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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 computationThu, 13 Nov 2008 12:22:02 -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/t1226604164yfi1q38ewspt3a4.htm/, Retrieved Sun, 19 May 2024 12:19:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24786, Retrieved Sun, 19 May 2024 12:19:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBox cox normality
Estimated Impact141

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] [workshop 2 Q4 Box...] [2008-11-13 10:40:54] [47f64d63202c1921bd27f3073f07a153]
F R  D    [Box-Cox Normality Plot] [Box cox normality] [2008-11-13 19:22:02] [962e6c9020896982bc8283b8971710a9] [Current]
Feedback Forum
2008-11-18 08:54:08 [Evelyn Gabriel] [reply] 
De student heeft deze figuur niet besproken. We kunnen duidelijk zien dat er nu een meer lineair verband wordt verkregen tussen de variabelen.
2008-11-20 12:28:19 [Hannes Van Hoof] [reply] 
Op de normal q-q plots is te merken dat de transformatie niet veel wijzigt en ze dus ook niet nuttig is.
2008-11-20 15:29:15 [Gert-Jan Geudens] [reply] 
De berekening is ongeveer idem aan deze van Q4. Al werken we hier nu naar een normaalverdeling toe. De optimale lambda is hier gelijk aan +2 maar de transformatie heeft ook hier weinig nut aangezien de correlatie slechts stijgt van 0.310 naar 0.320.
2008-11-20 17:44:03 [Marie-Lien Loos] [reply] 
Door de transformatie is er een lichte wijziging.
Geen grote verbetering.
2008-11-24 11:26:35 [Anouk Greeve] [reply] 
De verklaring van de student ontbreekt. Wanneer we kunnen spreken van lineariteit in de Normality Plot is er een normale verdeling. De correlatie stijgt echter amper bij de transformatie, dus deze is niet echt van nut.
2008-11-24 18:38:57 [Birgit Van Dyck] [reply] 
de student heeft geen verklaring gegeven. We werken hier toe naar een normaal verdeling. We merken dat de transformatie niet erg nuttig is geweest want er is geen grote wijziging.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
274452
267700
257841
255124
247377
247823
276919
294271
281758
270434
258848
256674
258882
255060
247698
244779
240901
239933
270247
283893
282348
273570
254756
254354
255843
254490
251995
246339
244019
245953
279806
283111
281097
275964
270694
271901
274412
272433
268361
268586
264768
269974
304744
309365
308347
298427
289231
291975
294912
293488
290555
284736
281818
287854
316263
325412
326011
328282
317480
317539
313737
312276
309391
302950
300316
304035
333476
337698
335932
323931
313927
314485
313218
309664
302963
298989
298423
301631
329765
335083
327616
309119
295916
291413
291542
284678
276475
272566
264981
263290
296806
303598
286994
276427
266424
267153
268381
262522
255542
253158
243803
250741
280445
285257

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24786&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24786&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24786&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Box-Cox Normality Plot
# observations x104
maximum correlation0.319914557772642
optimal lambda-2

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 104 \tabularnewline
maximum correlation & 0.319914557772642 \tabularnewline
optimal lambda & -2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24786&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]104[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.319914557772642[/C][/ROW]
[ROW][C]optimal lambda[/C][C]-2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24786&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24786&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 x104
maximum correlation0.319914557772642
optimal lambda-2


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')