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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 02:47:09 -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/t1226569696cc4jmqlbqc574nu.htm/, Retrieved Sun, 19 May 2024 09:17:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24524, Retrieved Sun, 19 May 2024 09:17:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149

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 normal] [2008-11-12 20:29:20] [7a664918911e34206ce9d0436dd7c1c8]
F    D    [Box-Cox Normality Plot] [] [2008-11-13 09:47:09] [8767719db498704e1fee27044c098ad0] [Current]
Feedback Forum
2008-11-20 14:09:27 [6066575aa30c0611e452e930b1dff53d] [reply] 
Hier werd geen uitleg bij gegeven. De optimale lambda bedraagt hier -1,94. De correlatie bedraagt bij deze lambda 14%.
2008-11-20 16:37:34 [Gert-Jan Geudens] [reply] 
Geen conclusie. De transformatie werkt hier hetzelfde als bij q3. Enkel werken we hier nu naar een normaalverdeling toe. De optimale lambda is hier -1.94. Deze transformatie is van minimaal nut aangezien de correlatie tussen beide variabelen slechts stijgt van 0.05 naar 0.14. We zien dan ook uit de histogrammen dat er nog steeds geen echte normaalverdeling te zien is.
2008-11-24 20:23:30 [4679c4d03f1d346a85e79d87ba60ec2b] [reply] 
Er wordt hier geen conclusie gegeven. De correlatie stijgt inderdaad niet veel. Er kan dus ook hier gezegd worden dat er geen verbetering ontstaat en dit is ook terug te vinden in de histogrammen en de normal Q-Q plot.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
45
24
18
20
22
39
55
35
38
47
1
57
50
33
19
2
7
15
56
53
24
48
2
49
46
32
37
10
8
16
55
46
46
45
6
45
52
44
35
15
44
51
58
23
44
43
6
51
53
47
19
18
38
43
23
43
18
43
6
31
49

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=24524&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=24524&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24524&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 x61
maximum correlation0.141983425082117
optimal lambda-1.94

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 61 \tabularnewline
maximum correlation & 0.141983425082117 \tabularnewline
optimal lambda & -1.94 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24524&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]61[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.141983425082117[/C][/ROW]
[ROW][C]optimal lambda[/C][C]-1.94[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24524&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24524&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 x61
maximum correlation0.141983425082117
optimal lambda-1.94


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')