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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, 01 Dec 2008 07:11:33 -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/01/t1228140930kgjksb7sv271h1s.htm/, Retrieved Sun, 05 May 2024 15:41:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26927, Retrieved Sun, 05 May 2024 15:41:38 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Q5 Non Stationary Time Series

Estimated Impact

273

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD    [Standard Deviation-Mean Plot] [Q5 Non Stationary...] [2008-12-01 14:11:33] [9f72e095d5529918bf5b0810c01bf6ce] [Current]
-   P       [Standard Deviation-Mean Plot] [q5] [2008-12-07 11:10:32] [1b742211e88d1643c42c5773474321b2] 

Feedback Forum

2008-12-04 12:28:29 [] [reply] 
de lamda moet -0.3 zijn en niet 0.3
2008-12-06 17:36:48 [a2386b643d711541400692649981f2dc] [reply] 
Je legt algemeen uit waar de Standard deviation voor staat en legt in duidelijke taal de grafiek uit. Je verklaart ook waarom de tijdreeks niet stationair is.
2008-12-08 23:15:56 [Jessica Alves Pires] [reply] 
Goed beantwoord. Ik geef theoretische uitleg over de standard deviation - mean plot. Mijn bevindingen zijn juist. Ik ben wel domweg een minteken vergeten over te typen. Ik had de tabel bijgevoegd om aan te tonen waar je de waarde van lambda kan vinden. Bij het overtypen ben ik de minteken vergeten, het is dus -0,3 en niet 0,3. Ook toon ik nog een ander grafiek waar de spreiding duidelijker te zien is. 

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Dataseries X:

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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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26927&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26927&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26927&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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	126.666666666667	13.7201466552812	44
2	139.666666666667	19.0708408230201	56
3	170.166666666667	18.4382671899964	54
4	197	22.9663785881568	71
5	225	28.4668866643972	92
6	238.916666666667	34.9244856364370	114
7	284	42.1404577789347	131
8	328.25	47.8617801591207	142
9	368.416666666667	57.8908979081	166
10	381	64.5304720126997	195
11	428.333333333333	69.8300968368398	217
12	476.166666666667	77.7371250179771	232

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 126.666666666667 & 13.7201466552812 & 44 \tabularnewline
2 & 139.666666666667 & 19.0708408230201 & 56 \tabularnewline
3 & 170.166666666667 & 18.4382671899964 & 54 \tabularnewline
4 & 197 & 22.9663785881568 & 71 \tabularnewline
5 & 225 & 28.4668866643972 & 92 \tabularnewline
6 & 238.916666666667 & 34.9244856364370 & 114 \tabularnewline
7 & 284 & 42.1404577789347 & 131 \tabularnewline
8 & 328.25 & 47.8617801591207 & 142 \tabularnewline
9 & 368.416666666667 & 57.8908979081 & 166 \tabularnewline
10 & 381 & 64.5304720126997 & 195 \tabularnewline
11 & 428.333333333333 & 69.8300968368398 & 217 \tabularnewline
12 & 476.166666666667 & 77.7371250179771 & 232 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26927&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]126.666666666667[/C][C]13.7201466552812[/C][C]44[/C][/ROW]
[ROW][C]2[/C][C]139.666666666667[/C][C]19.0708408230201[/C][C]56[/C][/ROW]
[ROW][C]3[/C][C]170.166666666667[/C][C]18.4382671899964[/C][C]54[/C][/ROW]
[ROW][C]4[/C][C]197[/C][C]22.9663785881568[/C][C]71[/C][/ROW]
[ROW][C]5[/C][C]225[/C][C]28.4668866643972[/C][C]92[/C][/ROW]
[ROW][C]6[/C][C]238.916666666667[/C][C]34.9244856364370[/C][C]114[/C][/ROW]
[ROW][C]7[/C][C]284[/C][C]42.1404577789347[/C][C]131[/C][/ROW]
[ROW][C]8[/C][C]328.25[/C][C]47.8617801591207[/C][C]142[/C][/ROW]
[ROW][C]9[/C][C]368.416666666667[/C][C]57.8908979081[/C][C]166[/C][/ROW]
[ROW][C]10[/C][C]381[/C][C]64.5304720126997[/C][C]195[/C][/ROW]
[ROW][C]11[/C][C]428.333333333333[/C][C]69.8300968368398[/C][C]217[/C][/ROW]
[ROW][C]12[/C][C]476.166666666667[/C][C]77.7371250179771[/C][C]232[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26927&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26927&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	126.666666666667	13.7201466552812	44
2	139.666666666667	19.0708408230201	56
3	170.166666666667	18.4382671899964	54
4	197	22.9663785881568	71
5	225	28.4668866643972	92
6	238.916666666667	34.9244856364370	114
7	284	42.1404577789347	131
8	328.25	47.8617801591207	142
9	368.416666666667	57.8908979081	166
10	381	64.5304720126997	195
11	428.333333333333	69.8300968368398	217
12	476.166666666667	77.7371250179771	232

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-11.4032541425579
beta	0.188613398899484
S.D.	0.00657733180244678
T-STAT	28.6762785525460
p-value	6.1917170560278e-11

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -11.4032541425579 \tabularnewline
beta & 0.188613398899484 \tabularnewline
S.D. & 0.00657733180244678 \tabularnewline
T-STAT & 28.6762785525460 \tabularnewline
p-value & 6.1917170560278e-11 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26927&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.4032541425579[/C][/ROW]
[ROW][C]beta[/C][C]0.188613398899484[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00657733180244678[/C][/ROW]
[ROW][C]T-STAT[/C][C]28.6762785525460[/C][/ROW]
[ROW][C]p-value[/C][C]6.1917170560278e-11[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26927&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26927&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	-11.4032541425579
beta	0.188613398899484
S.D.	0.00657733180244678
T-STAT	28.6762785525460
p-value	6.1917170560278e-11

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-3.70703989322047
beta	1.31259253972576
S.D.	0.0574958902763329
T-STAT	22.8293280340083
p-value	5.8658934502009e-10
Lambda	-0.312592539725755

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.70703989322047 \tabularnewline
beta & 1.31259253972576 \tabularnewline
S.D. & 0.0574958902763329 \tabularnewline
T-STAT & 22.8293280340083 \tabularnewline
p-value & 5.8658934502009e-10 \tabularnewline
Lambda & -0.312592539725755 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26927&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.70703989322047[/C][/ROW]
[ROW][C]beta[/C][C]1.31259253972576[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0574958902763329[/C][/ROW]
[ROW][C]T-STAT[/C][C]22.8293280340083[/C][/ROW]
[ROW][C]p-value[/C][C]5.8658934502009e-10[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.312592539725755[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26927&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26927&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	-3.70703989322047
beta	1.31259253972576
S.D.	0.0574958902763329
T-STAT	22.8293280340083
p-value	5.8658934502009e-10
Lambda	-0.312592539725755

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 500 ; par2 = 0.5 ;

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