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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

Tue, 02 Dec 2008 11:16:35 -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/02/t1228241845ogzd7y72ccln7xk.htm/, Retrieved Sun, 19 May 2024 10:09:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28197, Retrieved Sun, 19 May 2024 10:09:47 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

164

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

F     [(Partial) Autocorrelation Function] [nsts Q8 (1)] [2008-12-02 16:54:05] [b1bd16d1f47bfe13feacf1c27a0abba5]
F   PD  [(Partial) Autocorrelation Function] [nsts Q8 (2)] [2008-12-02 16:58:46] [b1bd16d1f47bfe13feacf1c27a0abba5]
F   PD    [(Partial) Autocorrelation Function] [nsts Q8 (5)] [2008-12-02 17:09:15] [b1bd16d1f47bfe13feacf1c27a0abba5]
-   PD      [(Partial) Autocorrelation Function] [nsts Q8 (6)] [2008-12-02 17:12:08] [b1bd16d1f47bfe13feacf1c27a0abba5]
-   P         [(Partial) Autocorrelation Function] [nsts Q8 (7)] [2008-12-02 17:14:26] [b1bd16d1f47bfe13feacf1c27a0abba5]
F RMPD            [Standard Deviation-Mean Plot] [nsts Q8 (11)] [2008-12-02 18:16:35] [e7b1048c2c3a353441b9143db4404b91] [Current]

Feedback Forum

2008-12-08 19:34:16 [Jasmine Hendrikx] [reply] 
Eigen evaluatie: 
Om de optimale lambda te berekenen, moeten we inderdaad gebruik maken van de Standard Deviation – Mean Plot. Het is inderdaad zo dat de optimale lambda -0.10 blijkt, maar de bespreking is wel een beetje onvolledig.   
Zo zou er nog vermeld kunnen worden dat de tijdreeks in mootjes gaat gehakt wordt. In de eerste tabel krijgen we voor het eerste jaar en voor de volgende jaren steeds het gemiddelde en de standaardafwijking. In de laatste kolom zien we de range (dit is het verschil tussen de grootste en kleinste waarde). De grafiek is niet in het document weergegeven, maar is eigenlijk wel nodig. Deze geeft het verband weer tussen het gemiddelde niveau en de standaardafwijking. Op de x-as zien we het gemiddelde en op de y-as de standaardafwijking. We moeten hier goed opletten op outliers, zeker wanneer deze zich links of rechts bevinden, aangezien zij de helling dan sterk zullen beïnvloeden. Uit de grafiek kunnen we afleiden dat de punten vrij verspreid zijn en dat er niet meteen een verband op te merken valt. We kunnen dus niet echt van een verband spreken tussen het gemiddelde en de standaardafwijking.  We zien uit de tweede tabel dat bèta gelijk is aan 0,07. Dit getal is niet significant verschillend van 0, doordat de p-waarde afgerond 0.57 bedraagt. De p-waarde is dus groter dan 5% waardoor we kunnen zeggen dat er geen significant verschil is.  Het eventuele verband tussen het gemiddelde en de standaardafwijking is aan het toeval te wijten. In de derde tabel krijg je dit in logaritmische vorm. Je vindt hier een theoretische lambda die je kan gebruiken in de transformatie. Indien lambda gelijk is aan 0, dan gebruiken we een logaritme, indien lambda verschillend is van 0, dan gebruiken we een exponent. We zien uit de vorige tabel dat er geen verband bestaat tussen het gemiddelde en de standaardafwijking, daarom mogen we in principe niet de waarde van lambda nemen die berekend is. We zoeken deze lambda om de variantie te stabiliseren en zo de tijdreeks meer stationair te maken. Uit de tabel blijkt dat lamda gelijk is -0.11. In Q9 werd deze lambda gebruikt, maar eigenlijk is dit niet echt correct, aangezien de p-waarde groter is dan 5%.  

