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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationThu, 27 Nov 2008 10:13:35 -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/Nov/27/t122780608428572ui4oodlczm.htm/, Retrieved Mon, 20 May 2024 12:14:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25862, Retrieved Mon, 20 May 2024 12:14:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact164

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:40:39] [b98453cac15ba1066b407e146608df68]
F RM D    [Standard Deviation-Mean Plot] [Q8 Standard devia...] [2008-11-27 17:13:35] [286e96bd53289970f8e5f25a93fb50b3] [Current]
Feedback Forum
2008-12-07 12:08:05 [Kevin Neelen] [reply] 
De ideale Lambdawaarde voor een stationaire variantie is -3,33.
2008-12-09 01:30:49 [Michael Van Spaandonck] [reply] 
Deze methode wordt gebruikt om te bepalen welke lambdawaarde de beste transformatie voor de gegevensreeks inhoudt.
De ideale lambdawaarde voor een stationaire variantie is -3,33. De p-waarde is echter iets te groot en dus is de lambdawaarde net niet significant. In verdere berekeningen die in een lambdatransformatie voorzien, moet deze daarom ingesteld worden op een standaardwaarde van 1, al kun je eventueel wel berekeningen uitvoeren met een dermate kleine overschrijding van de p-waarde.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
54.281
63.654
68.918
58.686
67.074
60.183
54.326
54.085
53.564
60.873
53.398
45.164
59.672
56.298
62.361
56.930
62.954
62.431
52.528
54.060
53.093
52.695
52.333
41.747
58.576
57.851
63.721
63.384
61.141
59.231
63.472
49.214
55.816
61.713
48.664
45.351
57.888
54.091
59.098
58.962
55.433
60.403
60.721
48.440
57.981
60.258
47.312
46.980
54.846
56.824
67.744
62.849
54.691
65.461
53.724
54.560
57.722
55.458
48.490
46.362

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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=25862&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=25862&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25862&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
157.85056.7082431313340823.754
255.59183333333335.9878911272262721.207
357.34456.332795268212218.37
455.63058333333335.2396066552285413.741
556.56091666666676.2819616863514821.382

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 57.8505 & 6.70824313133408 & 23.754 \tabularnewline
2 & 55.5918333333333 & 5.98789112722627 & 21.207 \tabularnewline
3 & 57.3445 & 6.3327952682122 & 18.37 \tabularnewline
4 & 55.6305833333333 & 5.23960665522854 & 13.741 \tabularnewline
5 & 56.5609166666667 & 6.28196168635148 & 21.382 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25862&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]57.8505[/C][C]6.70824313133408[/C][C]23.754[/C][/ROW]
[ROW][C]2[/C][C]55.5918333333333[/C][C]5.98789112722627[/C][C]21.207[/C][/ROW]
[ROW][C]3[/C][C]57.3445[/C][C]6.3327952682122[/C][C]18.37[/C][/ROW]
[ROW][C]4[/C][C]55.6305833333333[/C][C]5.23960665522854[/C][C]13.741[/C][/ROW]
[ROW][C]5[/C][C]56.5609166666667[/C][C]6.28196168635148[/C][C]21.382[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25862&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25862&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
157.85056.7082431313340823.754
255.59183333333335.9878911272262721.207
357.34456.332795268212218.37
455.63058333333335.2396066552285413.741
556.56091666666676.2819616863514821.382






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-19.9148010866678
beta0.459839104177675
S.D.0.168657341647647
T-STAT2.72646953690491
p-value0.0721548759321158

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -19.9148010866678 \tabularnewline
beta & 0.459839104177675 \tabularnewline
S.D. & 0.168657341647647 \tabularnewline
T-STAT & 2.72646953690491 \tabularnewline
p-value & 0.0721548759321158 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25862&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-19.9148010866678[/C][/ROW]
[ROW][C]beta[/C][C]0.459839104177675[/C][/ROW]
[ROW][C]S.D.[/C][C]0.168657341647647[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.72646953690491[/C][/ROW]
[ROW][C]p-value[/C][C]0.0721548759321158[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25862&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25862&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)
alpha-19.9148010866678
beta0.459839104177675
S.D.0.168657341647647
T-STAT2.72646953690491
p-value0.0721548759321158






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-15.684674695875
beta4.33401083717733
S.D.1.69060193424182
T-STAT2.56359036943904
p-value0.082954374496749
Lambda-3.33401083717733

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -15.684674695875 \tabularnewline
beta & 4.33401083717733 \tabularnewline
S.D. & 1.69060193424182 \tabularnewline
T-STAT & 2.56359036943904 \tabularnewline
p-value & 0.082954374496749 \tabularnewline
Lambda & -3.33401083717733 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25862&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-15.684674695875[/C][/ROW]
[ROW][C]beta[/C][C]4.33401083717733[/C][/ROW]
[ROW][C]S.D.[/C][C]1.69060193424182[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.56359036943904[/C][/ROW]
[ROW][C]p-value[/C][C]0.082954374496749[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.33401083717733[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25862&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25862&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)
alpha-15.684674695875
beta4.33401083717733
S.D.1.69060193424182
T-STAT2.56359036943904
p-value0.082954374496749
Lambda-3.33401083717733


Figures (Output of Computation)

Input Parameters & R Code

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')