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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationSat, 01 Nov 2008 09:02:44 -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/Nov/01/t1225551929y9cg8pdba4lf3wj.htm/, Retrieved Mon, 20 May 2024 11:40:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=20427, Retrieved Mon, 20 May 2024 11:40:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact204

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Mean Plot] [workshop 3] [2007-10-26 12:14:28] [e9ffc5de6f8a7be62f22b142b5b6b1a8]
F    D  [Mean Plot] [Hypothesis Testin...] [2008-10-30 12:52:34] [38f43994ada0e6172896e12525dcc585]
F   P     [Mean Plot] [Hypothesis Testin...] [2008-10-30 13:25:08] [38f43994ada0e6172896e12525dcc585]
F RMPD        [Pearson Correlation] [RNR - RNVM] [2008-11-01 15:02:44] [284c7cdb9fcda2adcbb08e211682c8d6] [Current]
F    D          [Pearson Correlation] [RNR – RCF] [2008-11-01 15:07:17] [38f43994ada0e6172896e12525dcc585]
-    D            [Pearson Correlation] [RNR – RLEZ] [2008-11-01 15:11:08] [38f43994ada0e6172896e12525dcc585]
-    D              [Pearson Correlation] [RNR – REV] [2008-11-01 15:15:26] [38f43994ada0e6172896e12525dcc585]
-   PD                [Pearson Correlation] [RNR – REV] [2008-11-02 15:32:16] [d32f94eec6fe2d8c421bd223368a5ced]
-   PD              [Pearson Correlation] [RNR – RLEZ] [2008-11-02 15:30:09] [d32f94eec6fe2d8c421bd223368a5ced]
F   PD            [Pearson Correlation] [RNR – RCF] [2008-11-02 15:27:31] [d32f94eec6fe2d8c421bd223368a5ced]
F   PD          [Pearson Correlation] [RNR - RNVM] [2008-11-02 15:24:58] [d32f94eec6fe2d8c421bd223368a5ced]
Feedback Forum
2008-11-09 14:48:41 [Nathalie Boden] [reply] 
De student heeft hier de verkeerde methode toegepast. We maken hier gebruik van om de Kendaal Tau Methode toe te passen. Het resultaat van deze methode bekom je op de onderstaande link:
http://www.freestatistics.org/blog/index.php?v=date/2008/Nov/02/t1225635822wnjya2sqclvdubd.htm

Zo zien we dat we in de bovenstaande tabel het volgende resultaat gaan nemen:
tau( RNR , RCF ) 0.80952380952381 0.0107142857142857

We zien dat het geen correlatiecoëfficiënt maar de betrouwbaarheid. Hoe kleiner= hoe beter en hoe groter= hoe meer toevallig. We merken op dat 0,01 de laagste waarde is, er is dus 1% kans dat de correlatie te wijten is aan toeval tussen RNR en RCF. We kunnen besluiten dat de cashflow de best gecorreleerde is.
2008-11-10 13:01:50 [Pieter Broos] [reply] 
Pearson Correlation vraagt in dit geval teveel tijd, we kunnen beter de Kendall Tau correlation matrix gebruiken.
In de Kendall Tau ( http://www.freestatistics.org/blog/date/2008/Nov/02/t1225636082etnjgpn3i90ytvk.htm ) zoeken we naar de hoogste tau waarden (= hoogste correlatie) en de kleinste p-value, deze p-value geeft ons hoe betrouwbaar de correlatie is, hoe kleiner de p-value hoe betrouwbaarder de correlatie.
2008-11-11 10:57:13 [Kevin Engels] [reply] 
De kendall Tau methode is hier het beste aangewezen om deze vraag op te lossen. Het resultaat wordt dan robuust voor outliers en een goede maatstaf om correlaties te berekenen.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4,8	
-4,2	
1,6	
5,2	
9,2	
4,6	
10,6
Dataseries Y:
Download CSV
Histogram 
4,2	
2,6	
3	
3,8	
4	
3,5	
4,1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=20427&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]4 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=20427&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=20427&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean4.542857142857143.6
Biased Variance20.56816326530610.311428571428571
Biased Standard Deviation4.535213695660450.55805785670356
Covariance2.61333333333333
Correlation0.885056581705508
Determination0.783325152820238
T-Test4.25159403195624
p-value (2 sided)0.00807948566831929
p-value (1 sided)0.00403974283415964
Degrees of Freedom5
Number of Observations7

