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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, 04 Dec 2011 06:32:17 -0500

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/2011/Dec/04/t1322998353acgn1clj0y86rwr.htm/, Retrieved Sun, 05 May 2024 17:49:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150578, Retrieved Sun, 05 May 2024 17:49:54 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

120

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

-     [Central Tendency] [Paper - Central T...] [2011-11-29 18:42:39] [2ca9890f29577b21e1107ae30466e88a]
- RM D  [Pearson Correlation] [Paper - Correlation] [2011-12-04 10:50:44] [2ca9890f29577b21e1107ae30466e88a]
- R  D      [Pearson Correlation] [Pearson correlation] [2011-12-04 11:32:17] [2489a3445a7d2af96337a363cd642931] [Current]

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Dataseries X:

Download CSV

Histogram

Boxplots

1.9
1.9
1.8
2
2.6
2.5
2.5
1.6
1.4
0.8
1.1
1.3
1.2
1.3
1.1
1.3
1.2
1.6
1.7
1.5
0.9
1.5
1.4
1.6
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
4.8
3.2
2.7
2.1
1.9
0.6
0.7
-0.2
-1
-1.7
-0.7
-1
-0.9
0
0.3
0.8
0.8
1.9
2.1
2.5
2.7
2.4
2.4
2.9
3.1
3
3.4
3.7
3.5
3.5
3.3
3.1
3.4
4
3.4
3.4

Dataseries Y:

Download CSV

Histogram

6.8
7.5
7.5
7.6
7.6
7.4
7.3
7.1
6.9
6.8
7.5
7.6
7.8
8
8.1
8.2
8.3
8.2
8
7.9
7.6
7.6
8.3
8.4
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6
8.7
8.5
8.3
8
8
8.8
8.7
8.5
8.1
7.8
7.6
7.4
7.1
6.9
6.7
6.6
6.5
7.1
7.2
6.9

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	'George Udny Yule' @ yule.wessa.net

\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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150578&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150578&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150578&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	'George Udny Yule' @ yule.wessa.net

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	2.15289256198347	7.84214876033058
Biased Variance	1.67191312068848	0.44376067208524
Biased Standard Deviation	1.29302479507876	0.666153639999993
Covariance	-0.276664600550964
Correlation	-0.318543107029924
Determination	0.101469711036277
T-Test	-3.66585541314363
p-value (2 sided)	0.000369690170320478
p-value (1 sided)	0.000184845085160239
Degrees of Freedom	119
Number of Observations	121

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2.15289256198347 & 7.84214876033058 \tabularnewline
Biased Variance & 1.67191312068848 & 0.44376067208524 \tabularnewline
Biased Standard Deviation & 1.29302479507876 & 0.666153639999993 \tabularnewline
Covariance & -0.276664600550964 \tabularnewline
Correlation & -0.318543107029924 \tabularnewline
Determination & 0.101469711036277 \tabularnewline
T-Test & -3.66585541314363 \tabularnewline
p-value (2 sided) & 0.000369690170320478 \tabularnewline
p-value (1 sided) & 0.000184845085160239 \tabularnewline
Degrees of Freedom & 119 \tabularnewline
Number of Observations & 121 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150578&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]2.15289256198347[/C][C]7.84214876033058[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1.67191312068848[/C][C]0.44376067208524[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.29302479507876[/C][C]0.666153639999993[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.276664600550964[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.318543107029924[/C][/ROW]
[ROW][C]Determination[/C][C]0.101469711036277[/C][/ROW]
[ROW][C]T-Test[/C][C]-3.66585541314363[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000369690170320478[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000184845085160239[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]119[/C][/ROW]
[ROW][C]Number of Observations[/C][C]121[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150578&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150578&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	2.15289256198347	7.84214876033058
Biased Variance	1.67191312068848	0.44376067208524
Biased Standard Deviation	1.29302479507876	0.666153639999993
Covariance	-0.276664600550964
Correlation	-0.318543107029924
Determination	0.101469711036277
T-Test	-3.66585541314363
p-value (2 sided)	0.000369690170320478
p-value (1 sided)	0.000184845085160239
Degrees of Freedom	119
Number of Observations	121

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