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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 09:57:14 -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/t1226595484topwjjqob1tgaqt.htm/, Retrieved Sun, 19 May 2024 10:43:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24705, Retrieved Sun, 19 May 2024 10:43:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125

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] [W4Q3] [2008-11-13 16:57:14] [434228f9e3c7eaa307f0fb12855e2147] [Current]
Feedback Forum
2008-11-22 12:33:35 [Sandra Hofmans] [reply] 
Juiste conclusie. Op de x-as van de box-cox normality plot vind je de waarde Lambda (deze varieert van -2 tot 2). De Y-as is de correlatiecoëfficiënt van de getransformeerde X en Y. De waarde van lambda die overeenkomt met de maximale correlatie op de box-cox plot is de optimale keuze van lambda.
2008-11-23 16:04:41 [Peter Van Doninck] [reply] 
De student heeft gelijk dat deze 'transformatie' (de normality plot) beter is als de linearity plot. Toch kan er nog aan toegevoegd worden dat de verkregen transformatie hier niet echt groot is. Echter is het wel belangrijk om te vermelden dat de correlatie nu bijna 1 bedraagt, wat een zeer grote waarde is!

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
111,4
114,1
121,8
127,6
129,9
128,0
123,5
124,0
127,4
127,6
128,4
131,4
135,1
134,0
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
207,0
206,6
210,6
211,1
215,0
223,9
238,2
238,9
229,6
232,2
222,1
221,6
227,3
221,0
213,6
243,4
253,8
265,3
268,2
268,5
266,9
268,4
250,8
231,2
192,0

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=24705&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=24705&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24705&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 correlation0.91486925864712
optimal lambda-1.42

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0.91486925864712 \tabularnewline
optimal lambda & -1.42 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24705&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]0.91486925864712[/C][/ROW]
[ROW][C]optimal lambda[/C][C]-1.42[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24705&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24705&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 correlation0.91486925864712
optimal lambda-1.42


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')