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 4.54285714285714 & 3.6 \tabularnewline
Biased Variance & 20.5681632653061 & 0.311428571428571 \tabularnewline
Biased Standard Deviation & 4.53521369566045 & 0.55805785670356 \tabularnewline
Covariance & 2.61333333333333 \tabularnewline
Correlation & 0.885056581705508 \tabularnewline
Determination & 0.783325152820238 \tabularnewline
T-Test & 4.25159403195624 \tabularnewline
p-value (2 sided) & 0.00807948566831929 \tabularnewline
p-value (1 sided) & 0.00403974283415964 \tabularnewline
Degrees of Freedom & 5 \tabularnewline
Number of Observations & 7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=20427&T=1

[TABLE]
[ROW][C]Pearson Product Moment Correlation - Ungrouped Data[/C][/ROW]
[ROW][C]Statistic[/C][C]Variable X[/C][C]Variable Y[/C][/ROW]
[ROW][C]Mean[/C][C]4.54285714285714[/C][C]3.6[/C][/ROW]
[ROW][C]Biased Variance[/C][C]20.5681632653061[/C][C]0.311428571428571[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.53521369566045[/C][C]0.55805785670356[/C][/ROW]
[ROW][C]Covariance[/C][C]2.61333333333333[/C][/ROW]
[ROW][C]Correlation[/C][C]0.885056581705508[/C][/ROW]
[ROW][C]Determination[/C][C]0.783325152820238[/C][/ROW]
[ROW][C]T-Test[/C][C]4.25159403195624[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00807948566831929[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00403974283415964[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]5[/C][/ROW]
[ROW][C]Number of Observations[/C][C]7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=20427&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=20427&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:

Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean4.542857142857143.6
Biased Variance20.56816326530610.311428571428571
Biased Standard Deviation4.535213695660450.55805785670356
Covariance2.61333333333333
Correlation0.885056581705508
Determination0.783325152820238
T-Test4.25159403195624
p-value (2 sided)0.00807948566831929
p-value (1 sided)0.00403974283415964
Degrees of Freedom5
Number of Observations7


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
bitmap(file='test1.png')
histx <- hist(x, plot=FALSE)
histy <- hist(y, plot=FALSE)
maxcounts <- max(c(histx$counts, histx$counts))
xrange <- c(min(x),max(x))
yrange <- c(min(y),max(y))
nf <- layout(matrix(c(2,0,1,3),2,2,byrow=TRUE), c(3,1), c(1,3), TRUE)
par(mar=c(4,4,1,1))
plot(x, y, xlim=xrange, ylim=yrange, xlab=xlab, ylab=ylab)
par(mar=c(0,4,1,1))
barplot(histx$counts, axes=FALSE, ylim=c(0, maxcounts), space=0)
par(mar=c(4,0,1,1))
barplot(histy$counts, axes=FALSE, xlim=c(0, maxcounts), space=0, horiz=TRUE)
dev.off()
lx = length(x)
makebiased = (lx-1)/lx
varx = var(x)*makebiased
vary = var(y)*makebiased
corxy <- cor.test(x,y,method='pearson')
cxy <- as.matrix(corxy$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm','Mean',''),header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased.htm','Biased Variance',''),header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased1.htm','Biased Standard Deviation',''),header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('covariance.htm','Covariance',''),header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('pearson_correlation.htm','Correlation',''),header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('coeff_of_determination.htm','Determination',''),header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ttest_statistic.htm','T-Test',''),header=TRUE)
a<-table.element(a,as.matrix(corxy$statistic)[1,1],2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (2 sided)',header=TRUE)
a<-table.element(a,(p2 <- as.matrix(corxy$p.value)[1,1]),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (1 sided)',header=TRUE)
a<-table.element(a,p2/2,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degrees of Freedom',header=TRUE)
a<-table.element(a,lx-2,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of Observations',header=TRUE)
a<-table.element(a,lx,2)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')