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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 13:20:28 -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/t1226607709ywk9dbrb0ch17mp.htm/, Retrieved Sun, 19 May 2024 10:46:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24822, Retrieved Sun, 19 May 2024 10:46:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148

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] [question 3 box-co...] [2008-11-12 15:13:33] [31c9f333c18b3396ccf9d2485dd39c8a]
F RM D    [Box-Cox Normality Plot] [Vincent Dolhain T...] [2008-11-13 20:20:28] [dcb9dbe132bac62365bf3d43fe342148] [Current]
F RMPD      [Maximum-likelihood Fitting - Normal Distribution] [Taak 2 Part 1 Oef5] [2008-11-13 20:29:43] [17bef6922a2795858ae28bf8ba596537]
Feedback Forum
2008-11-20 16:02:32 [Marie-Lien Loos] [reply] 
Methode juist.
Het doel van de box-cox linearity plot is om de data te tranformeren zodat ze normaler verdeeld wordt. Dat is hier duidelijk het geval.
2008-11-24 20:50:53 [Marlies Polfliet] [reply] 
De berekeningen zijn correct, maar er zijn geen conclusies uitgetrokken. De data van de Box-cox normality plot is normaler verdeeld als de box-cox plot, en dat is natuurlijk het doel van deze box- cox normality plot.

Theorie uit het elektronische handboek (aanvullend):
The Box-Cox normality plot is a plot of these correlation coefficients for various values of the lambda parameter. The value of lambda corresponding to the maximum correlation on the plot is then the optimal choice for lambda .
Box-Cox normality plots are formed by:
•Vertical axis: Correlation coefficient from the normal probability plot after applying Box-Cox transformation
Horizontal axis: Value for lambda
2008-11-24 21:25:20 [Erik Geysen] [reply] 
De student heeft geen conclusie gegeven, maar gebruikt de juiste methode.
De Box-cox Normality plot is normaler verdeeld dan de box-cox plot en dit is ook vrij logisch.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
109,86
108,68
113,38
117,12
116,23
114,75
115,81
115,86
117,8
117,11
116,31
118,38
121,57
121,65
124,2
126,12
128,6
128,16
130,12
135,83
138,05
134,99
132,38
128,94
128,12
127,84
132,43
134,13
134,78
133,13
129,08
134,48
132,86
134,08
134,54
134,51
135,97
136,09
139,14
135,63
136,55
138,83
138,84
135,37
132,22
134,75
135,98
136,06
138,05
139,59
140,58
139,81
140,77
140,96
143,59
142,7
145,11
146,7
148,53
148,99
149,65
151,11
154,82
156,56
157,6
155,24
160,68
163,22
164,55
166,76
159,05
159,82
164,95
162,89

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24822&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24822&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24822&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Box-Cox Normality Plot
# observations x74
maximum correlation0.965640752096923
optimal lambda-0.27

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 74 \tabularnewline
maximum correlation & 0.965640752096923 \tabularnewline
optimal lambda & -0.27 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24822&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]74[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.965640752096923[/C][/ROW]
[ROW][C]optimal lambda[/C][C]-0.27[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24822&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24822&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 x74
maximum correlation0.965640752096923
optimal lambda-0.27


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')