.1
5	2.21	0.0883176086632785	0.21
6	2.0625	0.0629152869605896	0.14
7	2.525	0.225757982509294	0.49
8	2.9925	0.231138486626525	0.46
9	3.3325	0.0830160627027484	0.200000000000000
10	3.7	0.10295630140987	0.25
11	4	0.117473401244708	0.270000000000000
12	4.3075	0.116440256498057	0.260000000000001
13	4.095	0.0793725393319378	0.18
14	3.825	0.157162336455017	0.37
15	4.44	0.112249721603218	0.270000000000000
16	2.8775	0.701349888904722	1.67
17	1.355	0.113578166916005	0.24
18	0.865	0.187349939951952	0.42

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2.3525 & 0.168794747153656 & 0.38 \tabularnewline
2 & 2.1375 & 0.133010024684858 & 0.26 \tabularnewline
3 & 2.2775 & 0.0713559154286921 & 0.17 \tabularnewline
4 & 2.2475 & 0.0478713553878169 & 0.1 \tabularnewline
5 & 2.21 & 0.0883176086632785 & 0.21 \tabularnewline
6 & 2.0625 & 0.0629152869605896 & 0.14 \tabularnewline
7 & 2.525 & 0.225757982509294 & 0.49 \tabularnewline
8 & 2.9925 & 0.231138486626525 & 0.46 \tabularnewline
9 & 3.3325 & 0.0830160627027484 & 0.200000000000000 \tabularnewline
10 & 3.7 & 0.10295630140987 & 0.25 \tabularnewline
11 & 4 & 0.117473401244708 & 0.270000000000000 \tabularnewline
12 & 4.3075 & 0.116440256498057 & 0.260000000000001 \tabularnewline
13 & 4.095 & 0.0793725393319378 & 0.18 \tabularnewline
14 & 3.825 & 0.157162336455017 & 0.37 \tabularnewline
15 & 4.44 & 0.112249721603218 & 0.270000000000000 \tabularnewline
16 & 2.8775 & 0.701349888904722 & 1.67 \tabularnewline
17 & 1.355 & 0.113578166916005 & 0.24 \tabularnewline
18 & 0.865 & 0.187349939951952 & 0.42 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70297&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]2.3525[/C][C]0.168794747153656[/C][C]0.38[/C][/ROW]
[ROW][C]2[/C][C]2.1375[/C][C]0.133010024684858[/C][C]0.26[/C][/ROW]
[ROW][C]3[/C][C]2.2775[/C][C]0.0713559154286921[/C][C]0.17[/C][/ROW]
[ROW][C]4[/C][C]2.2475[/C][C]0.0478713553878169[/C][C]0.1[/C][/ROW]
[ROW][C]5[/C][C]2.21[/C][C]0.0883176086632785[/C][C]0.21[/C][/ROW]
[ROW][C]6[/C][C]2.0625[/C][C]0.0629152869605896[/C][C]0.14[/C][/ROW]
[ROW][C]7[/C][C]2.525[/C][C]0.225757982509294[/C][C]0.49[/C][/ROW]
[ROW][C]8[/C][C]2.9925[/C][C]0.231138486626525[/C][C]0.46[/C][/ROW]
[ROW][C]9[/C][C]3.3325[/C][C]0.0830160627027484[/C][C]0.200000000000000[/C][/ROW]
[ROW][C]10[/C][C]3.7[/C][C]0.10295630140987[/C][C]0.25[/C][/ROW]
[ROW][C]11[/C][C]4[/C][C]0.117473401244708[/C][C]0.270000000000000[/C][/ROW]
[ROW][C]12[/C][C]4.3075[/C][C]0.116440256498057[/C][C]0.260000000000001[/C][/ROW]
[ROW][C]13[/C][C]4.095[/C][C]0.0793725393319378[/C][C]0.18[/C][/ROW]
[ROW][C]14[/C][C]3.825[/C][C]0.157162336455017[/C][C]0.37[/C][/ROW]
[ROW][C]15[/C][C]4.44[/C][C]0.112249721603218[/C][C]0.270000000000000[/C][/ROW]
[ROW][C]16[/C][C]2.8775[/C][C]0.701349888904722[/C][C]1.67[/C][/ROW]
[ROW][C]17[/C][C]1.355[/C][C]0.113578166916005[/C][C]0.24[/C][/ROW]
[ROW][C]18[/C][C]0.865[/C][C]0.187349939951952[/C][C]0.42[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70297&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70297&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	2.3525	0.168794747153656	0.38
2	2.1375	0.133010024684858	0.26
3	2.2775	0.0713559154286921	0.17
4	2.2475	0.0478713553878169	0.1
5	2.21	0.0883176086632785	0.21
6	2.0625	0.0629152869605896	0.14
7	2.525	0.225757982509294	0.49
8	2.9925	0.231138486626525	0.46
9	3.3325	0.0830160627027484	0.200000000000000
10	3.7	0.10295630140987	0.25
11	4	0.117473401244708	0.270000000000000
12	4.3075	0.116440256498057	0.260000000000001
13	4.095	0.0793725393319378	0.18
14	3.825	0.157162336455017	0.37
15	4.44	0.112249721603218	0.270000000000000
16	2.8775	0.701349888904722	1.67
17	1.355	0.113578166916005	0.24
18	0.865	0.187349939951952	0.42

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.171546304794913
beta	-0.00557576597791742
S.D.	0.0352500424854487
T-STAT	-0.158177567593546
p-value	0.876296041203469

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.171546304794913 \tabularnewline
beta & -0.00557576597791742 \tabularnewline
S.D. & 0.0352500424854487 \tabularnewline
T-STAT & -0.158177567593546 \tabularnewline
p-value & 0.876296041203469 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70297&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.171546304794913[/C][/ROW]
[ROW][C]beta[/C][C]-0.00557576597791742[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0352500424854487[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.158177567593546[/C][/ROW]
[ROW][C]p-value[/C][C]0.876296041203469[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70297&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70297&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	0.171546304794913
beta	-0.00557576597791742
S.D.	0.0352500424854487
T-STAT	-0.158177567593546
p-value	0.876296041203469

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-2.03031711422846
beta	-0.0514557240627455
S.D.	0.356004404297386
T-STAT	-0.144536762583876
p-value	0.88688158992004
Lambda	1.05145572406275

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.03031711422846 \tabularnewline
beta & -0.0514557240627455 \tabularnewline
S.D. & 0.356004404297386 \tabularnewline
T-STAT & -0.144536762583876 \tabularnewline
p-value & 0.88688158992004 \tabularnewline
Lambda & 1.05145572406275 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70297&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.03031711422846[/C][/ROW]
[ROW][C]beta[/C][C]-0.0514557240627455[/C][/ROW]
[ROW][C]S.D.[/C][C]0.356004404297386[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.144536762583876[/C][/ROW]
[ROW][C]p-value[/C][C]0.88688158992004[/C][/ROW]
[ROW][C]Lambda[/C][C]1.05145572406275[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70297&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70297&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	-2.03031711422846
beta	-0.0514557240627455
S.D.	0.356004404297386
T-STAT	-0.144536762583876
p-value	0.88688158992004
Lambda	1.05145572406275

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code