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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 computationThu, 13 Nov 2008 02:23:12 -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/t1226568262uuyzeuu4cczth18.htm/, Retrieved Sun, 19 May 2024 11:15:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24512, Retrieved Sun, 19 May 2024 11:15:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBox Cox Normality plot
Estimated Impact143

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 09:23:12] [3bdbbe597ac6c61989658933956ee6ac] [Current]
Feedback Forum
2008-11-14 15:16:32 [c798c834ef86cb6aaf2fcb10ea683230] [reply] 
Er is slechts een correlatie die maximum 0.194 bedraagt, wat zeer weinig is.
Na transformatie liggen de waarnemingen allemaal zeer dicht bij de rechte op de scatterplot, wat duidt op een normale verdeling. Ook voor de transformatie waren er niet zoveel afwijkingen.
Op het histogram is de transformatie iets duidelijker te zien. Er is nog altijd geen normale verdeling, maar meer dan voor de transformatie.
2008-11-23 16:48:59 [Peter Van Doninck] [reply] 
De correlatie is zeer laag zoals de student aanhaalt. Ze merkt ook correct op dat de gegevens bijna op een rechte liggen en de normaalverdeling zo goed als benaderen. Veder dient aangevuld te worden dat er geen zinvolle transformatie mogelijk is hier omdat we een stijgende rechte hebben! (want de optimale lambda wordt bereikt in het grenspunt)
2008-11-24 14:38:50 [Vincent Dolhain] [reply] 
Omdat de box-cox linearity plot een rechte is, is er dus geen zinnige transformatie. Daardoor heeft de computer als lambda 2 genomen. De transformatie zorgt niet voor grote veranderingen.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
91
120,7
127,9
112,4
93,1
107,5
107,3
114,8
120,8
112,2
123,3
100,6
86,7
123,6
125,3
111,1
98,4
102,3
105
128,2
124,7
116,1
131,2
97,7
88,8
132,8
113,9
112,6
104,3
107,5
106
117,3
123,1
114,3
132
92,3
93,7
121,3
113,6
116,3
98,3
111,9
109,3
133,2
118
131,6
134,1
96,7
99,8
128,3
134,9
130,7
107,3
121,6
120,6
140,5
124,8
129,9
159,4
111
110,1
132,7
135
118,6
94
117,9
114,7
113,6
130,6
117,1
123,2
106,1
87,9

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=24512&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=24512&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24512&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 x73
maximum correlation0.194164627543040
optimal lambda2

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 73 \tabularnewline
maximum correlation & 0.194164627543040 \tabularnewline
optimal lambda & 2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24512&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]73[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.194164627543040[/C][/ROW]
[ROW][C]optimal lambda[/C][C]2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24512&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24512&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 x73
maximum correlation0.194164627543040
optimal lambda2


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')