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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 14:30:58 -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/t1224534700frrjd2xneuk94vh.htm/, Retrieved Fri, 31 Oct 2025 21:28:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18093, Retrieved Fri, 31 Oct 2025 21:28:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact327

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]
-   PD  [Pearson Correlation] [Correlatie - Vlaa...] [2008-10-19 12:38:17] [46c5a5fbda57fdfa1d4ef48658f82a0c]
-   PD      [Pearson Correlation] [Correlatie Consum...] [2008-10-20 20:30:58] [96c9291ce335a5c9abba7b920811c2df] [Current]
-    D        [Pearson Correlation] [Correlatie Fin. S...] [2008-10-20 20:35:16] [70cb582895831af4be81fec73c607e93]
-    D          [Pearson Correlation] [Correlatie consum...] [2008-10-20 20:39:41] [70cb582895831af4be81fec73c607e93]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6
4
2
0
4
4
4
7
4
6
5
8
9
8
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9
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9
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10
6
8
9
9
8
9
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12
11
10
13
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9
Dataseries Y:
Download CSV
Histogram 
11
9
7
9
11
13
17
17
14
16
12
19
18
18
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21
22
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6
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5

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'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18093&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18093&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18093&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean9.3666666666666715.2833333333333
Biased Variance8.4322222222222217.1030555555556
Biased Standard Deviation2.903828889969624.13558406462202
Covariance6.64011299435028
Correlation0.543711296320194
Determination0.295621973746186
T-Test4.93377628659360
p-value (2 sided)7.13694118692487e-06
p-value (1 sided)3.56847059346244e-06
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 9.36666666666667 & 15.2833333333333 \tabularnewline
Biased Variance & 8.43222222222222 & 17.1030555555556 \tabularnewline
Biased Standard Deviation & 2.90382888996962 & 4.13558406462202 \tabularnewline
Covariance & 6.64011299435028 \tabularnewline
Correlation & 0.543711296320194 \tabularnewline
Determination & 0.295621973746186 \tabularnewline
T-Test & 4.93377628659360 \tabularnewline
p-value (2 sided) & 7.13694118692487e-06 \tabularnewline
p-value (1 sided) & 3.56847059346244e-06 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18093&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]9.36666666666667[/C][C]15.2833333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]8.43222222222222[/C][C]17.1030555555556[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.90382888996962[/C][C]4.13558406462202[/C][/ROW]
[ROW][C]Covariance[/C][C]6.64011299435028[/C][/ROW]
[ROW][C]Correlation[/C][C]0.543711296320194[/C][/ROW]
[ROW][C]Determination[/C][C]0.295621973746186[/C][/ROW]
[ROW][C]T-Test[/C][C]4.93377628659360[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]7.13694118692487e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]3.56847059346244e-06[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]58[/C][/ROW]
[ROW][C]Number of Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18093&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18093&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
Mean9.3666666666666715.2833333333333
Biased Variance8.4322222222222217.1030555555556
Biased Standard Deviation2.903828889969624.13558406462202
Covariance6.64011299435028
Correlation0.543711296320194
Determination0.295621973746186
T-Test4.93377628659360
p-value (2 sided)7.13694118692487e-06
p-value (1 sided)3.56847059346244e-06
Degrees of Freedom58
Number of Observations60


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')