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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationTue, 02 Dec 2008 15:04:14 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/02/t122825561171rzqqbtcjyaczo.htm/, Retrieved Fri, 17 May 2024 02:01:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28505, Retrieved Fri, 17 May 2024 02:01:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157

Tree of Dependent Computations

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  [Spectral Analysis] [Non stationary ti...] [2008-12-02 21:06:35] [74be16979710d4c4e7c6647856088456]
F   P     [Spectral Analysis] [Non stationary ti...] [2008-12-02 21:32:09] [74be16979710d4c4e7c6647856088456]
F RM D        [Standard Deviation-Mean Plot] [Non stationary ti...] [2008-12-02 22:04:14] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2008-12-04 12:28:57 [72e979bcc364082694890d2eccc1a66f] [reply] 
Voor de lambda-waarde moeten we ook kijken naar de p-value. Deze ligt hier heel hoog namelijk 0,97. Om binnen het betrouwbaarheidsinterval te liggen moet deze lager zijn dan 0,05. Het lijkt me dus niet zo goed om deze lambda-waarde te gebruiken.
2008-12-06 18:15:06 [Britt Severijns] [reply] 
zoals de student hierboven opmerkt is deze lambda niet goed want de p-value is groter dan 0.05.
2008-12-07 17:43:05 [Sandra Hofmans] [reply] 
We gaan Lambda introduceren om zo de variantie gelijk te krijgen. Het Standard Deviation Plot gaat na of de spreiding afhankelijk is van het niveau van de tijdreeks. In de grafiek zien we dat er een verband bestaat tussen het gemiddelde en de standaardfout. In de eerste tabel staat de vergelijking van de regressielijn die we door deze punten kunnen tekenen geschreven. In de 2e tabel staat diezelfde regresievergelijking maar dan in de logaritmische vorm. Je ziet hier da de waarde voor Lambda 1 bedraagt.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101,2
100,5
98
106,6
90,1
96,9
125,9
112
100
123,9
79,8
83,4
113,6
112,9
104
109,9
99
106,3
128,9
111,1
102,9
130
87
87,5
117,6
103,4
110,8
112,6
102,5
112,4
135,6
105,1
127,7
137
91
90,5
122,4
123,3
124,3
120
118,1
119
142,7
123,6
129,6
151,6
110,4
99,2
130,5
136,2
129,7
128
121,6
135,8
143,8
147,5
136,2
156,6
123,3
100,4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28505&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]2 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=28505&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28505&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1101.52514.137578872057146.1
2107.75833333333313.402337539218743
3112.18333333333315.304297277285146.5
4123.68333333333313.553653203159552.4
5132.46666666666714.262814546500956.2

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 101.525 & 14.1375788720571 & 46.1 \tabularnewline
2 & 107.758333333333 & 13.4023375392187 & 43 \tabularnewline
3 & 112.183333333333 & 15.3042972772851 & 46.5 \tabularnewline
4 & 123.683333333333 & 13.5536532031595 & 52.4 \tabularnewline
5 & 132.466666666667 & 14.2628145465009 & 56.2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28505&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]101.525[/C][C]14.1375788720571[/C][C]46.1[/C][/ROW]
[ROW][C]2[/C][C]107.758333333333[/C][C]13.4023375392187[/C][C]43[/C][/ROW]
[ROW][C]3[/C][C]112.183333333333[/C][C]15.3042972772851[/C][C]46.5[/C][/ROW]
[ROW][C]4[/C][C]123.683333333333[/C][C]13.5536532031595[/C][C]52.4[/C][/ROW]
[ROW][C]5[/C][C]132.466666666667[/C][C]14.2628145465009[/C][C]56.2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28505&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28505&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1101.52514.137578872057146.1
2107.75833333333313.402337539218743
3112.18333333333315.304297277285146.5
4123.68333333333313.553653203159552.4
5132.46666666666714.262814546500956.2






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha14.2866372174161
beta-0.00133740020577491
S.D.0.0348061487136123
T-STAT-0.0384242513234988
p-value0.971763396477687

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 14.2866372174161 \tabularnewline
beta & -0.00133740020577491 \tabularnewline
S.D. & 0.0348061487136123 \tabularnewline
T-STAT & -0.0384242513234988 \tabularnewline
p-value & 0.971763396477687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28505&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]14.2866372174161[/C][/ROW]
[ROW][C]beta[/C][C]-0.00133740020577491[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0348061487136123[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0384242513234988[/C][/ROW]
[ROW][C]p-value[/C][C]0.971763396477687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28505&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28505&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha14.2866372174161
beta-0.00133740020577491
S.D.0.0348061487136123
T-STAT-0.0384242513234988
p-value0.971763396477687






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.68022434779774
beta-0.0069300270500781
S.D.0.283143213790619
T-STAT-0.0244753422033373
p-value0.982010443491644
Lambda1.00693002705008

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.68022434779774 \tabularnewline
beta & -0.0069300270500781 \tabularnewline
S.D. & 0.283143213790619 \tabularnewline
T-STAT & -0.0244753422033373 \tabularnewline
p-value & 0.982010443491644 \tabularnewline
Lambda & 1.00693002705008 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28505&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.68022434779774[/C][/ROW]
[ROW][C]beta[/C][C]-0.0069300270500781[/C][/ROW]
[ROW][C]S.D.[/C][C]0.283143213790619[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0244753422033373[/C][/ROW]
[ROW][C]p-value[/C][C]0.982010443491644[/C][/ROW]
[ROW][C]Lambda[/C][C]1.00693002705008[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28505&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28505&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.68022434779774
beta-0.0069300270500781
S.D.0.283143213790619
T-STAT-0.0244753422033373
p-value0.982010443491644
Lambda1.00693002705008


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 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')