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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, 09 Dec 2008 09:57:22 -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/09/t1228841918w6pat422t1b6grt.htm/, Retrieved Sun, 19 May 2024 08:45:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31580, Retrieved Sun, 19 May 2024 08:45:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsk_vanderheggen
Estimated Impact207

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Standard Deviation-Mean Plot] [eigen tijdreeks A...] [2008-12-09 16:57:22] [2731fa16c50d4727d0297daf34574cde] [Current]
- RMPD    [ARIMA Backward Selection] [] [2008-12-14 13:26:22] [367e7d6b927a953ac0842a6750211350]
-         [Standard Deviation-Mean Plot] [Paper SDMP] [2008-12-18 15:09:25] [1640119c345fbfa2091dc1243f79f7a6]
Feedback Forum
2008-12-14 13:31:24 [Glenn Maras] [reply] 
De student heeft stap 1 tot 3 correct uitgevoerd maar stap 4 is niet echt correct opgelost. Er zijn foute, of geen, waarden gegeven voor p P q Q. Stap 5 was helemaal niet opgelost. Hier moest nochtans gewoon de lambda, d en D ingevuld worden en de andere waarden op het maximum plaatsen zodat er uiteindelijk kon gezien worden welke processen er juist gelden. De berekening van step 5 voor de eerste tijdreeks:
http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/14/t12292610829b17prlns06xp9t.htm
en voor de 2de(= eigen) tijdreeks:
http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/14/t12292612283hpkspetm2t3sgc.htm
2008-12-14 13:52:16 [Jasmine Hendrikx] [reply] 
Evaluatie stap 1:
De berekening is goed uitgevoerd en de conclusie is ook correct. Bèta is niet significant verschillend van 0, aangezien de p-waarde groter is dan 5%. Er is dus geen significant verband tussen het gemiddelde en de standaardafwijking.
Hierbij zou er nog vermeld kunnen worden dat met de Standard Deviation –Mean Plot de tijdreeks in mootjes gehakt gaat worden. 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 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 er inderdaad links een outlier is, waardoor de helling dus sterk beïnvloed wordt. Rechts zien we ook een outlier. De student vermeldt ook correct dat er geen lambda transformatie nodig is, aangezien er geen significant verband is tussen de standaardafwijking en het gemiddelde. Daarom moeten we dus lambda gelijk houden aan 1.
2008-12-16 13:59:11 [Peter Van Doninck] [reply] 
De p-waarde bedraagt hier inderdaad 0,32, wat vrij groot is! Hierdoor moet je lambda gelijkstellen aan 1! De grafiek toont hier verder aan dat de invloed van outliers vrij groot is! Hier zullen we moeten rekening houden bij volgende berekeningen!

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5,5
5,3
5,2
5,3
5,3
5
4,8
4,9
5,3
6
6,2
6,4
6,4
6,4
6,2
6,1
6
5,9
6,2
6,2
6,4
6,8
6,9
7
7
6,9
6,7
6,6
6,5
6,4
6,5
6,5
6,6
6,7
6,8
7,2
7,6
7,6
7,3
6,4
6,1
6,3
7,1
7,5
7,4
7,1
6,8
6,9
7,2
7,4
7,3
6,9
6,9
6,8
7,1
7,2
7,1
7
6,9
7
7,4
7,5
7,5
7,4
7,3
7
6,7
6,5
6,5
6,5
6,6
6,8
6,9
6,9
6,8
6,8
6,5
6,1
6
5,9
5,8
5,9
5,9
6,2
6,3
6,2
6
5,8
5,5
5,5
5,7
5,8

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'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=31580&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=31580&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31580&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
15.433333333333330.5087119801890641.6
26.3750.3545163158189171.1
36.70.237410270130920.8
47.008333333333330.5177895910561171.5
57.066666666666670.1825741858350550.6
66.9750.4202272112689861
76.308333333333330.4399552318822971.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5.43333333333333 & 0.508711980189064 & 1.6 \tabularnewline
2 & 6.375 & 0.354516315818917 & 1.1 \tabularnewline
3 & 6.7 & 0.23741027013092 & 0.8 \tabularnewline
4 & 7.00833333333333 & 0.517789591056117 & 1.5 \tabularnewline
5 & 7.06666666666667 & 0.182574185835055 & 0.6 \tabularnewline
6 & 6.975 & 0.420227211268986 & 1 \tabularnewline
7 & 6.30833333333333 & 0.439955231882297 & 1.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31580&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]5.43333333333333[/C][C]0.508711980189064[/C][C]1.6[/C][/ROW]
[ROW][C]2[/C][C]6.375[/C][C]0.354516315818917[/C][C]1.1[/C][/ROW]
[ROW][C]3[/C][C]6.7[/C][C]0.23741027013092[/C][C]0.8[/C][/ROW]
[ROW][C]4[/C][C]7.00833333333333[/C][C]0.517789591056117[/C][C]1.5[/C][/ROW]
[ROW][C]5[/C][C]7.06666666666667[/C][C]0.182574185835055[/C][C]0.6[/C][/ROW]
[ROW][C]6[/C][C]6.975[/C][C]0.420227211268986[/C][C]1[/C][/ROW]
[ROW][C]7[/C][C]6.30833333333333[/C][C]0.439955231882297[/C][C]1.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31580&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31580&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
15.433333333333330.5087119801890641.6
26.3750.3545163158189171.1
36.70.237410270130920.8
47.008333333333330.5177895910561171.5
57.066666666666670.1825741858350550.6
66.9750.4202272112689861
76.308333333333330.4399552318822971.1






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.02011660363127
beta-0.0976663831229108
S.D.0.0899128609553385
T-STAT-1.08623373881322
p-value0.326946075736779

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.02011660363127 \tabularnewline
beta & -0.0976663831229108 \tabularnewline
S.D. & 0.0899128609553385 \tabularnewline
T-STAT & -1.08623373881322 \tabularnewline
p-value & 0.326946075736779 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31580&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.02011660363127[/C][/ROW]
[ROW][C]beta[/C][C]-0.0976663831229108[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0899128609553385[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.08623373881322[/C][/ROW]
[ROW][C]p-value[/C][C]0.326946075736779[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31580&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31580&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)
alpha1.02011660363127
beta-0.0976663831229108
S.D.0.0899128609553385
T-STAT-1.08623373881322
p-value0.326946075736779






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.54106893075445
beta-1.90236405060300
S.D.1.71561108454999
T-STAT-1.10885507078779
p-value0.317958245814863
Lambda2.90236405060300

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.54106893075445 \tabularnewline
beta & -1.90236405060300 \tabularnewline
S.D. & 1.71561108454999 \tabularnewline
T-STAT & -1.10885507078779 \tabularnewline
p-value & 0.317958245814863 \tabularnewline
Lambda & 2.90236405060300 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31580&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.54106893075445[/C][/ROW]
[ROW][C]beta[/C][C]-1.90236405060300[/C][/ROW]
[ROW][C]S.D.[/C][C]1.71561108454999[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.10885507078779[/C][/ROW]
[ROW][C]p-value[/C][C]0.317958245814863[/C][/ROW]
[ROW][C]Lambda[/C][C]2.90236405060300[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31580&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31580&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)
alpha2.54106893075445
beta-1.90236405060300
S.D.1.71561108454999
T-STAT-1.10885507078779
p-value0.317958245814863
Lambda2.90236405060300


Figures (Output of Computation)

Input Parameters & R Code

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')