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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_tukeylambda.wasp
Title produced by softwareTukey lambda PPCC Plot
Date of computationMon, 27 Oct 2008 14:36:46 -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/t12251398375wowfem0eotj0ne.htm/, Retrieved Tue, 25 Aug 2026 13:46:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=19588, Retrieved Tue, 25 Aug 2026 13:46:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact418

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Tukey lambda PPCC Plot] [Investigating dis...] [2007-10-22 19:59:15] [b9964c45117f7aac638ab9056d451faa]
F    D    [Tukey lambda PPCC Plot] [Q8] [2008-10-27 20:36:46] [84a986a411c52e49a8807521f8b9f7a0] [Current]
Feedback Forum
2008-10-31 21:09:10 [Ruben Jacobs] [reply] 
Correcte berekening en interpretatie. Je kan hier misschien nog verder uitleggen wat deze uitkomst betekent.
2008-11-01 15:09:17 [Stijn Van de Velde] [reply] 
Correct

De hoogste correaltie waarde scheelt echter amper 0.4% met deze van Approx. Normal (lambda=0.14).
We nemen daarom best deze laatste, omdat deze er op duid dat de tijdreeks een normaal verdeling heeft.
2008-11-02 14:47:47 [Ciska Tanghe] [reply] 
Dit antwoord is niet correct. De maximum correlatie ligt niet bij lambda gelijk aan 0, maar wel bij lambda gelijk aan 0,14. Dit wijst op een normaalverdeling.
2008-11-03 18:31:40 [9142cf052ad32d043faa9486189092cf] [reply] 
De student heeft de waardes verkeerd afgelezen de maximumcorrelatie vind je bij Approx. Normal (lambda=0.14)= 0.914850198806278. Dit duidt op een normaalverdeling.

De normaalverdeling heeft een belangrijke rol: namelijk aan de hand van deze normaal verdeling kan je een uitspraak doen over de populatie.
Voorwaarden voor normaal verdeling
*Steekproeven onafhankelijk getrokken
*A-select
2008-11-03 21:03:41 [Chi-Kwong Man] [reply] 
De maximumcorrelatie ligt bij Approx. Normal (lambda=0.14)0.914850198806278 en niet bij lambda=0.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
118,63
121,83
119,97
124,98
129,99
126,60
121,71
119,28
122,63
116,74
114,23
113,23
112,75
113,54
115,30
121,05
119,51
116,78
117,17
117,50
119,65
120,97
117,18
116,87
119,46
122,52
124,10
118,39
113,10
113,94
114,58
118,79
120,44
118,37
118,44
117,93
117,76
118,29
121,11
124,86
131,17
130,16
131,76
134,70
135,32
140,23
136,31
131,62
128,90
133,89
138,21
146,12
144,69
149,18
156,60
158,87
164,85
162,89
153,31
150,91

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=19588&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=19588&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19588&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)0.626424514845301
Exact Logistic (lambda=0)0.910645490522627
Approx. Normal (lambda=0.14)0.914850198806278
U-shaped (lambda=0.5)0.910284968826802
Exactly Uniform (lambda=1)0.89975260841076

\begin{tabular}{lllllllll}
\hline
Tukey Lambda - Key Values \tabularnewline
Distribution (lambda) & Correlation \tabularnewline
Approx. Cauchy (lambda=-1) & 0.626424514845301 \tabularnewline
Exact Logistic (lambda=0) & 0.910645490522627 \tabularnewline
Approx. Normal (lambda=0.14) & 0.914850198806278 \tabularnewline
U-shaped (lambda=0.5) & 0.910284968826802 \tabularnewline
Exactly Uniform (lambda=1) & 0.89975260841076 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19588&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]0.626424514845301[/C][/ROW]
[ROW][C]Exact Logistic (lambda=0)[/C][C]0.910645490522627[/C][/ROW]
[ROW][C]Approx. Normal (lambda=0.14)[/C][C]0.914850198806278[/C][/ROW]
[ROW][C]U-shaped (lambda=0.5)[/C][C]0.910284968826802[/C][/ROW]
[ROW][C]Exactly Uniform (lambda=1)[/C][C]0.89975260841076[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=19588&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19588&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)0.626424514845301
Exact Logistic (lambda=0)0.910645490522627
Approx. Normal (lambda=0.14)0.914850198806278
U-shaped (lambda=0.5)0.910284968826802
Exactly Uniform (lambda=1)0.89975260841076


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')