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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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28197&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28197&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28197&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	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	102.5	5.86282587774251	20.6
2	106.133333333333	6.06889735878892	21.5
3	112.866666666667	9.82402744049075	25
4	115	9.44573015609795	31.2
5	116.3	8.46253776680172	29
6	120.216666666667	7.26458824877518	17.7
7	120.633333333333	5.72464105001485	19.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 102.5 & 5.86282587774251 & 20.6 \tabularnewline
2 & 106.133333333333 & 6.06889735878892 & 21.5 \tabularnewline
3 & 112.866666666667 & 9.82402744049075 & 25 \tabularnewline
4 & 115 & 9.44573015609795 & 31.2 \tabularnewline
5 & 116.3 & 8.46253776680172 & 29 \tabularnewline
6 & 120.216666666667 & 7.26458824877518 & 17.7 \tabularnewline
7 & 120.633333333333 & 5.72464105001485 & 19.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28197&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]102.5[/C][C]5.86282587774251[/C][C]20.6[/C][/ROW]
[ROW][C]2[/C][C]106.133333333333[/C][C]6.06889735878892[/C][C]21.5[/C][/ROW]
[ROW][C]3[/C][C]112.866666666667[/C][C]9.82402744049075[/C][C]25[/C][/ROW]
[ROW][C]4[/C][C]115[/C][C]9.44573015609795[/C][C]31.2[/C][/ROW]
[ROW][C]5[/C][C]116.3[/C][C]8.46253776680172[/C][C]29[/C][/ROW]
[ROW][C]6[/C][C]120.216666666667[/C][C]7.26458824877518[/C][C]17.7[/C][/ROW]
[ROW][C]7[/C][C]120.633333333333[/C][C]5.72464105001485[/C][C]19.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28197&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28197&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	102.5	5.86282587774251	20.6
2	106.133333333333	6.06889735878892	21.5
3	112.866666666667	9.82402744049075	25
4	115	9.44573015609795	31.2
5	116.3	8.46253776680172	29
6	120.216666666667	7.26458824877518	17.7
7	120.633333333333	5.72464105001485	19.3

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	0.0883228019571733
beta	0.0655641508032655
S.D.	0.109336391638342
T-STAT	0.599655337265344
p-value	0.57487272141009

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0883228019571733 \tabularnewline
beta & 0.0655641508032655 \tabularnewline
S.D. & 0.109336391638342 \tabularnewline
T-STAT & 0.599655337265344 \tabularnewline
p-value & 0.57487272141009 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28197&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0883228019571733[/C][/ROW]
[ROW][C]beta[/C][C]0.0655641508032655[/C][/ROW]
[ROW][C]S.D.[/C][C]0.109336391638342[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.599655337265344[/C][/ROW]
[ROW][C]p-value[/C][C]0.57487272141009[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28197&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28197&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	0.0883228019571733
beta	0.0655641508032655
S.D.	0.109336391638342
T-STAT	0.599655337265344
p-value	0.57487272141009

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-3.24352702691584
beta	1.10773375025661
S.D.	1.59850245769463
T-STAT	0.69298220026148
p-value	0.519184667485418
Lambda	-0.107733750256608

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.24352702691584 \tabularnewline
beta & 1.10773375025661 \tabularnewline
S.D. & 1.59850245769463 \tabularnewline
T-STAT & 0.69298220026148 \tabularnewline
p-value & 0.519184667485418 \tabularnewline
Lambda & -0.107733750256608 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28197&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.24352702691584[/C][/ROW]
[ROW][C]beta[/C][C]1.10773375025661[/C][/ROW]
[ROW][C]S.D.[/C][C]1.59850245769463[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.69298220026148[/C][/ROW]
[ROW][C]p-value[/C][C]0.519184667485418[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.107733750256608[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28197&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28197&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	-3.24352702691584
beta	1.10773375025661
S.D.	1.59850245769463
T-STAT	0.69298220026148
p-value	0.519184667485418
Lambda	-0.107733750256608

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code