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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_correlation.wasp

Title produced by software

Pearson Correlation

Date of computation

Sun, 06 Dec 2009 02:48:28 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/06/t1260093009e1hs2a472evgu3h.htm/, Retrieved Sun, 05 May 2024 20:53:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64326, Retrieved Sun, 05 May 2024 20:53:10 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

156

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Pearson Correlation] [Correlatie] [2009-12-06 09:48:28] [87085ce7f5378f281469a8b1f0969170] [Current]

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Dataseries X:

Download CSV

Histogram

Boxplots

3,9
3,6
3,3
3,2
3,4
3,4
3,5
3,2
3,3
3,3
3,4
3,7
3,9
4
3,7
3,9
4,2
4,4
4,3
4,2
4,3
4,3
4,3
4,5
5
5,2
5,2
5,4
5,5
5,4
5,5
5,4
5,7
5,7
6,1
6,5
6,9
6,8
6,7
6,6
6,5
6,4
6,1
6,2
6,3
6,4
6,5
6,7
7
7
6,8
6,7
6,7
6,5
6,4
6,1
6,2
6
6,1
6,1
6,2

Dataseries Y:

Download CSV

Histogram

4,2
4,5
4,6
4,9
4,9
4,5
4,6
4,7
4,7
4,3
4,2
4,4
4
3,8
3,6
3,6
3,3
3,4
3,4
3,3
3,3
3,2
3,1
3,1
2,4
2,4
2,4
2,1
2
2
2,1
2,1
2
2
2
1,7
1,3
1,2
1,1
1,4
1,5
1,4
1,1
1,1
1
1,4
1,3
1,2
1,5
1,6
1,8
1,5
1,3
1,6
1,6
1,8
1,8
1,6
1,8
2
1,3

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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=64326&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=64326&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64326&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	5.24098360655738	2.57377049180328
Biased Variance	1.59914001612470	1.52750873421123
Biased Standard Deviation	1.26457107990207	1.23592424290942
Covariance	-1.53757377049180
Correlation	-0.967658866922448
Determination	0.936363682733636
T-Test	-29.4642755337011
p-value (2 sided)	5.46723447673283e-37
p-value (1 sided)	2.73361723836642e-37
Degrees of Freedom	59
Number of Observations	61

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 5.24098360655738 & 2.57377049180328 \tabularnewline
Biased Variance & 1.59914001612470 & 1.52750873421123 \tabularnewline
Biased Standard Deviation & 1.26457107990207 & 1.23592424290942 \tabularnewline
Covariance & -1.53757377049180 \tabularnewline
Correlation & -0.967658866922448 \tabularnewline
Determination & 0.936363682733636 \tabularnewline
T-Test & -29.4642755337011 \tabularnewline
p-value (2 sided) & 5.46723447673283e-37 \tabularnewline
p-value (1 sided) & 2.73361723836642e-37 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64326&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]5.24098360655738[/C][C]2.57377049180328[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1.59914001612470[/C][C]1.52750873421123[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.26457107990207[/C][C]1.23592424290942[/C][/ROW]
[ROW][C]Covariance[/C][C]-1.53757377049180[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.967658866922448[/C][/ROW]
[ROW][C]Determination[/C][C]0.936363682733636[/C][/ROW]
[ROW][C]T-Test[/C][C]-29.4642755337011[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]5.46723447673283e-37[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.73361723836642e-37[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]59[/C][/ROW]
[ROW][C]Number of Observations[/C][C]61[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64326&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64326&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	5.24098360655738	2.57377049180328
Biased Variance	1.59914001612470	1.52750873421123
Biased Standard Deviation	1.26457107990207	1.23592424290942
Covariance	-1.53757377049180
Correlation	-0.967658866922448
Determination	0.936363682733636
T-Test	-29.4642755337011
p-value (2 sided)	5.46723447673283e-37
p-value (1 sided)	2.73361723836642e-37
Degrees of Freedom	59
Number of Observations	61

Figure 1

PNG link

Postscript link

PDF link

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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code