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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 15:27:23 -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/t1225143107qsjk1qt4pl4d773.htm/, Retrieved Sun, 19 May 2024 14:45:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=19639, Retrieved Sun, 19 May 2024 14:45:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q6 Distributions] [2007-10-22 19:20:42] [b731da8b544846036771bbf9bf2f34ce]
F RM D    [Tukey lambda PPCC Plot] [Q8 investigating ...] [2008-10-27 21:27:23] [02e7fb326979b65614900650d62c19a6] [Current]
Feedback Forum
2008-10-30 11:50:57 [Tamara Witters] [reply] 
je hebt een verkeerde conclusie gemaakt. De autocorrelatie is echter het grootst bij: U-shaped (lambda=0.5) 0.994658757909938
Bijgevolg jouw datareeks heeft geen normaalverdeling.
2008-11-01 17:40:18 [Natascha Meeus] [reply] 
Deze vraag is niet correct opgelost. De autocorrelatie is maximaal bij U-shaped (lambda=0.5) 0.994658757909938 zoals in de weergegeven kader zichtbaar is.
2008-11-03 11:30:57 [Astrid Sniekers] [reply] 
De student heeft een verkeerde conclusie getrokken.
Aan de hand van de grootste correlatie kunnen we al dan niet zeggen of de dataset normaal verdeeld is. De grootste correlatie licht hier rond lambda = 0,5 = U-shaped namelijk 0,994658757909938. We kunnen dus besluiten dat de dataset ‘industrial production’ niet normaal verdeeld is.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
17272.1
19769.9
20038.9
18173.4
16414.3
16938.7
18395.3
17284.5
16457.6
19396.4
16854
16956.1
15467.4
18154.3
17568.6
18063.7
15692.4
15155.4
17396.1
16803.3
15533
19268.2
16247.7
16012.5
16979.9
17504
15130
16677.5
13836.8
13028.1
15937.8
14734.4
14985.2
17197.3
14711.2
13333.7
14931.4
15000.7
14247.9
15525.5
12002.4
12642.6
15620.1
12543.6
13729.7
15456.4
13297.3
12223.3
13174.6
13123.5
13805.7
13816.6
10376.3
11989.9
13121.7
11986.4
12730.9
13687.6
12731.1
12261.6

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=19639&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=19639&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19639&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)0.668091223520502
Exact Logistic (lambda=0)0.982588358857502
Approx. Normal (lambda=0.14)0.99096844325566
U-shaped (lambda=0.5)0.994658757909938
Exactly Uniform (lambda=1)0.990239978667652

\begin{tabular}{lllllllll}
\hline
Tukey Lambda - Key Values \tabularnewline
Distribution (lambda) & Correlation \tabularnewline
Approx. Cauchy (lambda=-1) & 0.668091223520502 \tabularnewline
Exact Logistic (lambda=0) & 0.982588358857502 \tabularnewline
Approx. Normal (lambda=0.14) & 0.99096844325566 \tabularnewline
U-shaped (lambda=0.5) & 0.994658757909938 \tabularnewline
Exactly Uniform (lambda=1) & 0.990239978667652 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19639&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]0.668091223520502[/C][/ROW]
[ROW][C]Exact Logistic (lambda=0)[/C][C]0.982588358857502[/C][/ROW]
[ROW][C]Approx. Normal (lambda=0.14)[/C][C]0.99096844325566[/C][/ROW]
[ROW][C]U-shaped (lambda=0.5)[/C][C]0.994658757909938[/C][/ROW]
[ROW][C]Exactly Uniform (lambda=1)[/C][C]0.990239978667652[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=19639&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19639&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)0.668091223520502
Exact Logistic (lambda=0)0.982588358857502
Approx. Normal (lambda=0.14)0.99096844325566
U-shaped (lambda=0.5)0.994658757909938
Exactly Uniform (lambda=1)0.990239978667652


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')