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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

Sun, 27 Jun 2010 23:38:17 +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/Jun/28/t1277681912akhpe9nd5osu4zg.htm/, Retrieved Sat, 27 Apr 2024 14:18:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77876, Retrieved Sat, 27 Apr 2024 14:18:24 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

285

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

-       [Pearson Correlation] [] [2010-06-27 23:38:17] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

21.1
18.6
19.2
16.4
20.3
20.3
17.5
17.6
19.3
16.7
21.5
16.0
19.3
20.1
18.5
18.7
18.8
18.6
18.5
18.4
19.1
19.0
18.9
19.5
20.1
18.0
18.3
18.8
18.5
18.8

Dataseries Y:

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Histogram

21.6
17.9
19.3
16.6
20.9
22.1
18.1
18.8
21.0
18.3
20.1
17.8
19.7
21.6
18.2
19.5
19.5
19.3
19.2
19.1
19.8
19.7
19.5
20.2
21.7
18.7
19.1
19.6
19.4
19.6

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	'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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77876&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77876&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77876&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	18.8133333333333	19.53
Biased Variance	1.47648888888889	1.54076666666667
Biased Standard Deviation	1.21510859139786	1.24127622496633
Covariance	1.3168275862069
Correlation	0.843960518943398
Determination	0.71226935753521
T-Test	8.32545712239144
p-value (2 sided)	4.65899341328679e-09
p-value (1 sided)	2.3294967066434e-09
Degrees of Freedom	28
Number of Observations	30

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 18.8133333333333 & 19.53 \tabularnewline
Biased Variance & 1.47648888888889 & 1.54076666666667 \tabularnewline
Biased Standard Deviation & 1.21510859139786 & 1.24127622496633 \tabularnewline
Covariance & 1.3168275862069 \tabularnewline
Correlation & 0.843960518943398 \tabularnewline
Determination & 0.71226935753521 \tabularnewline
T-Test & 8.32545712239144 \tabularnewline
p-value (2 sided) & 4.65899341328679e-09 \tabularnewline
p-value (1 sided) & 2.3294967066434e-09 \tabularnewline
Degrees of Freedom & 28 \tabularnewline
Number of Observations & 30 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77876&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]18.8133333333333[/C][C]19.53[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1.47648888888889[/C][C]1.54076666666667[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.21510859139786[/C][C]1.24127622496633[/C][/ROW]
[ROW][C]Covariance[/C][C]1.3168275862069[/C][/ROW]
[ROW][C]Correlation[/C][C]0.843960518943398[/C][/ROW]
[ROW][C]Determination[/C][C]0.71226935753521[/C][/ROW]
[ROW][C]T-Test[/C][C]8.32545712239144[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]4.65899341328679e-09[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.3294967066434e-09[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]28[/C][/ROW]
[ROW][C]Number of Observations[/C][C]30[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77876&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77876&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	18.8133333333333	19.53
Biased Variance	1.47648888888889	1.54076666666667
Biased Standard Deviation	1.21510859139786	1.24127622496633
Covariance	1.3168275862069
Correlation	0.843960518943398
Determination	0.71226935753521
T-Test	8.32545712239144
p-value (2 sided)	4.65899341328679e-09
p-value (1 sided)	2.3294967066434e-09
Degrees of Freedom	28
Number of Observations	30

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