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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

Thu, 21 Jan 2016 14:05:59 +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/2016/Jan/21/t1453385175rfsid13e7ooqhxz.htm/, Retrieved Mon, 29 Apr 2024 04:41:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=289885, Retrieved Mon, 29 Apr 2024 04:41:30 +0000

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

-       [Box-Cox Normality Plot] [] [2016-01-21 14:05:59] [074449c5cdcdb4dafd7dd3585d12ae02] [Current]

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Histogram

Boxplots

1.4
1.5
1.8
1.8
1.8
1.7
1.5
1.1
1.3
1.6
1.9
1.9
2
2.2
2.2
2
2.3
2.6
3.2
3.2
3.1
2.8
2.3
1.9
1.9
2
2
1.8
1.6
1.4
0.2
0.3
0.4
0.7
1
1.1
0.8
0.8
1
1.1
1
0.8
1.6
1.5
1.6
1.6
1.6
1.9
2
1.9
2
2.1
2.3
2.3
2.6
2.6
2.7
2.6
2.6
2.4
2.5
2.5
2.5
2.4
2.1
2.1
2.3
2.3
2.3
2.9
2.8
2.9
3
3
2.9
2.6
2.8
2.9
3.1
2.8
2.4
1.6
1.5
1.7

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 5 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289885&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289885&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289885&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	5 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Box-Cox Normality Plot
# observations x	84
maximum correlation	0.992613173536299
optimal lambda	1.37
transformation formula	for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 84 \tabularnewline
maximum correlation & 0.992613173536299 \tabularnewline
optimal lambda & 1.37 \tabularnewline
transformation formula & for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289885&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]84[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.992613173536299[/C][/ROW]
[ROW][C]optimal lambda[/C][C]1.37[/C][/ROW]
[ROW][C]transformation formula[/C][C]for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289885&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289885&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	84
maximum correlation	0.992613173536299
optimal lambda	1.37
transformation formula	for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

Maximum Likelihood Estimation of Lambda

> summary(mypT)
bcPower Transformation to Normality 
  Est.Power Std.Err. Wald Lower Bound Wald Upper Bound
x    1.2483   0.2299           0.7977           1.6988
Likelihood ratio tests about transformation parameters
                            LRT df         pval
LR test, lambda = (0) 43.569629  1 4.091394e-11
LR test, lambda = (1)  1.251589  1 2.632493e-01

\begin{tabular}{lllllllll}
\hline
Maximum Likelihood Estimation of Lambda \tabularnewline
> summary(mypT)
bcPower Transformation to Normality 
  Est.Power Std.Err. Wald Lower Bound Wald Upper Bound
x    1.2483   0.2299           0.7977           1.6988
Likelihood ratio tests about transformation parameters
                            LRT df         pval
LR test, lambda = (0) 43.569629  1 4.091394e-11
LR test, lambda = (1)  1.251589  1 2.632493e-01
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289885&T=2

[TABLE]
[ROW][C]Maximum Likelihood Estimation of Lambda[/C][/ROW]
[ROW][C]> summary(mypT)
bcPower Transformation to Normality 
  Est.Power Std.Err. Wald Lower Bound Wald Upper Bound
x    1.2483   0.2299           0.7977           1.6988
Likelihood ratio tests about transformation parameters
                            LRT df         pval
LR test, lambda = (0) 43.569629  1 4.091394e-11
LR test, lambda = (1)  1.251589  1 2.632493e-01
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289885&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289885&T=2

As an alternative you can also use a QR Code:

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

Maximum Likelihood Estimation of Lambda

> summary(mypT)
bcPower Transformation to Normality 
  Est.Power Std.Err. Wald Lower Bound Wald Upper Bound
x    1.2483   0.2299           0.7977           1.6988
Likelihood ratio tests about transformation parameters
                            LRT df         pval
LR test, lambda = (0) 43.569629  1 4.091394e-11
LR test, lambda = (1)  1.251589  1 2.632493e-01

Figure 1

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Postscript link

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Figure 2

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Figure 3

PNG link

Postscript link

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Figure 4

PNG link

Postscript link

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Figure 5

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Full Box-Cox transform ; par2 = -1 ; par3 = 2 ; par4 = 0 ; par5 = No ;

Parameters (R input):

par1 = Full Box-Cox transform ; par2 = -1 ; par3 = 2 ; par4 = 0 ; par5 = No ;

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

library(car)
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),sort(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)
}
mypT <- powerTransform(x)
summary(mypT)
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')
qqPlot(x)
grid()
mtext('Original Data')
dev.off()
bitmap(file='test5.png')
qqPlot(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.row.start(a)
a<-table.element(a,'transformation formula',header=TRUE)
if (par1 == 'Full Box-Cox transform') {
a<-table.element(a,'for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda')
} else {
a<-table.element(a,'for all lambda <> 0 : T(Y) = Y^lambda')
}
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')
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Maximum Likelihood Estimation of Lambda',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('',RC.texteval('summary(mypT)'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')

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Input Parameters & R Code