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Author*Unverified author*
R Software Modulerwasp_boxcoxnorm.wasp
Title produced by softwareBox-Cox Normality Plot
Date of computationMon, 24 Feb 2020 22:56:15 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2020/Feb/24/t1582581523l8uymiw9o3tn7rw.htm/, Retrieved Wed, 21 Apr 2021 08:32:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319083, Retrieved Wed, 21 Apr 2021 08:32:42 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact45
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Box-Cox Normality Plot] [] [2020-02-24 21:56:15] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
202485.00
231302.13
227730.77
40384.62
1456659.16
33035.47
53823.15
58371.02
64177.03
22558.09




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319083&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319083&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319083&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 Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Box-Cox Normality Plot
# observations x10
maximum correlation0.981668841261037
optimal lambda-0.5
transformation formulafor all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 10 \tabularnewline
maximum correlation & 0.981668841261037 \tabularnewline
optimal lambda & -0.5 \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=319083&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]10[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.981668841261037[/C][/ROW]
[ROW][C]optimal lambda[/C][C]-0.5[/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=319083&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319083&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 x10
maximum correlation0.981668841261037
optimal lambda-0.5
transformation formulafor all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda







Obs.OriginalTransformed
12024851.99555539093736
2231302.131.9958414667372
3227730.771.99580898574151
440384.621.99004773353814
51456659.161.99834289120019
633035.471.98899627442939
753823.151.99137924227414
858371.021.99172188692317
964177.031.99210521716409
1022558.091.98668384526218

\begin{tabular}{lllllllll}
\hline
Obs. & Original & Transformed \tabularnewline
1 & 202485 & 1.99555539093736 \tabularnewline
2 & 231302.13 & 1.9958414667372 \tabularnewline
3 & 227730.77 & 1.99580898574151 \tabularnewline
4 & 40384.62 & 1.99004773353814 \tabularnewline
5 & 1456659.16 & 1.99834289120019 \tabularnewline
6 & 33035.47 & 1.98899627442939 \tabularnewline
7 & 53823.15 & 1.99137924227414 \tabularnewline
8 & 58371.02 & 1.99172188692317 \tabularnewline
9 & 64177.03 & 1.99210521716409 \tabularnewline
10 & 22558.09 & 1.98668384526218 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319083&T=2

[TABLE]
[ROW][C]Obs.[/C][C]Original[/C][C]Transformed[/C][/ROW]
[ROW][C]1[/C][C]202485[/C][C]1.99555539093736[/C][/ROW]
[ROW][C]2[/C][C]231302.13[/C][C]1.9958414667372[/C][/ROW]
[ROW][C]3[/C][C]227730.77[/C][C]1.99580898574151[/C][/ROW]
[ROW][C]4[/C][C]40384.62[/C][C]1.99004773353814[/C][/ROW]
[ROW][C]5[/C][C]1456659.16[/C][C]1.99834289120019[/C][/ROW]
[ROW][C]6[/C][C]33035.47[/C][C]1.98899627442939[/C][/ROW]
[ROW][C]7[/C][C]53823.15[/C][C]1.99137924227414[/C][/ROW]
[ROW][C]8[/C][C]58371.02[/C][C]1.99172188692317[/C][/ROW]
[ROW][C]9[/C][C]64177.03[/C][C]1.99210521716409[/C][/ROW]
[ROW][C]10[/C][C]22558.09[/C][C]1.98668384526218[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319083&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319083&T=2

As an alternative you can also use a QR Code:  

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

Obs.OriginalTransformed
12024851.99555539093736
2231302.131.9958414667372
3227730.771.99580898574151
440384.621.99004773353814
51456659.161.99834289120019
633035.471.98899627442939
753823.151.99137924227414
858371.021.99172188692317
964177.031.99210521716409
1022558.091.98668384526218







Maximum Likelihood Estimation of Lambda
> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd
x    -0.382           0      -0.9516       0.1876
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df    pval
LR test, lambda = (0) 1.935387  1 0.16417
Likelihood ratio test that no transformation is needed
                           LRT df       pval
LR test, lambda = (1) 26.94696  1 2.0912e-07

\begin{tabular}{lllllllll}
\hline
Maximum Likelihood Estimation of Lambda \tabularnewline
> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd
x    -0.382           0      -0.9516       0.1876
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df    pval
LR test, lambda = (0) 1.935387  1 0.16417
Likelihood ratio test that no transformation is needed
                           LRT df       pval
LR test, lambda = (1) 26.94696  1 2.0912e-07
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=319083&T=3

[TABLE]
[ROW][C]Maximum Likelihood Estimation of Lambda[/C][/ROW]
[ROW][C]
> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd
x    -0.382           0      -0.9516       0.1876
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df    pval
LR test, lambda = (0) 1.935387  1 0.16417
Likelihood ratio test that no transformation is needed
                           LRT df       pval
LR test, lambda = (1) 26.94696  1 2.0912e-07
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319083&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319083&T=3

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 Rounded Pwr Wald Lwr Bnd Wald Upr Bnd
x    -0.382           0      -0.9516       0.1876
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df    pval
LR test, lambda = (0) 1.935387  1 0.16417
Likelihood ratio test that no transformation is needed
                           LRT df       pval
LR test, lambda = (1) 26.94696  1 2.0912e-07



Parameters (Session):
par1 = Full Box-Cox transform ; par2 = -2 ; par3 = 2 ; par4 = 0 ; par5 = Yes ;
Parameters (R input):
par1 = Full Box-Cox transform ; par2 = -2 ; par3 = 2 ; par4 = 0 ; par5 = Yes ;
R code (references can be found in the software module):
par5 <- 'No'
par4 <- '0'
par3 <- '2'
par2 <- '-2'
par1 <- 'Full Box-Cox transform'
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
}
}
print(c)
print(mx)
print(mxli)
print(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')