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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_tukeylambda.wasp
Title produced by softwareTukey lambda PPCC Plot
Date of computationMon, 27 Oct 2008 03:27:26 -0600
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/Oct/27/t12250997550blwlz4ivekndkc.htm/, Retrieved Sat, 01 Aug 2026 14:19:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=19135, Retrieved Sat, 01 Aug 2026 14:19:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact441

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Explorative Data Analysis] [Investigating dis...] [2007-10-22 19:45:25] [b9964c45117f7aac638ab9056d451faa]
F RMPD    [Tukey lambda PPCC Plot] [Investigating dis...] [2008-10-27 09:27:26] [6aa66640011d9b98524a5838bcf7301d] [Current]
Feedback Forum
2008-10-29 16:15:11 [Nathalie Koulouris] [reply] 
De student heeft hier de juiste methode gebruikt. De correlatiewaarde is inderdaad het hoogst bij exactly uniform
2008-11-02 16:45:18 [Kristof Augustyns] [reply] 
Berekening is juist en het is dus zo dat de correlatie zo dicht mogelijk bij '1' moet liggen om het beste resultaat te verkrijgen.
Hier zie je dat 0.984601687130114 de hoogste correlatie waarde is die bij '1' ligt en dit is inderdaad bij de exactly uniform (lambda = 1)

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
93,5
95,4
101,2
101,5
101,9
101,7
100,1
97,4
96,5
99,2
102,2
105,3
111,1
114,9
124,5
142,2
159,7
165,2
198,6
207,8
219,6
239,6
235,3
218,5
213,8
205,5
198,4
198,5
190,2
180,7
193,6
192,8
195,5
197,2
196,9
178,9
172,4
156,4
143,7
153,6
168,8
185,8
199,9
205,4
197,5
199,6
200,5
193,7
179,6
169,1
169,8
195,5
194,8
204,5
203,8
204,8
204,9
240
248,3
258,4
254,9
288,3
333,6
346,3
357,5
490,7
468,2
471,2
517,1
609,2
682
614

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19135&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]2 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=19135&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19135&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Tukey Lambda - Key Values
Distribution (lambda)Correlation
Approx. Cauchy (lambda=-1)0.660768418511512
Exact Logistic (lambda=0)0.873586921930298
Approx. Normal (lambda=0.14)0.865507147781941
U-shaped (lambda=0.5)0.838278690673534
Exactly Uniform (lambda=1)0.81340488288357

\begin{tabular}{lllllllll}
\hline
Tukey Lambda - Key Values \tabularnewline
Distribution (lambda) & Correlation \tabularnewline
Approx. Cauchy (lambda=-1) & 0.660768418511512 \tabularnewline
Exact Logistic (lambda=0) & 0.873586921930298 \tabularnewline
Approx. Normal (lambda=0.14) & 0.865507147781941 \tabularnewline
U-shaped (lambda=0.5) & 0.838278690673534 \tabularnewline
Exactly Uniform (lambda=1) & 0.81340488288357 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19135&T=1

[TABLE]
[ROW][C]Tukey Lambda - Key Values[/C][/ROW]
[ROW][C]Distribution (lambda)[/C][C]Correlation[/C][/ROW]
[ROW][C]Approx. Cauchy (lambda=-1)[/C][C]0.660768418511512[/C][/ROW]
[ROW][C]Exact Logistic (lambda=0)[/C][C]0.873586921930298[/C][/ROW]
[ROW][C]Approx. Normal (lambda=0.14)[/C][C]0.865507147781941[/C][/ROW]
[ROW][C]U-shaped (lambda=0.5)[/C][C]0.838278690673534[/C][/ROW]
[ROW][C]Exactly Uniform (lambda=1)[/C][C]0.81340488288357[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=19135&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19135&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:

Tukey Lambda - Key Values
Distribution (lambda)Correlation
Approx. Cauchy (lambda=-1)0.660768418511512
Exact Logistic (lambda=0)0.873586921930298
Approx. Normal (lambda=0.14)0.865507147781941
U-shaped (lambda=0.5)0.838278690673534
Exactly Uniform (lambda=1)0.81340488288357


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
gp <- function(lambda, p)
{
(p^lambda-(1-p)^lambda)/lambda
}
sortx <- sort(x)
c <- array(NA,dim=c(201))
for (i in 1:201)
{
if (i != 101) c[i] <- cor(gp(ppoints(x), lambda=(i-101)/100),sortx)
}
bitmap(file='test1.png')
plot((-100:100)/100,c[1:201],xlab='lambda',ylab='correlation',main='PPCC Plot - Tukey lambda')
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Tukey Lambda - Key Values',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Distribution (lambda)',1,TRUE)
a<-table.element(a,'Correlation',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Approx. Cauchy (lambda=-1)',header=TRUE)
a<-table.element(a,c[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Exact Logistic (lambda=0)',header=TRUE)
a<-table.element(a,(c[100]+c[102])/2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Approx. Normal (lambda=0.14)',header=TRUE)
a<-table.element(a,c[115])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'U-shaped (lambda=0.5)',header=TRUE)
a<-table.element(a,c[151])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Exactly Uniform (lambda=1)',header=TRUE)
a<-table.element(a,c[201])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')