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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 computationTue, 11 Nov 2008 08:25:03 -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/11/t1226417139g5tijooruup2cwn.htm/, Retrieved Sun, 19 May 2024 12:02:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23594, Retrieved Sun, 19 May 2024 12:02:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

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] [2008-11-11 15:25:03] [8758b22b4a10c08c31202f233362e983] [Current]
Feedback Forum
2008-11-19 20:49:54 [Nathalie Koulouris] [reply] 
De student heeft de correcte berekeningsmethode gebruikt maar niet verder gemotiveerd.
2008-11-21 16:07:19 [Matthieu Blondeau] [reply] 
Er is toch wel een grote afwijking terug te vinden in de grafiek met transformed data. In de originele data kan men een normaalverdeling terug vinden. Dit is niet meer het geval bij de transformed data.
2008-11-23 16:57:46 [Michaël De Kuyer] [reply] 
Bij deze methode probeert men de data zodaning te transformeren dat men een meer normale verdeling krijgt. Aan de QQ-plots ziet men echter dat de transformatie niet veel invloed heeft op de verdeling van de tijdreeks. Dit is omdat de QQ-plots sterk overeen komen.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3202,1
3650,2
2805,1
3957,5
3941,3
3905,4
3546,9
3208,7
3402
3661,1
3073,9
3419,2
3532,8
3693,1
2622,9
3130,8
3487,5
3349,7
3044,2
3266
3351,5
3606,8
3419,5
3829,5
3505,1
3845,3
2566,6
3658,5
3954
3460,1
3454,1
3412,8
3418
3349,5
3423,4
3242,8
3277,2
3833
2606,3
3643,8
3686,4
3281,6
3669,3
3191,5
3512,7
3970,7
3601,2
3610
4172,1
3956,2
3142,7
3884,3
3892,2
3613
3730,5
3481,3
3649,5
4215,2
4066,6
4196,8
4536,6
4441,6
3548,3
4735,9
4130,6
4356,2
4159,6
3988
4167,8
4902,2
3909,4
4697,6
4308,9
4420,4
3544,2
4433
4479,7
4533,2
4237,5
4207,4
4394
5148,4
4202,2
4682,5
4884,3
5288,9
4505,2
4611,5
5081,1
4523,1
4412,8
4647,4
4778,6
4495,3
4633,5
4360,5
4517,9

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 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=23594&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]4 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=23594&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23594&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Box-Cox Normality Plot
# observations x97
maximum correlation0.731971785175401
optimal lambda2

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 97 \tabularnewline
maximum correlation & 0.731971785175401 \tabularnewline
optimal lambda & 2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23594&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]97[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.731971785175401[/C][/ROW]
[ROW][C]optimal lambda[/C][C]2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23594&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23594&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 x97
maximum correlation0.731971785175401
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')