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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 computationTue, 02 Dec 2008 13:01:53 -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/t1228248200ugg85p3g8ddlukh.htm/, Retrieved Sat, 25 May 2024 01:53:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28315, Retrieved Sat, 25 May 2024 01:53:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137

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] [Non stat time ser...] [2008-12-02 20:01:53] [c5d6d05aee6be5527ac4a30a8c3b8fe5] [Current]
Feedback Forum
2008-12-08 16:55:37 [Jonas Janssens] [reply] 
Uit de grafieken die je weergeeft kom je de meest optimale waarde voor Lambda niet te weten. Hiervoor moet je kijken naar de 'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)'-tabel, waar je de waarde voor Lambda kan aflezen: -0.3015. Deze heb je nodig om je tijdreeks stationair te maken.
2008-12-09 22:53:04 [Gert-Jan Geudens] [reply] 
Ok maar vergeet ook hier de lambda niet te vermelden. Tevens willen we opmerken dat transformatie hier weinig zin heeft aangezien de p-waarde groot is. We zien dan ook in de grafieken dat we zeer moeilijk een gepaste regressierechte kunnen tekenen.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
109,1
111,4
114,1
121,8
127,6
129,9
128
123,5
124
127,4
127,6
128,4
131,4
135,1
134
144,5
147,3
150,9
148,7
141,4
138,9
139,8
145,6
147,9
148,5
151,1
157,5
167,5
172,3
173,5
187,5
205,5
195,1
204,5
204,5
201,7
207
206,6
210,6
211,1
215
223,9
238,2
238,9
229,6
232,2
222,1
221,6
227,3
221
213,6
243,4
253,8
265,3
268,2
268,5
266,9
268,4
250,8
231,2
192

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time15 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 & 15 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28315&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]15 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=28315&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28315&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 time15 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1122.7333333333337.2127832647489420.8
2142.1256.3589771904836219.5
3180.76666666666721.722101578109357
4221.411.557130817260532.3
5248.220.418797044078654.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 122.733333333333 & 7.21278326474894 & 20.8 \tabularnewline
2 & 142.125 & 6.35897719048362 & 19.5 \tabularnewline
3 & 180.766666666667 & 21.7221015781093 & 57 \tabularnewline
4 & 221.4 & 11.5571308172605 & 32.3 \tabularnewline
5 & 248.2 & 20.4187970440786 & 54.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28315&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]122.733333333333[/C][C]7.21278326474894[/C][C]20.8[/C][/ROW]
[ROW][C]2[/C][C]142.125[/C][C]6.35897719048362[/C][C]19.5[/C][/ROW]
[ROW][C]3[/C][C]180.766666666667[/C][C]21.7221015781093[/C][C]57[/C][/ROW]
[ROW][C]4[/C][C]221.4[/C][C]11.5571308172605[/C][C]32.3[/C][/ROW]
[ROW][C]5[/C][C]248.2[/C][C]20.4187970440786[/C][C]54.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28315&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28315&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
1122.7333333333337.2127832647489420.8
2142.1256.3589771904836219.5
3180.76666666666721.722101578109357
4221.411.557130817260532.3
5248.220.418797044078654.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-3.61631659409428
beta0.0932572568113331
S.D.0.0586357066340247
T-STAT1.59045165761196
p-value0.209959512742049

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -3.61631659409428 \tabularnewline
beta & 0.0932572568113331 \tabularnewline
S.D. & 0.0586357066340247 \tabularnewline
T-STAT & 1.59045165761196 \tabularnewline
p-value & 0.209959512742049 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28315&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.61631659409428[/C][/ROW]
[ROW][C]beta[/C][C]0.0932572568113331[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0586357066340247[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.59045165761196[/C][/ROW]
[ROW][C]p-value[/C][C]0.209959512742049[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28315&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28315&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-3.61631659409428
beta0.0932572568113331
S.D.0.0586357066340247
T-STAT1.59045165761196
p-value0.209959512742049






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.1246430011468
beta1.46807441366554
S.D.0.72674884687335
T-STAT2.020057437974
p-value0.136648615380470
Lambda-0.468074413665539

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.1246430011468 \tabularnewline
beta & 1.46807441366554 \tabularnewline
S.D. & 0.72674884687335 \tabularnewline
T-STAT & 2.020057437974 \tabularnewline
p-value & 0.136648615380470 \tabularnewline
Lambda & -0.468074413665539 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28315&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.1246430011468[/C][/ROW]
[ROW][C]beta[/C][C]1.46807441366554[/C][/ROW]
[ROW][C]S.D.[/C][C]0.72674884687335[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.020057437974[/C][/ROW]
[ROW][C]p-value[/C][C]0.136648615380470[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.468074413665539[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28315&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28315&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-5.1246430011468
beta1.46807441366554
S.D.0.72674884687335
T-STAT2.020057437974
p-value0.136648615380470
Lambda-0.468074413665539


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')