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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

Wed, 17 Dec 2008 07:26:38 -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/2008/Dec/17/t1229524237gaflobju6rtp9cq.htm/, Retrieved Tue, 10 Feb 2026 14:19:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34367, Retrieved Tue, 10 Feb 2026 14:19:56 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

491

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

F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
- RMPD  [Pearson Correlation] [correlation] [2008-10-17 11:28:19] [1df53680523b3d683eb04eb09d7bca8b]
F   P     [Pearson Correlation] [] [2008-10-20 14:18:47] [4c8dfb519edec2da3492d7e6be9a5685]
-    D        [Pearson Correlation] [Vergelijking basi...] [2008-12-17 14:26:38] [708e5cce6cfef15b7edd0dea71956401] [Current]

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Dataseries X:

Download CSV

Histogram

Boxplots

2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.21
2.25
2.25
2.45
2.50
2.50
2.64
2.75
2.93
3.00
3.17
3.25
3.39
3.50
3.50
3.65
3.75
3.75
3.90
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.18
4.25
4.25
3.97
3.42

Dataseries Y:

Download CSV

Histogram

1.7
1.4
1.8
1.7
1.4
1.2
1
1.7
2.4
2
2.1
2
1.8
2.7
2.3
1.9
2
2.3
2.8
2.4
2.3
2.7
2.7
2.9
3
2.2
2.3
2.8
2.8
2.8
2.2
2.6
2.8
2.5
2.4
2.3
1.9
1.7
2
2.1
1.7
1.8
1.8
1.8
1.3
1.3
1.3
1.2
1.4
2.2
2.9
3.1
3.5
3.6
4.4
4.1
5.1
5.8
5.9
5.4
5.5

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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34367&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34367&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34367&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	'George Udny Yule' @ 72.249.76.132

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	2.8755737704918	2.50327868852459
Biased Variance	0.779342703574308	1.28326793872615
Biased Standard Deviation	0.882803887380605	1.13281416778135
Covariance	0.381348087431694
Correlation	0.375076693771388
Determination	0.140682526210475
T-Test	3.10791593666088
p-value (2 sided)	0.00289757586307759
p-value (1 sided)	0.00144878793153880
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 & 2.8755737704918 & 2.50327868852459 \tabularnewline
Biased Variance & 0.779342703574308 & 1.28326793872615 \tabularnewline
Biased Standard Deviation & 0.882803887380605 & 1.13281416778135 \tabularnewline
Covariance & 0.381348087431694 \tabularnewline
Correlation & 0.375076693771388 \tabularnewline
Determination & 0.140682526210475 \tabularnewline
T-Test & 3.10791593666088 \tabularnewline
p-value (2 sided) & 0.00289757586307759 \tabularnewline
p-value (1 sided) & 0.00144878793153880 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34367&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]2.8755737704918[/C][C]2.50327868852459[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.779342703574308[/C][C]1.28326793872615[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.882803887380605[/C][C]1.13281416778135[/C][/ROW]
[ROW][C]Covariance[/C][C]0.381348087431694[/C][/ROW]
[ROW][C]Correlation[/C][C]0.375076693771388[/C][/ROW]
[ROW][C]Determination[/C][C]0.140682526210475[/C][/ROW]
[ROW][C]T-Test[/C][C]3.10791593666088[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00289757586307759[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00144878793153880[/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=34367&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34367&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	2.8755737704918	2.50327868852459
Biased Variance	0.779342703574308	1.28326793872615
Biased Standard Deviation	0.882803887380605	1.13281416778135
Covariance	0.381348087431694
Correlation	0.375076693771388
Determination	0.140682526210475
T-Test	3.10791593666088
p-value (2 sided)	0.00289757586307759
p-value (1 sided)	0.00144878793153880
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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code