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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 15:29:05 -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/t1226442627grpa96cki5jomkn.htm/, Retrieved Mon, 20 May 2024 05:46:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24004, Retrieved Mon, 20 May 2024 05:46:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150

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] [Various EDA topic...] [2008-11-11 22:29:05] [382e90e66f02be5ed86892bdc1574692] [Current]
F RM D    [Partial Correlation] [Various EDA topic...] [2008-11-11 22:49:47] [d32f94eec6fe2d8c421bd223368a5ced]
F RMP       [Trivariate Scatterplots] [Various EDA topic...] [2008-11-11 23:06:10] [d32f94eec6fe2d8c421bd223368a5ced]
F    D    [Box-Cox Normality Plot] [Q4] [2008-11-12 13:48:50] [74be16979710d4c4e7c6647856088456]
F    D    [Box-Cox Normality Plot] [] [2008-11-12 13:51:20] [8d2ae74f923b31b35e9e42977c3c4399]
Feedback Forum
2008-11-21 18:46:48 [Evelien Blockx] [reply] 
Hier is de optimale lambda duidelijk -0,51.
Toch lijkt het dat de transformatie de data niet normaliseert. Het histogram en de Q-Q Plot zijn veranderd door de transformatie, maar ze lijken helemaal geen normaalverdeling te hebben.
2008-11-23 09:37:33 [Inge Meelberghs] [reply] 
In tegenstelling tot de box cox linearity plot zien we hier wel een duidelijk verschil nadat de data getransformeert is. Dit kunnen we waarnemen in zowel de histogram als de Q-Q plot. De optimale lambda waarde bedraagt -0,51. Dit kunnen we ook heel duidelijk zien op de box cox normality plot waar er zich in dat punt een maximum bevind. De data is dus zeker en vast getransformeerd, al heeft dit niet tot een normaalverdeling geleid.
2008-11-23 12:43:34 [Pieter Broos] [reply] 
berekening goed gemaakt, lambda bereikt hier een maximum bij -0.51
2008-11-24 20:42:16 [Dorien Janssens] [reply] 
Q5: De link die hier gegeven werd is niet correct. Hier moest er gebruik gemaakt worden van de 'Maximum-likelihood Normal Distribution Fitting'. http://www.freestatistics.org/blog/date/2008/Nov/23/t12274560019d1kfvdiq8zudlq.htm Hier kunnen we vaststellen dat er geen sprake is van een normaalverdeling.
2008-11-24 21:01:58 [Yara Van Overstraeten] [reply] 
Er wordt hier inderdaad een maximum bereikt bij lambda -0,51, dit bevindt zich ongeveer in het midden van de grafiek, wat ideaal is. Men kan hier dus zeker van een transformatie spreken van de data, maar deze heeft niet geleid tot een normaalverdeling.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
24,67
25,59
26,09
28,37
27,34
24,46
27,46
30,23
32,33
29,87
24,87
25,48
27,28
28,24
29,58
26,95
29,08
28,76
29,59
30,7
30,52
32,67
33,19
37,13
35,54
37,75
41,84
42,94
49,14
44,61
40,22
44,23
45,85
53,38
53,26
51,8
55,3
57,81
63,96
63,77
59,15
56,12
57,42
63,52
61,71
63,01
68,18
72,03
69,75
74,41
74,33
64,24
60,03
59,44
62,5
55,04
58,34
61,92
67,65
67,68

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24004&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24004&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24004&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Box-Cox Normality Plot
# observations x60
maximum correlation0.894762806585675
optimal lambda-0.51

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0.894762806585675 \tabularnewline
optimal lambda & -0.51 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24004&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]0.894762806585675[/C][/ROW]
[ROW][C]optimal lambda[/C][C]-0.51[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24004&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24004&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 correlation0.894762806585675
optimal lambda-0.51


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')