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Author's title

Author

*Unverified author*

R Software Module

rwasp_correlation.wasp

Title produced by software

Pearson Correlation

Date of computation

Sat, 20 Dec 2008 02:29:23 -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/20/t1229765416qbyvrfpwzcdhdpb.htm/, Retrieved Sun, 19 May 2024 09:38:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35310, Retrieved Sun, 19 May 2024 09:38:07 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

192

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

-       [Pearson Correlation] [] [2008-12-20 09:29:23] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-    D    [Pearson Correlation] [] [2008-12-21 20:12:05] [74be16979710d4c4e7c6647856088456] 
- RMPD    [Mean Plot] [] [2008-12-21 20:16:58] [74be16979710d4c4e7c6647856088456] 

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Dataseries X:

Download CSV

Histogram

Boxplots

6.6
6.6
6.6
6.6
6.6
6.6
6.8
6.8
6.9
7
7
7
7.1
7.1
7.3
7.4
7.6
7.8
7.9
7.7
7.7
7.8
7.9
8
8.1
8.2
8.1
8.2
8.3
8.4
8.4
8.5
8.6
8.6
8.6
8.5
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

Dataseries Y:

Download CSV

Histogram

7.7
7.6
7.5
7.5
7.4
7.4
7.3
7.2
7.2
7.2
7.2
7.2
7.3
7.3
7.4
7.4
7.4
7.4
7.5
7.6
7.6
7.7
7.8
7.9
8
8
8.1
8.1
8.3
8.3
8.4
8.6
8.7
8.7
8.7
8.8
8.8
8.8
8.8
8.8
8.8
8.9
8.9
9
8.9
8.9
8.9
8.9
8.9

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	'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 & 2 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=35310&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35310&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35310&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	7.81224489795918	8.05510204081633
Biased Variance	0.506788837984173	0.425331112036651
Biased Standard Deviation	0.711891029571362	0.652174142416465
Covariance	0.414936224489796
Correlation	0.87548641613134
Determination	0.766476464830498
T-Test	12.4203265060391
p-value (2 sided)	2.22044604925031e-16
p-value (1 sided)	1.11022302462516e-16
Degrees of Freedom	47
Number of Observations	49

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 7.81224489795918 & 8.05510204081633 \tabularnewline
Biased Variance & 0.506788837984173 & 0.425331112036651 \tabularnewline
Biased Standard Deviation & 0.711891029571362 & 0.652174142416465 \tabularnewline
Covariance & 0.414936224489796 \tabularnewline
Correlation & 0.87548641613134 \tabularnewline
Determination & 0.766476464830498 \tabularnewline
T-Test & 12.4203265060391 \tabularnewline
p-value (2 sided) & 2.22044604925031e-16 \tabularnewline
p-value (1 sided) & 1.11022302462516e-16 \tabularnewline
Degrees of Freedom & 47 \tabularnewline
Number of Observations & 49 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35310&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]7.81224489795918[/C][C]8.05510204081633[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.506788837984173[/C][C]0.425331112036651[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.711891029571362[/C][C]0.652174142416465[/C][/ROW]
[ROW][C]Covariance[/C][C]0.414936224489796[/C][/ROW]
[ROW][C]Correlation[/C][C]0.87548641613134[/C][/ROW]
[ROW][C]Determination[/C][C]0.766476464830498[/C][/ROW]
[ROW][C]T-Test[/C][C]12.4203265060391[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.22044604925031e-16[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.11022302462516e-16[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]47[/C][/ROW]
[ROW][C]Number of Observations[/C][C]49[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35310&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35310&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	7.81224489795918	8.05510204081633
Biased Variance	0.506788837984173	0.425331112036651
Biased Standard Deviation	0.711891029571362	0.652174142416465
Covariance	0.414936224489796
Correlation	0.87548641613134
Determination	0.766476464830498
T-Test	12.4203265060391
p-value (2 sided)	2.22044604925031e-16
p-value (1 sided)	1.11022302462516e-16
Degrees of Freedom	47
Number of Observations	49

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