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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

Mon, 13 Dec 2010 18:40:36 +0000

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/2010/Dec/13/t1292265542dugw5v6ra74j9w8.htm/, Retrieved Mon, 06 May 2024 15:18:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109058, Retrieved Mon, 06 May 2024 15:18:08 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Sciene DMA

Estimated Impact

110

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

-       [Pearson Correlation] [Sciene Paper Corr...] [2010-12-13 18:40:36] [f92ba2b01007f169e2985fcc57236bd0] [Current]

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Dataseries X:

Download CSV

Histogram

Boxplots

6,3
2,1
9,1
15,8
5,2
10,9
8,3
11
3,2
6,3
8,6
6,6
9,5
3,3
11
4,7
10,4
7,4
2,1
7,7
17,9
6,1
11,9
10,8
13,8
14,3
15,2
10
11,9
6,5
7,5
10,6
7,4
8,4
5,7
4,9
3,2
11
4,9
13,2
9,7
12,8

Dataseries Y:

Download CSV

Histogram

2
1,8
0,7
3,9
1
3,6
1,4
1,5
0,7
2,1
0
4,1
1,2
0,5
3,4
1,5
3,4
0,8
0,8
1,4
2
1,9
1,3
2
5,6
3,1
1,8
0,9
1,8
1,9
0,9
2,6
2,4
1,2
0,9
0,5
0,6
2,3
0,5
2,6
0,6
6,6

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109058&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109058&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109058&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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	8.74285714285714	1.9
Biased Variance	14.375306122449	1.88285714285714
Biased Standard Deviation	3.79147809204392	1.37217241732121
Covariance	2.7619512195122
Correlation	0.518242868230141
Determination	0.268575670471404
T-Test	3.83246880750495
p-value (2 sided)	0.0004388331368681
p-value (1 sided)	0.00021941656843405
Degrees of Freedom	40
Number of Observations	42

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 8.74285714285714 & 1.9 \tabularnewline
Biased Variance & 14.375306122449 & 1.88285714285714 \tabularnewline
Biased Standard Deviation & 3.79147809204392 & 1.37217241732121 \tabularnewline
Covariance & 2.7619512195122 \tabularnewline
Correlation & 0.518242868230141 \tabularnewline
Determination & 0.268575670471404 \tabularnewline
T-Test & 3.83246880750495 \tabularnewline
p-value (2 sided) & 0.0004388331368681 \tabularnewline
p-value (1 sided) & 0.00021941656843405 \tabularnewline
Degrees of Freedom & 40 \tabularnewline
Number of Observations & 42 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109058&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]8.74285714285714[/C][C]1.9[/C][/ROW]
[ROW][C]Biased Variance[/C][C]14.375306122449[/C][C]1.88285714285714[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]3.79147809204392[/C][C]1.37217241732121[/C][/ROW]
[ROW][C]Covariance[/C][C]2.7619512195122[/C][/ROW]
[ROW][C]Correlation[/C][C]0.518242868230141[/C][/ROW]
[ROW][C]Determination[/C][C]0.268575670471404[/C][/ROW]
[ROW][C]T-Test[/C][C]3.83246880750495[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0004388331368681[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00021941656843405[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]40[/C][/ROW]
[ROW][C]Number of Observations[/C][C]42[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109058&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109058&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	8.74285714285714	1.9
Biased Variance	14.375306122449	1.88285714285714
Biased Standard Deviation	3.79147809204392	1.37217241732121
Covariance	2.7619512195122
Correlation	0.518242868230141
Determination	0.268575670471404
T-Test	3.83246880750495
p-value (2 sided)	0.0004388331368681
p-value (1 sided)	0.00021941656843405
Degrees of Freedom	40
Number of Observations	42

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code