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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 computationWed, 12 Nov 2008 10:53:57 -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/12/t1226512468q3pzsercyugitxq.htm/, Retrieved Sun, 19 May 2024 08:50:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24328, Retrieved Sun, 19 May 2024 08:50:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Kernel Density Estimation] [Bel20 en Downjones] [2008-11-12 17:23:23] [74be16979710d4c4e7c6647856088456]
F RMPD    [Box-Cox Normality Plot] [kelly] [2008-11-12 17:53:57] [d41d8cd98f00b204e9800998ecf8427e] [Current]
F    D      [Box-Cox Normality Plot] [Box cox normality...] [2008-11-13 22:31:24] [74be16979710d4c4e7c6647856088456]
Feedback Forum
2008-11-15 14:06:14 [Hundra Smet] [reply] 
Theorie: The Box-Cox normality plot is a plot of these correlation coefficients
for various values of the parameter. The value of corresponding
to the maximum correlation on the plot is then the optimal choice for lambda.
de optimale keuze voor lambda is bij de student -2.

ook hier zien we op de getransfomeerde plots niet echt een verschil met die van de originele.

dit zien we zowel in plots, staafdiagrammen en tabel.
2008-11-16 15:21:00 [074508d5a5a3592082de3e836d27af7d] [reply] 
Ik zie wel een verschil met de originele plot. Op de scatterplot lijkt het of de transformatie de correlatie alleen maar heeft verslechterd. Dit kan je zien aan de bolletjes die nog verder van de lijn liggen.
2008-11-20 10:36:50 [Hannes Van Hoof] [reply] 
De transformatie heeft niet veel veranderd aan de originele data, dit is duidelijk te zien op de normal q-q plots.
2008-11-24 21:03:23 [Jonas Scheltjens] [reply] 
Q4: De student geeft de normal Q-Q plots. Deze werden echter niet gevraagd. Ook hier werd geen uitleg bij gezet. De Box-Cox normality plot kent hier een dalende verloop, in tegenstelling tot in Q3. Net zoals in Q3 tracht de lijn in de plot de gegevens in een wetmatigheid te gieten. In deze module wordt getracht na te gaan of de gegevens al dan niet normaal verdeeld zijn. De werking van deze plot is analoog aan deze van de box-cox linearity plot. Het verschil zit in het feit dat de normality plot de normaal verdeling onderzoekt en de linearity plot het lineair verband.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2174,56
2196,72
2350,44
2440,25
2408,64
2472,81
2407,6
2454,62
2448,05
2497,84
2645,64
2756,76
2849,27
2921,44
2981,85
3080,58
3106,22
3119,31
3061,26
3097,31
3161,69
3257,16
3277,01
3295,32
3363,99
3494,17
3667,03
3813,06
3917,96
3895,51
3801,06
3570,12
3701,61
3862,27
3970,1
4138,52
4199,75
4290,89
4443,91
4502,64
4356,98
4591,27
4696,96
4621,4
4562,84
4202,52
4296,49
4435,23
4105,18
4116,68
3844,49
3720,98
3674,4
3857,62
3801,06
3504,37
3032,6
3047,03
2962,34
2197,82

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 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=24328&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]5 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=24328&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24328&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 time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Box-Cox Normality Plot
# observations x60
maximum correlation0.594934429878129
optimal lambda-1.41

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0.594934429878129 \tabularnewline
optimal lambda & -1.41 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24328&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]0.594934429878129[/C][/ROW]
[ROW][C]optimal lambda[/C][C]-1.41[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24328&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24328&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 correlation0.594934429878129
optimal lambda-1.41


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')