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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_boxcoxnorm.wasp
Title produced by softwareBox-Cox Normality Plot
Date of computationSat, 08 Nov 2008 06:05:01 -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/08/t1226149555mtym3njs04dxg3q.htm/, Retrieved Sat, 18 May 2024 23:30:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=22591, Retrieved Sat, 18 May 2024 23:30:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact187

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Box-Cox Linearity Plot] [Q3 Box-Cox linear...] [2008-11-08 12:51:34] [2d4aec5ed1856c4828162be37be304d9]
F RM D    [Box-Cox Normality Plot] [Q4 Box-Cox normal...] [2008-11-08 13:05:01] [d7f41258beeebb8716e3f5d39f3cdc01] [Current]
Feedback Forum
2008-11-14 13:21:46 [Dana Molenberghs] [reply] 
De box-cox normality plot dient ervoor om een lambda coefficient te zoeken, die van je tijdreeks een normaalverdeling maakt. We hebben hier een optimal lambda op 1,03 wanneer je je data vermenigvuldigd met deze transformatieparameter, kan je een normaalverdeling bekomen.
2008-11-20 13:08:54 [Evelien Blockx] [reply] 
Hier kan je wel duidelijk een optimale Lambda zien.

Dan kan je gaan kijken of de getransformeerde tijdreeks meer naar de normaalverdeling neigt (normaliseert de transformatie de data?).

Het lijkt me dat er vrij weinig verandert is in het histogram en de QQ plot.
2008-11-23 21:35:21 [Isabel Wilms] [reply] 
box-cox normality plot: hier transformeren we ook de tijdreeks. Omdat we eerst geen normaalverdeling hadden en voor sommige tests een normaalverdeling aangewezen is, proberen we de r-code te veranderen zodat we een normaalverdeling krijgen. Hier veranderen we dus niet de x (zoals bij box-cox lineairity plot) maar wel de y gaan we bewerken. Dit wordt dan, ((y tot de macht lambda)-1)/ lambda. Hier zoeken we dan ook het max uit de grafiek, dus de lambdawaarde met de hoogste correlatie. (wanneer deze niet in de grafiek ligt, moet je de grafieklimieten aanpassen). Deze waarde gebruiken we dan om de tijdreeks normaal te maken. De optimale lambdawaarde is hier 1.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
148.8
146.7
118.8
99.4
97.6
110.2
146.6
136.4
126.2
154.9
109
128.5
144.9
136.3
134.8
103.4
106.6
119.2
149.3
150.2
142.9
163.6
98.2
138.2
143.7
132.8
149.4
128.8
98.9
106.2
140.7
133
156.4
157.7
107.9
133.6
148.1
205.6
193.1
117.5
116.4
129.5
157.1
157
158.4
161.7
116.9
161.1
155.7
160.8
145.4
111
144.8
149.2
156.6
182.5
171.3
172.7
133
148.1

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'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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22591&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22591&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22591&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'George Udny Yule' @ 72.249.76.132






Box-Cox Normality Plot
# observations x60
maximum correlation0.383478667658644
optimal lambda1.03

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0.383478667658644 \tabularnewline
optimal lambda & 1.03 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22591&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]60[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.383478667658644[/C][/ROW]
[ROW][C]optimal lambda[/C][C]1.03[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22591&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22591&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:

Box-Cox Normality Plot
# observations x60
maximum correlation0.383478667658644
optimal lambda1.03


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
n <- length(x)
c <- array(NA,dim=c(401))
l <- array(NA,dim=c(401))
mx <- 0
mxli <- -999
for (i in 1:401)
{
l[i] <- (i-201)/100
if (l[i] != 0)
{
x1 <- (x^l[i] - 1) / l[i]
} else {
x1 <- log(x)
}
c[i] <- cor(qnorm(ppoints(x), mean=0, sd=1),x1)
if (mx < c[i])
{
mx <- c[i]
mxli <- l[i]
}
}
c
mx
mxli
if (mxli != 0)
{
x1 <- (x^mxli - 1) / mxli
} else {
x1 <- log(x)
}
bitmap(file='test1.png')
plot(l,c,main='Box-Cox Normality Plot',xlab='Lambda',ylab='correlation')
mtext(paste('Optimal Lambda =',mxli))
grid()
dev.off()
bitmap(file='test2.png')
hist(x,main='Histogram of Original Data',xlab='X',ylab='frequency')
grid()
dev.off()
bitmap(file='test3.png')
hist(x1,main='Histogram of Transformed Data',xlab='X',ylab='frequency')
grid()
dev.off()
bitmap(file='test4.png')
qqnorm(x)
qqline(x)
grid()
mtext('Original Data')
dev.off()
bitmap(file='test5.png')
qqnorm(x1)
qqline(x1)
grid()
mtext('Transformed Data')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Box-Cox Normality Plot',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'# observations x',header=TRUE)
a<-table.element(a,n)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'maximum correlation',header=TRUE)
a<-table.element(a,mx)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'optimal lambda',header=TRUE)
a<-table.element(a,mxli)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')