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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 computationMon, 20 Oct 2008 07:54:43 -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/20/t1224510940vpcu52p5kujctik.htm/, Retrieved Thu, 12 Feb 2026 16:24:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17293, Retrieved Thu, 12 Feb 2026 16:24:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact434

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [werkloosheid mannen] [2008-10-13 15:39:35] [e43247bc0ab243a5af99ac7f55ba0b41]
F RMPD    [Pearson Correlation] [corrolation tijdr...] [2008-10-20 13:54:43] [f24298b2e4c2a19d76cf4460ec5d2246] [Current]
-    D      [Pearson Correlation] [correlatie werklo...] [2008-10-27 11:54:01] [e43247bc0ab243a5af99ac7f55ba0b41]
-    D        [Pearson Correlation] [tijdreeks 1 en 3] [2008-10-27 17:39:06] [e43247bc0ab243a5af99ac7f55ba0b41]
-    D          [Pearson Correlation] [tijdreeks 1 en 4] [2008-10-27 17:41:55] [e43247bc0ab243a5af99ac7f55ba0b41]
-    D          [Pearson Correlation] [tijdreeks 2 en 4] [2008-10-27 17:45:56] [e43247bc0ab243a5af99ac7f55ba0b41]
-    D          [Pearson Correlation] [tijdreeks 3 en 4] [2008-10-27 17:49:24] [e43247bc0ab243a5af99ac7f55ba0b41]
-    D            [Pearson Correlation] [tijdreeks 2 en 3] [2008-10-27 17:52:32] [e43247bc0ab243a5af99ac7f55ba0b41]
Feedback Forum
2008-10-27 17:58:25 [Lindsay Heyndrickx] [reply] 
Hier heb ik volledig foute berekeningen gemaakt. Ik heb hier niet de juiste gegevens ingevoerd en de grafiek klopt helemaal niet. Ik heb hier ook geen uitleg gegeven bij de correlaties.
Bij al deze tijdreeksen is er correlatie maar het is hier niet omdat er correlatie is dat er een verband bestaat tussen de tijdreeksen. Deze correlaties zijn eerder toevallig.
Dit zijn de blogs die ik had moeten maken:
tijdreeks 1 en 2:
http://www.freestatistics.org/blog/date/2008/Oct/27/t1225108512fqoggkizdawzt1g.htm ,
Tijdreeks 1 en 3
http://www.freestatistics.org/blog/date/2008/Oct/27/t1225129193ikw8rk05iprayz5.htm ,
Tijdreeks 1 en 4
http://www.freestatistics.org/blog/date/2008/Oct/27/t12251293581mg0tb30sh90c4j.htm ,
Tijdreeks 2 en 4:
http://www.freestatistics.org/blog/date/2008/Oct/27/t1225129598i6flnxu4240wufq.htm ,
Tijdreeks 3 en 4
http://www.freestatistics.org/blog/date/2008/Oct/27/t1225129823upolwispdlipmms.htm ,
Tijdreeks 2 en 3:
http://www.freestatistics.org/blog/date/2008/Oct/27/t1225130006u452bop81hl0c9r.htm ,
2008-10-27 17:59:11 [Lindsay Heyndrickx] [reply] 
Hier heb ik volledig foute berekeningen gemaakt. Ik heb hier niet de juiste gegevens ingevoerd en de grafiek klopt helemaal niet. Ik heb hier ook geen uitleg gegeven bij de correlaties.
Bij al deze tijdreeksen is er correlatie maar het is hier niet omdat er correlatie is dat er een verband bestaat tussen de tijdreeksen. Deze correlaties zijn eerder toevallig.
Dit zijn de blogs die ik had moeten maken:
tijdreeks 1 en 2:
http://www.freestatistics.org/blog/date/2008/Oct/27/t1225108512fqoggkizdawzt1g.htm ,
Tijdreeks 1 en 3
http://www.freestatistics.org/blog/date/2008/Oct/27/t1225129193ikw8rk05iprayz5.htm ,
Tijdreeks 1 en 4
http://www.freestatistics.org/blog/date/2008/Oct/27/t12251293581mg0tb30sh90c4j.htm ,
Tijdreeks 2 en 4:
http://www.freestatistics.org/blog/date/2008/Oct/27/t1225129598i6flnxu4240wufq.htm ,
Tijdreeks 3 en 4
http://www.freestatistics.org/blog/date/2008/Oct/27/t1225129823upolwispdlipmms.htm ,
Tijdreeks 2 en 3:
http://www.freestatistics.org/blog/date/2008/Oct/27/t1225130006u452bop81hl0c9r.htm ,

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20
40
30
50
60
Dataseries Y:
Download CSV
Histogram 
80
60
10
20
30

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17293&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17293&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17293&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'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean4040
Biased Variance200680
Biased Standard Deviation14.142135623731026.0768096208106
Covariance-225
Correlation-0.488093530091976
Determination0.238235294117647
T-Test-0.968619604501136
p-value (2 sided)0.404182538276366
p-value (1 sided)0.202091269138183
Degrees of Freedom3
Number of Observations5

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 40 & 40 \tabularnewline
Biased Variance & 200 & 680 \tabularnewline
Biased Standard Deviation & 14.1421356237310 & 26.0768096208106 \tabularnewline
Covariance & -225 \tabularnewline
Correlation & -0.488093530091976 \tabularnewline
Determination & 0.238235294117647 \tabularnewline
T-Test & -0.968619604501136 \tabularnewline
p-value (2 sided) & 0.404182538276366 \tabularnewline
p-value (1 sided) & 0.202091269138183 \tabularnewline
Degrees of Freedom & 3 \tabularnewline
Number of Observations & 5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17293&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]40[/C][C]40[/C][/ROW]
[ROW][C]Biased Variance[/C][C]200[/C][C]680[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]14.1421356237310[/C][C]26.0768096208106[/C][/ROW]
[ROW][C]Covariance[/C][C]-225[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.488093530091976[/C][/ROW]
[ROW][C]Determination[/C][C]0.238235294117647[/C][/ROW]
[ROW][C]T-Test[/C][C]-0.968619604501136[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.404182538276366[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.202091269138183[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]3[/C][/ROW]
[ROW][C]Number of Observations[/C][C]5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17293&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17293&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
Mean4040
Biased Variance200680
Biased Standard Deviation14.142135623731026.0768096208106
Covariance-225
Correlation-0.488093530091976
Determination0.238235294117647
T-Test-0.968619604501136
p-value (2 sided)0.404182538276366
p-value (1 sided)0.202091269138183
Degrees of Freedom3
Number of Observations5


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')