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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

Mon, 08 Dec 2008 12:47:44 -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/2008/Dec/08/t12287657434r18goakbbzychl.htm/, Retrieved Thu, 16 May 2024 04:29:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30864, Retrieved Thu, 16 May 2024 04:29:58 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

183

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD    [Standard Deviation-Mean Plot] [SD mean plot step 1] [2008-12-08 19:47:44] [35348cd8592af0baf5f138bd59921307] [Current]
F    D      [Standard Deviation-Mean Plot] [SD mean plot step 1] [2008-12-08 19:54:49] [7d3039e6253bb5fb3b26df1537d500b4] 
- RM D        [Variance Reduction Matrix] [VRM Step 2] [2008-12-08 20:02:11] [7d3039e6253bb5fb3b26df1537d500b4] 
- RM D        [(Partial) Autocorrelation Function] [ACF Step 2] [2008-12-08 20:08:11] [7d3039e6253bb5fb3b26df1537d500b4] 
-               [(Partial) Autocorrelation Function] [ACF Step 3] [2008-12-08 20:23:11] [7d3039e6253bb5fb3b26df1537d500b4] 
- RMP             [ARIMA Backward Selection] [Arima backward se...] [2008-12-15 09:51:35] [7d3039e6253bb5fb3b26df1537d500b4] 
F RM D        [Spectral Analysis] [cumulative period...] [2008-12-08 20:14:38] [7d3039e6253bb5fb3b26df1537d500b4] 
-               [Spectral Analysis] [cumulative period...] [2008-12-08 20:28:31] [7d3039e6253bb5fb3b26df1537d500b4] 
F RMPD            [ARIMA Forecasting] [Arima forecasting...] [2008-12-15 19:14:36] [7d3039e6253bb5fb3b26df1537d500b4] 
-   P               [ARIMA Forecasting] [Arima Forecast st...] [2008-12-19 17:28:32] [7d3039e6253bb5fb3b26df1537d500b4] 

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Dataseries X:

Download CSV

Histogram

Boxplots

21,1
21,0
20,4
19,5
18,6
18,8
23,7
24,8
25,0
23,6
22,3
21,8
20,8
19,7
18,3
17,4
17,0
18,1
23,9
25,6
25,3
23,6
21,9
21,4
20,6
20,5
20,2
20,6
19,7
19,3
22,8
23,5
23,8
22,6
22,0
21,7
20,7
20,2
19,1
19,5
18,7
18,6
22,2
23,2
23,5
21,3
20,0
18,7
18,9
18,3
18,4
19,9
19,2
18,5
20,9
20,5
19,4
18,1
17,0
17,0
17,3
16,7
15,5
15,3
13,7
14,1
17,3
18,1

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30864&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30864&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30864&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	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	21.7166666666667	2.21311517727361	6.4
2	21.0833333333333	3.04655791862147	8.6
3	21.4416666666667	1.50239707457681	4.5
4	20.475	1.73840313349506	4.9
5	18.8416666666667	1.22434274266447	3.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 21.7166666666667 & 2.21311517727361 & 6.4 \tabularnewline
2 & 21.0833333333333 & 3.04655791862147 & 8.6 \tabularnewline
3 & 21.4416666666667 & 1.50239707457681 & 4.5 \tabularnewline
4 & 20.475 & 1.73840313349506 & 4.9 \tabularnewline
5 & 18.8416666666667 & 1.22434274266447 & 3.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30864&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]21.7166666666667[/C][C]2.21311517727361[/C][C]6.4[/C][/ROW]
[ROW][C]2[/C][C]21.0833333333333[/C][C]3.04655791862147[/C][C]8.6[/C][/ROW]
[ROW][C]3[/C][C]21.4416666666667[/C][C]1.50239707457681[/C][C]4.5[/C][/ROW]
[ROW][C]4[/C][C]20.475[/C][C]1.73840313349506[/C][C]4.9[/C][/ROW]
[ROW][C]5[/C][C]18.8416666666667[/C][C]1.22434274266447[/C][C]3.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30864&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30864&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	21.7166666666667	2.21311517727361	6.4
2	21.0833333333333	3.04655791862147	8.6
3	21.4416666666667	1.50239707457681	4.5
4	20.475	1.73840313349506	4.9
5	18.8416666666667	1.22434274266447	3.9

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-4.98913556231869
beta	0.334791925886134
S.D.	0.30457354485543
T-STAT	1.09921538341436
p-value	0.351976192056336

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.98913556231869 \tabularnewline
beta & 0.334791925886134 \tabularnewline
S.D. & 0.30457354485543 \tabularnewline
T-STAT & 1.09921538341436 \tabularnewline
p-value & 0.351976192056336 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30864&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.98913556231869[/C][/ROW]
[ROW][C]beta[/C][C]0.334791925886134[/C][/ROW]
[ROW][C]S.D.[/C][C]0.30457354485543[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.09921538341436[/C][/ROW]
[ROW][C]p-value[/C][C]0.351976192056336[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30864&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30864&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	-4.98913556231869
beta	0.334791925886134
S.D.	0.30457354485543
T-STAT	1.09921538341436
p-value	0.351976192056336

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-11.1649512598056
beta	3.88822375091385
S.D.	2.81118079289622
T-STAT	1.38312831417292
p-value	0.260587972362049
Lambda	-2.88822375091385

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.1649512598056 \tabularnewline
beta & 3.88822375091385 \tabularnewline
S.D. & 2.81118079289622 \tabularnewline
T-STAT & 1.38312831417292 \tabularnewline
p-value & 0.260587972362049 \tabularnewline
Lambda & -2.88822375091385 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30864&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.1649512598056[/C][/ROW]
[ROW][C]beta[/C][C]3.88822375091385[/C][/ROW]
[ROW][C]S.D.[/C][C]2.81118079289622[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.38312831417292[/C][/ROW]
[ROW][C]p-value[/C][C]0.260587972362049[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.88822375091385[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30864&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30864&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	-11.1649512598056
beta	3.88822375091385
S.D.	2.81118079289622
T-STAT	1.38312831417292
p-value	0.260587972362049
Lambda	-2.88822375091385

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 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