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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, 24 Oct 2008 08:32:43 -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/24/t1224858820yzid2hvnyod2ifo.htm/, Retrieved Fri, 17 May 2024 05:04:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18625, Retrieved Fri, 17 May 2024 05:04:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161

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...] [2007-10-21 16:01:20] [b9964c45117f7aac638ab9056d451faa]
F    D    [Tukey lambda PPCC Plot] [Investigating Dis...] [2008-10-24 14:32:43] [a3db428e3d00990025d790b4cc7b8bfa] [Current]
Feedback Forum
2008-11-02 10:40:46 [e669982111077c8b9a8b032a3ef0fe4b] [reply] 
De student geeft op deze vraag een correct antwoord. We gingen op zoek naar de maximum correlatie die de beste distributie aangeeft. Deze vinden we dus bij de approx. Normal (lambda=0.14) nl. 0,989505916159088, door de tukey lambda ppcc-plot te gebruiken. Hiermee kunnen we de maximale correlatie gaan bekijken.

Voor een normaalverdeling te bekomen mag er geen auto-correlatie optreden en moet er een aselecte kiezing plaatsgevonden hebben.
2008-11-03 18:01:53 [Nathalie Boden] [reply] 
2008-11-03 18:08:35 [Nathalie Boden] [reply] 
De student geeft op deze vraag een goed antwoord. We gaan kijken naar een maximale correlatie. Zij is het grootste bij Approx. Normal = 0.98950591615908
De maximumcorrelatie is rond Lamda=0.14. Om van een normale verdeling te spreken moet er steeds voldaan worden aan volgende voorwaarden namelijk de steekproeven moeten onafhankelijk van elkaar zijn en alle individuen moeten een kans hebben om in de steekproef terecht te komen (m.a.w ze moeten onafhankelijk zijn van elkaar bijgevolg kunnen we besluiten dat er geen sprake is van autocorrelatie.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
110.40
96.40
101.90
106.20
81.00
94.70
101.00
109.40
102.30
90.70
96.20
96.10
106.00
103.10
102.00
104.70
86.00
92.10
106.90
112.60
101.70
92.00
97.40
97.00
105.40
102.70
98.10
104.50
87.40
89.90
109.80
111.70
98.60
96.90
95.10
97.00
112.70
102.90
97.40
111.40
87.40
96.80
114.10
110.30
103.90
101.60
94.60
95.90
104.70
102.80
98.10
113.90
80.90
95.70
113.20
105.90
108.80
102.30
99.00
100.70
115.50

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18625&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18625&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18625&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Tukey Lambda - Key Values
Distribution (lambda)Correlation
Approx. Cauchy (lambda=-1)0.681034394717584
Exact Logistic (lambda=0)0.984820721672163
Approx. Normal (lambda=0.14)0.989505916159088
U-shaped (lambda=0.5)0.985385537255734
Exactly Uniform (lambda=1)0.97511352322751

\begin{tabular}{lllllllll}
\hline
Tukey Lambda - Key Values \tabularnewline
Distribution (lambda) & Correlation \tabularnewline
Approx. Cauchy (lambda=-1) & 0.681034394717584 \tabularnewline
Exact Logistic (lambda=0) & 0.984820721672163 \tabularnewline
Approx. Normal (lambda=0.14) & 0.989505916159088 \tabularnewline
U-shaped (lambda=0.5) & 0.985385537255734 \tabularnewline
Exactly Uniform (lambda=1) & 0.97511352322751 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18625&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]0.681034394717584[/C][/ROW]
[ROW][C]Exact Logistic (lambda=0)[/C][C]0.984820721672163[/C][/ROW]
[ROW][C]Approx. Normal (lambda=0.14)[/C][C]0.989505916159088[/C][/ROW]
[ROW][C]U-shaped (lambda=0.5)[/C][C]0.985385537255734[/C][/ROW]
[ROW][C]Exactly Uniform (lambda=1)[/C][C]0.97511352322751[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18625&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18625&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)0.681034394717584
Exact Logistic (lambda=0)0.984820721672163
Approx. Normal (lambda=0.14)0.989505916159088
U-shaped (lambda=0.5)0.985385537255734
Exactly Uniform (lambda=1)0.97511352322751


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')