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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_boxcoxnorm.wasp

Title produced by software

Box-Cox Normality Plot

Date of computation

Tue, 16 Dec 2014 20:25:35 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/16/t1418761561uq1g19wv7d91jvt.htm/, Retrieved Tue, 14 May 2024 11:00:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=269934, Retrieved Tue, 14 May 2024 11:00:37 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

103

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Percentiles] [Intrinsic Motivat...] [2010-10-12 12:10:58] [b98453cac15ba1066b407e146608df68]
- RMPD  [Kernel Density Estimation] [] [2011-10-18 22:42:23] [b98453cac15ba1066b407e146608df68]
- RMPD    [Percentiles] [] [2011-10-18 22:46:45] [b98453cac15ba1066b407e146608df68]
- RMPD      [Notched Boxplots] [] [2011-10-18 22:58:56] [b98453cac15ba1066b407e146608df68]
-    D        [Notched Boxplots] [] [2011-10-18 23:02:48] [b98453cac15ba1066b407e146608df68]
- RMP           [Notched Boxplots] [total motivation ...] [2014-10-16 16:31:11] [673773038936aef3a5778d7e6bda5c1e]
- RMPD              [Box-Cox Normality Plot] [box cox] [2014-12-16 20:25:35] [ec1b40d1a9751af99658fe8fca4f9eca] [Current]

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Dataseries X:

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Histogram

Boxplots

4.3
4.9
5.6
5.7
5.9
6.3
6.4
6.4
6.4
6.7
6.7
7.3
7.4
7.6
7.7
7.7
7.9
7.9
8
8.2
8.3
8.3
8.5
8.6
8.8
8.8
9
9
9.1
9.2
9.3
9.3
9.3
9.6
9.6
9.6
9.7
9.9
9.9
9.9
10
10.1
10.3
10.3
10.3
10.4
10.5
10.6
10.7
10.8
10.8
10.8
10.9
10.9
10.9
11.1
11.1
11.1
11.2
11.3
11.3
11.4
11.4
11.4
11.4
11.4
11.5
11.6
11.6
11.7
11.7
11.8
11.8
11.8
11.9
12
12.1
12.2
12.2
12.3
12.3
12.3
12.5
12.6
12.6
12.6
12.6
12.7
12.7
12.8
12.9
13
13
13
13.2
13.2
13.3
13.3
13.3
13.4
13.4
13.5
13.6
13.8
13.8
14.2
14.3
14.5
14.6
14.8
15.9
16.1

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269934&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269934&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269934&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Box-Cox Normality Plot
# observations x	112
maximum correlation	0.995801174781737
optimal lambda	1.67

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 112 \tabularnewline
maximum correlation & 0.995801174781737 \tabularnewline
optimal lambda & 1.67 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269934&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]112[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.995801174781737[/C][/ROW]
[ROW][C]optimal lambda[/C][C]1.67[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269934&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269934&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Box-Cox Normality Plot
# observations x	112
maximum correlation	0.995801174781737
optimal lambda	1.67

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = Full Box-Cox transform ; par2 = -8 ; par3 = 8 ; par4 = 0 ; par5 = No ;

R code (references can be found in the software module):

par2 <- abs(as.numeric(par2)*100)
par3 <- as.numeric(par3)*100
if(par4=='') par4 <- 0
par4 <- as.numeric(par4)
numlam <- par2 + par3 + 1
x <- x + par4
n <- length(x)
c <- array(NA,dim=c(numlam))
l <- array(NA,dim=c(numlam))
mx <- -1
mxli <- -999
for (i in 1:numlam)
{
l[i] <- (i-par2-1)/100
if (l[i] != 0)
{
if (par1 == 'Full Box-Cox transform') x1 <- (x^l[i] - 1) / l[i]
if (par1 == 'Simple Box-Cox transform') x1 <- x^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]
x1.best <- x1
}
}
c
mx
mxli
x1.best
if (mxli != 0)
{
if (par1 == 'Full Box-Cox transform') x1 <- (x^mxli - 1) / mxli
if (par1 == 'Simple Box-Cox transform') x1 <- x^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)
if(mx<0) {
a<-table.row.start(a)
a<-table.element(a,'Warning: maximum correlation is negative! The Box-Cox transformation must not be used.',2)
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
if(par5=='Yes') {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Obs.',header=T)
a<-table.element(a,'Original',header=T)
a<-table.element(a,'Transformed',header=T)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i)
a<-table.element(a,x[i])
a<-table.element(a,x1.best[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
}

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Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code