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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, 19 Oct 2008 08:21:48 -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/19/t1224426228f1kc7zm0pm1xrth.htm/, Retrieved Sat, 18 May 2024 16:49:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16868, Retrieved Sat, 18 May 2024 16:49:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Investigating ass...] [2007-10-22 22:08:56] [8cd6641b921d30ebe00b648d1481bba0]
F R PD    [Pearson Correlation] [werkloosheid] [2008-10-19 14:21:48] [f6a332ba2d530c028d935c5a5bbb53af] [Current]
F    D      [Pearson Correlation] [werkloosheid] [2008-10-19 14:27:27] [d2d412c7f4d35ffbf5ee5ee89db327d4]
F    D        [Pearson Correlation] [werkloosheid] [2008-10-19 14:36:18] [d2d412c7f4d35ffbf5ee5ee89db327d4]
Feedback Forum
2008-10-25 13:35:02 [Stijn Van de Velde] [reply] 
Deze resultaten zijn te verklaren doordat het totale werkloosheid voor de helft bestaat uit de werkloosheid bij mannen. Op die manier is het logisch dat de reeksen zo sterk geassocieerd met elkaar worden.
2008-10-27 23:25:27 [Steven Symons] [reply] 
we hebben een positieve correlatie van 0,9540... We kunnen dus stellen dat de totale werkloosheid voor 95% geassocieerd is met de werkloosheid bij mannen. Je kan dit ook zeer mooi afleiden uit de grafiek, wanneer we een denkbeeldige lijn trekken zien we dat de punten zeer dicht bij de lijn liggen wat duidt op een positieve correlatie

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.4
7.2
7.1
6.9
6.8
6.8
6.8
6.9
6.7
6.6
6.5
6.4
6.3
6.3
6.3
6.5
6.6
6.5
6.4
6.5
6.7
7.1
7.1
7.2
7.2
7.3
7.3
7.3
7.3
7.4
7.6
7.6
7.6
7.7
7.8
7.9
8.1
8.1
8.1
8.2
8.2
8.2
8.2
8.2
8.2
8.3
8.3
8.4
8.4
8.4
8.3
8
8
8.2
8.6
8.7
8.7
8.5
8.4
8.4
8.4
8.5
8.5
8.5
8.5
8.5
8.4
8.4
8.4
8.5
8.6
8.6
8.6
8.6
8.5
8.4
8.4
8.3
8.2
8.1
8.2
8.1
8
7.9
7.8
7.7
7.7
7.9
7.8
7.6
7.4
7.3
7.1
7.1
7
7
7
6.9
6.8
6.7
6.6
6.6
Dataseries Y:
Download CSV
Histogram 
6.2
6.1
5.9
5.6
5.5
5.5
5.6
5.7
5.6
5.4
5.3
5.3
5.4
5.5
5.6
5.7
5.8
5.8
5.7
5.9
6.1
6.4
6.4
6.3
6.2
6.2
6.3
6.5
6.6
6.6
6.7
6.6
6.7
7
7.2
7.3
7.5
7.6
7.7
7.8
7.8
7.7
7.6
7.6
7.7
7.8
7.8
7.8
7.7
7.6
7.4
7.1
7.1
7.3
7.6
7.8
7.7
7.6
7.5
7.5
7.5
7.6
7.6
7.7
7.8
7.7
7.6
7.6
7.6
7.7
7.8
7.8
7.9
7.9
7.8
7.8
7.7
7.5
7.1
6.9
7.1
7.1
7.1
7
6.9
6.8
6.7
6.8
6.8
6.7
6.8
6.7
6.6
6.4
6.4
6.4
6.5
6.5
6.4
6.3
6.2
6.3

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=16868&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=16868&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16868&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
Mean7.664705882352946.85882352941176
Biased Variance0.5342445213379470.616343713956171
Biased Standard Deviation0.730920324890440.78507561034347
Covariance0.552888759464182
Correlation0.954063845612906
Determination0.910237821505687
T-Test31.8442295884809
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom100
Number of Observations102

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 7.66470588235294 & 6.85882352941176 \tabularnewline
Biased Variance & 0.534244521337947 & 0.616343713956171 \tabularnewline
Biased Standard Deviation & 0.73092032489044 & 0.78507561034347 \tabularnewline
Covariance & 0.552888759464182 \tabularnewline
Correlation & 0.954063845612906 \tabularnewline
Determination & 0.910237821505687 \tabularnewline
T-Test & 31.8442295884809 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 100 \tabularnewline
Number of Observations & 102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16868&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]7.66470588235294[/C][C]6.85882352941176[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.534244521337947[/C][C]0.616343713956171[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.73092032489044[/C][C]0.78507561034347[/C][/ROW]
[ROW][C]Covariance[/C][C]0.552888759464182[/C][/ROW]
[ROW][C]Correlation[/C][C]0.954063845612906[/C][/ROW]
[ROW][C]Determination[/C][C]0.910237821505687[/C][/ROW]
[ROW][C]T-Test[/C][C]31.8442295884809[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]100[/C][/ROW]
[ROW][C]Number of Observations[/C][C]102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16868&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16868&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
Mean7.664705882352946.85882352941176
Biased Variance0.5342445213379470.616343713956171
Biased Standard Deviation0.730920324890440.78507561034347
Covariance0.552888759464182
Correlation0.954063845612906
Determination0.910237821505687
T-Test31.8442295884809
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom100
Number of Observations102


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = grey ; par2 = grey ; par3 = TRUE ; par4 = Totaal ; par5 = Metalen prod ;
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')