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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 computationFri, 15 Oct 2010 17:01:05 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/15/t1287162021lfu63422g761l7s.htm/, Retrieved Sun, 09 Nov 2025 02:13:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=83616, Retrieved Sun, 09 Nov 2025 02:13:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact553

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Percentiles] [Intrinsic Motivat...] [2010-10-12 12:10:58] [b98453cac15ba1066b407e146608df68]
- RM D    [Tukey lambda PPCC Plot] [Tukey-lambda: Int...] [2010-10-15 17:01:05] [985dc1be4332e19cbfb874db0b8f53d7] [Current]
- RM D      [Cronbach Alpha] [Cronbach Alpha - ...] [2010-12-12 15:12:27] [3cdf9c5e1f396891d2638627ccb7b98d]
- RM D      [Cronbach Alpha] [Cronbach Alpha - ...] [2010-12-12 15:22:42] [3cdf9c5e1f396891d2638627ccb7b98d]
- RM D      [Cronbach Alpha] [Cronbach Alpha - ...] [2010-12-12 15:33:24] [3cdf9c5e1f396891d2638627ccb7b98d]
-    D        [Cronbach Alpha] [Cronbach Alpha - ...] [2010-12-16 16:28:52] [3cdf9c5e1f396891d2638627ccb7b98d]
-    D        [Cronbach Alpha] [Cronbach Alpha - ...] [2010-12-16 16:38:21] [74be16979710d4c4e7c6647856088456]
-    D        [Cronbach Alpha] [Cronbach Alpha - ...] [2010-12-16 16:38:21] [3cdf9c5e1f396891d2638627ccb7b98d]
- R         [Tukey lambda PPCC Plot] [WS3.3] [2011-10-18 14:15:31] [9b13650c94c5192ca5135ec8a1fa39f7]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21
16
19
18
16
23
17
12
19
16
19
20
13
20
27
17
8
25
26
13
19
15
5
16
14
24
24
9
19
19
25
19
18
15
12
21
12
15
28
25
19
20
24
26
25
12
12
15
17
14
16
11
20
11
22
20
19
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17
27
25
19
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24
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19
11
22
22
16
20
24
16
16
22
24
16
27
11
21
20
20
27
20
12
8
21
18
24
16
18
20
20
19
17
16
26
15
22
17
23
21
19
14
17
12
24
18
20
16
20
22
12
16
17
22
12
14
23
15
17
28
20
23
13
18
23
19
23
12
16
23
13
22
18
23
20
10
17
18
15
23
17
17
22
20
20
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22
18
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16
16
17
18

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=83616&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=83616&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=83616&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Tukey Lambda - Key Values
Distribution (lambda)Correlation
Approx. Cauchy (lambda=-1)0.56242445502817
Exact Logistic (lambda=0)0.989690695953362
Approx. Normal (lambda=0.14)0.994220675676583
U-shaped (lambda=0.5)0.987562176002712
Exactly Uniform (lambda=1)0.975815658147389

\begin{tabular}{lllllllll}
\hline
Tukey Lambda - Key Values \tabularnewline
Distribution (lambda) & Correlation \tabularnewline
Approx. Cauchy (lambda=-1) & 0.56242445502817 \tabularnewline
Exact Logistic (lambda=0) & 0.989690695953362 \tabularnewline
Approx. Normal (lambda=0.14) & 0.994220675676583 \tabularnewline
U-shaped (lambda=0.5) & 0.987562176002712 \tabularnewline
Exactly Uniform (lambda=1) & 0.975815658147389 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=83616&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]0.56242445502817[/C][/ROW]
[ROW][C]Exact Logistic (lambda=0)[/C][C]0.989690695953362[/C][/ROW]
[ROW][C]Approx. Normal (lambda=0.14)[/C][C]0.994220675676583[/C][/ROW]
[ROW][C]U-shaped (lambda=0.5)[/C][C]0.987562176002712[/C][/ROW]
[ROW][C]Exactly Uniform (lambda=1)[/C][C]0.975815658147389[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=83616&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=83616&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)0.56242445502817
Exact Logistic (lambda=0)0.989690695953362
Approx. Normal (lambda=0.14)0.994220675676583
U-shaped (lambda=0.5)0.987562176002712
Exactly Uniform (lambda=1)0.975815658147389


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')