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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 computationSat, 23 Jan 2010 11:59:13 -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/2010/Jan/23/t1264273188gxio3i0vp4y7psw.htm/, Retrieved Thu, 06 Nov 2025 01:23:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72374, Retrieved Thu, 06 Nov 2025 01:23:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact351

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 normality...] [2008-11-11 18:30:54] [12d343c4448a5f9e527bb31caeac580b]
- R  D  [Box-Cox Normality Plot] [VAC Box-Cox Norma...] [2008-12-14 11:10:52] [379d6c32f73e3218fd773d79e4063d07]
-  M D      [Box-Cox Normality Plot] [Box-Cox Linearity...] [2010-01-23 18:59:13] [f32a893c5a60da9308cd5d37e6977c4f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
188.5
188.6
191.9
193.5
194.9
194.9
196.2
196.2
198
198.6
201.3
203.5
204.1
204.8
206.5
207.8
208.6
209.7
210
211.7
212.4
213.7
214.8
216.4
217.5
218.6
220.4
221.8
222.5
223.4
225.5
226.5
227.8
228.5
229.1
229.9
230.8
231.9
236
237.5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72374&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72374&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72374&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Box-Cox Normality Plot
# observations x40
maximum correlation0.985144860474215
optimal lambda1.09

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 40 \tabularnewline
maximum correlation & 0.985144860474215 \tabularnewline
optimal lambda & 1.09 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72374&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]40[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.985144860474215[/C][/ROW]
[ROW][C]optimal lambda[/C][C]1.09[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72374&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72374&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 x40
maximum correlation0.985144860474215
optimal lambda1.09


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')