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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 computationSun, 02 Nov 2008 08:27:31 -0700
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/02/t1225639684q9zk3wx8j0zh7gz.htm/, Retrieved Sun, 19 May 2024 08:46:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=20606, Retrieved Sun, 19 May 2024 08:46:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact170

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] [38f43994ada0e6172896e12525dcc585]
F    D        [Pearson Correlation] [RNR – RCF] [2008-11-01 15:07:17] [38f43994ada0e6172896e12525dcc585]
F   PD            [Pearson Correlation] [RNR – RCF] [2008-11-02 15:27:31] [382e90e66f02be5ed86892bdc1574692] [Current]
Feedback Forum
2008-11-05 19:59:39 [Gert De la Haye] [reply] 
je hebt de juiste oplossing gevonden, ondanks dat je de juiste techniek gebruikt hebt! Maar dit bewijst dat er verschillende manieren zijn om tot de oplossing te komen, hoewel de 'juiste' correlatie 0,80 bedroeg. Maar je hebt er toch al de juiste compinatie uitgepikt!
2008-11-10 12:25:41 [Kim De Vos] [reply] 
Correcte oplossing bekomen door gebruik van een andere techniek.

Kendall tau correlation plot:
Gegevens staan verkeerd -> tabel moet getransponeerd worden in bruikbare tabellen.
Kendall tau corr. plot = veel robuuster voor outliers --> goede maatstaf om outliers te berekenen.
Getallen zeggen niets over de correlatie, maar wel iets over de betrouwbaarheid --> ze moeten liggen onder 0.05
bv. 0.01 ==> zeer betrouwbaar

Uit deze computation stel je vast dat RCF de beste predictor voor RNR met een correlatie van 80,95% en een kleine p-waarde van 0,01.

link: http://www.freestatistics.org/blog/date/2008/Oct/30/t1225367503fss9syamkr4k1b8.htm

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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 
20.8	
17.1	
22.3	
25.1	
27.7	
24.9	
29.5

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=20606&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=20606&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=20606&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






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean4.5428571428571423.9142857142857
Biased Variance20.568163265306115.2355102040816
Biased Standard Deviation4.535213695660453.90326916879705
Covariance19.3042857142857
Correlation0.934718181651295
Determination0.873698079109504
T-Test5.88112912470809
p-value (2 sided)0.00201871267116260
p-value (1 sided)0.00100935633558130
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 & 23.9142857142857 \tabularnewline
Biased Variance & 20.5681632653061 & 15.2355102040816 \tabularnewline
Biased Standard Deviation & 4.53521369566045 & 3.90326916879705 \tabularnewline
Covariance & 19.3042857142857 \tabularnewline
Correlation & 0.934718181651295 \tabularnewline
Determination & 0.873698079109504 \tabularnewline
T-Test & 5.88112912470809 \tabularnewline
p-value (2 sided) & 0.00201871267116260 \tabularnewline
p-value (1 sided) & 0.00100935633558130 \tabularnewline
Degrees of Freedom & 5 \tabularnewline
Number of Observations & 7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=20606&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]23.9142857142857[/C][/ROW]
[ROW][C]Biased Variance[/C][C]20.5681632653061[/C][C]15.2355102040816[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.53521369566045[/C][C]3.90326916879705[/C][/ROW]
[ROW][C]Covariance[/C][C]19.3042857142857[/C][/ROW]
[ROW][C]Correlation[/C][C]0.934718181651295[/C][/ROW]
[ROW][C]Determination[/C][C]0.873698079109504[/C][/ROW]
[ROW][C]T-Test[/C][C]5.88112912470809[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00201871267116260[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00100935633558130[/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=20606&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=20606&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
Mean4.5428571428571423.9142857142857
Biased Variance20.568163265306115.2355102040816
Biased Standard Deviation4.535213695660453.90326916879705
Covariance19.3042857142857
Correlation0.934718181651295
Determination0.873698079109504
T-Test5.88112912470809
p-value (2 sided)0.00201871267116260
p-value (1 sided)0.00100935633558130
Degrees of Freedom5
Number of Observations7


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = TRUE ;
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')