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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 computationSat, 16 Oct 2010 15:22:54 +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/16/t1287242534535t9oatc0rpg2s.htm/, Retrieved Sun, 28 Apr 2024 12:08:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=83861, Retrieved Sun, 28 Apr 2024 12:08:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Tukey lambda PPCC Plot] [Intrinsic Motivat...] [2010-10-12 12:09:04] [b98453cac15ba1066b407e146608df68]
F    D    [Tukey lambda PPCC Plot] [Ws 3 - Q3- Intrin...] [2010-10-16 15:22:54] [0829c729852d8a4b1b0c41cf0848af95] [Current]
Feedback Forum
2010-10-24 06:30:02 [6f5a430a34dfbeab884e51a2f2a26434] [reply] 
Je conclusie is goed. Een normaalverdeling is hier van toepassing dit zien we aan de drie grafieken, de histogram en de normaalverdeling lopen ongeveer gelijk, soms kan de histogram er iets bovenuitkomen, maar dit kan veranderen als je het aantal klassen aanpast.

Ook de QQ-plot laat duidelijk zien dat alle punten ongeveer op de rechte liggen, je ziet er inderdaad een paar studenten die niet op de rechte liggen en dus kan men deze als outliers beschouwen.

Maar merk wel op dat de Tukey lambda eerder voor een U-shaped zou gaan dan voor de normaalverdeling, maar aangezien er slechts een klein verschil is in de correlatiewaarden kan men ervan uitgaan dat de normaalverdeling volstaat(aangezien de waarde 0.9947>0.9943).

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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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'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=83861&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=83861&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=83861&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'George Udny Yule' @ 72.249.76.132






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=83861&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=83861&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=83861&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')