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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_tukeylambda.wasp

Title produced by software

Tukey lambda PPCC Plot

Date of computation

Tue, 20 Dec 2016 13:22:30 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/20/t1482236682kptivwagztvfomc.htm/, Retrieved Thu, 06 Nov 2025 17:41:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301629, Retrieved Thu, 06 Nov 2025 17:41:29 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

234

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Tukey lambda PPCC Plot] [Tukey Lambda resi...] [2016-12-20 12:22:30] [16e0888ced5f28ae20ce1ff74f042113] [Current]

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Dataseries X:

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Histogram

Boxplots

-2.574
-3.04
0.4953
0.9604
-1.04
0.4255
-0.5745
0.9604
-0.03959
0.9604
-4.04
-3.04
1.96
3.426
-0.03959
-1.04
-4.04
-1.04
2.96
3.96
2.96
-3.04
0.9604
-2.04
1.426
0.9604
-2.04
4.96
-1.04
0.9604
-0.5745
-4.04
-0.03959
-1.109
0.9604
-1.04
4.426
0.9604
-3.04
-0.03959
-3.04
0.4255
-5.04
-1.04
-1.04
-2.04
2.96
1.96
1.426
1.96
1.495
-1.505
-0.5745
-2.04
-3.04
-1.04
0.4953
-1.04
-0.03959
-1.04
0.9604
-0.5047
-0.03959
-1.04
-2.109
-0.03959
2.96
0.9604
0.9604
-1.04
-2.04
-0.03959
-2.574
-0.5047
3.96
1.426
3.96
1.96
-2.04
-0.03959
0.4255
-0.03959
-0.03959
-1.04
-2.505
-1.04
0.9604
-1.04
-0.03959
0.9604
-1.04
-0.5047
2.96
0.4953
-1.04
-0.03959
2.495
-6.04
0.9604
-4.04
0.9604
0.9604
-0.03959
0.9604
3.96
-0.03959
4.96
1.96
2.96
3.96
-1.04
-4.04
0.4255
-1.04
-2.04
-1.04
-2.04
-1.04
1.96
-2.04
-0.03959
2.96
-0.03959
-2.04
-0.03959
2.96
-1.04
-3.04
-0.03959
-2.574
2.96
0.4953
-3.574
1.426
1.96
2.96
1.426
-2.04
0.4953
-4.505
-0.5745
2.96
2.96
1.96
0.4953
1.96
1.495
1.426
1.96
0.4255
2.96
-0.03959
-2.04
0.9604
-0.03959
0.9604
-0.03959
-1.04
1.96
-1.04
-0.5047
-1.04
-1.04
0.9604
-0.5745
-0.03959
-1.04
-2.04

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	0 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301629&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

0 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301629&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301629&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	0 seconds
R Server	Big Analytics Cloud Computing Center

Tukey Lambda - Key Values
Distribution (lambda)	Correlation
Approx. Cauchy (lambda=-1)	0.567140320876522
Exact Logistic (lambda=0)	0.990883857786197
Approx. Normal (lambda=0.14)	0.99372469472454
U-shaped (lambda=0.5)	0.983897027345486
Exactly Uniform (lambda=1)	0.970133390067597

\begin{tabular}{lllllllll}
\hline
Tukey Lambda - Key Values \tabularnewline
Distribution (lambda) & Correlation \tabularnewline
Approx. Cauchy (lambda=-1) & 0.567140320876522 \tabularnewline
Exact Logistic (lambda=0) & 0.990883857786197 \tabularnewline
Approx. Normal (lambda=0.14) & 0.99372469472454 \tabularnewline
U-shaped (lambda=0.5) & 0.983897027345486 \tabularnewline
Exactly Uniform (lambda=1) & 0.970133390067597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301629&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]0.567140320876522[/C][/ROW]
[ROW][C]Exact Logistic (lambda=0)[/C][C]0.990883857786197[/C][/ROW]
[ROW][C]Approx. Normal (lambda=0.14)[/C][C]0.99372469472454[/C][/ROW]
[ROW][C]U-shaped (lambda=0.5)[/C][C]0.983897027345486[/C][/ROW]
[ROW][C]Exactly Uniform (lambda=1)[/C][C]0.970133390067597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301629&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301629&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Tukey Lambda - Key Values
Distribution (lambda)	Correlation
Approx. Cauchy (lambda=-1)	0.567140320876522
Exact Logistic (lambda=0)	0.990883857786197
Approx. Normal (lambda=0.14)	0.99372469472454
U-shaped (lambda=0.5)	0.983897027345486
Exactly Uniform (lambda=1)	0.970133390067597

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code