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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 02:07:42 -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/t1226394514dm7oibaw4spd9q8.htm/, Retrieved Sun, 19 May 2024 09:45:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=23234, Retrieved Sun, 19 May 2024 09:45:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact215

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Box-Cox Normality Plot] [] [2007-11-01 20:52:37] [74be16979710d4c4e7c6647856088456]
F R  D    [Box-Cox Normality Plot] [box cox normality...] [2008-11-11 09:07:42] [8a2d94dac8ebd598299eaec920908ca6] [Current]
Feedback Forum
2008-11-14 17:53:21 [Kevin Neelen] [reply] 
Als we deze Box-Cox Normality plot bestuderen, kunnen we zien dat het lineaire verband een negatief verband is aangezien de grafiek een dalend verloop kent. Hierdoor komen we tot het besluit dat er een negatieve correlatie is t.o.v. een positieve bij Q3. We zien ook dat de optimale Lambda-waarde -999 bedraagt.
2008-11-17 20:56:59 [Kevin Engels] [reply] 
We zien duidelijk een negatief verband: het antwoord van de student klopt.
2008-11-21 10:01:48 [90714a39acc78a7b2ecd294ecc6b2864] [reply] 
Gezien een bepaalde transformatie zoals de Box-Cox plot van hierboven, is het nuttig om de normaliteit van de resulterende transformatie te bepalen. Ook hier is de maximumwaarde van de lambda de beste keuze. Hier is de optimale lambda gelijk aan -999 en vindt er geen correlatie plaats want die is 0.
Wanneer we kunnen spreken van lineariteit in de Normality Plot is er een normale verdeling.
2008-11-21 11:30:43 [Stijn Van de Velde] [reply] 
Dit antwoord is juist.

De optimale lambda van -999 is naar alle waarschijnlijkheid gewoon het kleinste getal da mogelijk is, want volgens mij blijft de grafiek tot in -oneindig dalen.
2008-11-23 16:21:59 [Karen Van den Broeck] [reply] 
De student zijn uitleg is correct. We kunnen hier duidelijk zien dat het gaat om een negatief verband aangezien de grafiek een dalend verloop heeft.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2,1
2,2
2,2
2,7
3,1
3,2
3,1
3,1
2,8
3
2,8
2,7
3,2
3,1
3
2
1,7
1,2
1,4
1,3
1,3
1,1
0,9
1,2
0,9
1,3
1,4
1,5
1,1
1,6
1,5
1,6
1,7
1,6
1,7
1,6
1,6
1,3
1,1
1,6
1,9
1,6
1,7
1,6
1,4
2,1
1,9
1,7
1,8
2
2,5
2,1
2,1
2,3
2,4
2,4
2,3
1,7
2
2,3

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=23234&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=23234&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23234&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
optimal lambda-999

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 60 \tabularnewline
maximum correlation & 0 \tabularnewline
optimal lambda & -999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=23234&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[/C][/ROW]
[ROW][C]optimal lambda[/C][C]-999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=23234&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=23234&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
optimal lambda-999


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')