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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_boxcoxnorm.wasp
Title produced by softwareBox-Cox Normality Plot
Date of computationThu, 13 Nov 2008 15:07:18 -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/13/t122661407871s6oppnfeh6i7c.htm/, Retrieved Mon, 20 May 2024 11:17:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24862, Retrieved Mon, 20 May 2024 11:17:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161

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 Normality Plot] [Box-Cox Normality...] [2008-11-13 22:07:18] [6af198e0108e278de39b2b3c538c1a2b] [Current]
Feedback Forum
2008-11-16 13:08:33 [Nicolaj Wuyts] [reply] 
We zien dat er bij gebruik van de Box-Cox normality plot een klein verschil te merken is ten opzichte van de originele grafiek. Vooral de onderste waarden liggen nu iets korter naar de grafiek toe. We kunnen dus stellen dat de normality plot een grotere invloed heeft dan de linearity plot.
2008-11-16 15:28:29 [Julie Govaerts] [reply] 
deze soort plot heeft veel weg van de box cox linearity plot maar nu gaan we nagaan of de correlatie tussen de 2 variabelen normaal verdeeld is

de transformatie heeft ook dit keer weer niet veel veranderd
2008-11-22 13:18:37 [Gilliam Schoorel] [reply] 
De box-cox normality plot is een transformatie om de normaalverdeling van de tijdreeks te verbeteren. De maximum lambda die bereikt moet worden is -0,83. Je kan op de plot zien dat deze ook bereikt is geweest. Op de QQ-plots zie je ook dat deze transformatie niet echt veel nut heeft gehad en er niet veel verschil merkbaar is in de correlatie.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
93
87
89
91
108
124
104
107
116
70
126
119
102
88
71
76
84
125
122
93
117
71
118
115
101
106
79
77
85
124
115
115
114
75
114
121
113
104
84
113
120
127
92
113
112
75
120
122
116
88
87
107
112
92
112
87
112
75
100
118

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=24862&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=24862&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24862&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






Box-Cox Normality Plot
# observations x60
maximum correlation0.099012144668132
optimal lambda-0.83

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0.099012144668132 \tabularnewline
optimal lambda & -0.83 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24862&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]0.099012144668132[/C][/ROW]
[ROW][C]optimal lambda[/C][C]-0.83[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24862&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24862&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 correlation0.099012144668132
optimal lambda-0.83


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')