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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 11:58:12 -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/t1225130435f099seb4lmshd2i.htm/, Retrieved Thu, 06 Nov 2025 17:04:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=19343, Retrieved Thu, 06 Nov 2025 17:04:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact317

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]
-    D    [Tukey lambda PPCC Plot] [investigating dis...] [2008-10-27 17:58:12] [577b699a0819d2125728ba9ae2c57238] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
58,44
58,96
59,43
60,03
60,47
60,48
60,68
60,77
60,91
60,95
60,95
60,95
60,93
60,93
60,93
60,93
61,8
62,74
62,86
62,86
62,92
62,92
62,92
62,92
62,95
64,17
65,33
65,68
65,97
66,58
66,78
66,83
66,85
66,86
66,86
66,86
66,96
67,66
68,44
68,56
68,65
68,68
68,69
68,71
68,71
68,82
69,75
70,43
70,91
71,47
71,87
72,31
72,56
73,23
73,57
73,72
73,68
73,76
73,76
73,78

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19343&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=19343&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19343&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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132






Tukey Lambda - Key Values
Distribution (lambda)Correlation
Approx. Cauchy (lambda=-1)0.577317610976892
Exact Logistic (lambda=0)0.950961286938421
Approx. Normal (lambda=0.14)0.96721703136645
U-shaped (lambda=0.5)0.984823646182256
Exactly Uniform (lambda=1)0.988698842522769

\begin{tabular}{lllllllll}
\hline
Tukey Lambda - Key Values \tabularnewline
Distribution (lambda) & Correlation \tabularnewline
Approx. Cauchy (lambda=-1) & 0.577317610976892 \tabularnewline
Exact Logistic (lambda=0) & 0.950961286938421 \tabularnewline
Approx. Normal (lambda=0.14) & 0.96721703136645 \tabularnewline
U-shaped (lambda=0.5) & 0.984823646182256 \tabularnewline
Exactly Uniform (lambda=1) & 0.988698842522769 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19343&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]0.577317610976892[/C][/ROW]
[ROW][C]Exact Logistic (lambda=0)[/C][C]0.950961286938421[/C][/ROW]
[ROW][C]Approx. Normal (lambda=0.14)[/C][C]0.96721703136645[/C][/ROW]
[ROW][C]U-shaped (lambda=0.5)[/C][C]0.984823646182256[/C][/ROW]
[ROW][C]Exactly Uniform (lambda=1)[/C][C]0.988698842522769[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=19343&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19343&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)0.577317610976892
Exact Logistic (lambda=0)0.950961286938421
Approx. Normal (lambda=0.14)0.96721703136645
U-shaped (lambda=0.5)0.984823646182256
Exactly Uniform (lambda=1)0.988698842522769


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')