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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

Wed, 12 Dec 2007 09:08:42 -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/2007/Dec/12/t1197474810p9chzmnmviab2bv.htm/, Retrieved Thu, 02 May 2024 19:01:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3233, Retrieved Thu, 02 May 2024 19:01:26 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

195

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

-       [Pearson Correlation] [] [2007-12-12 16:08:42] [01c398ee8ca2f8c0964b19b0b10c7536] [Current]

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Dataseries X:

Download CSV

Histogram

Boxplots

6.3
6.5
6.6
6.6
6.5
6.7
6.9
6.9
7.1
7.2
6.8
6.9
7.2
6.7
6.7
6.7
7.7
7.8
7.8
8.1
8.2
8.2
7.7
7.7
7.8
7.6
7.6
7.5
7.2
7.5
7.4
7.7
7.8
7.8
7.6
7.5
7.7
8.0
7.9
7.7
6.6
6.6
6.7
7.8
7.9
7.9
8.0
7.8
8.1
7.6
7.6
7.5
7.4
7.4
7.5
7.6
7.7
7.7
7.7
7.7
7.8
6.4
6.4
6.3
6.2
6.2
6.3
6.3
6.3
6.3
6.6
6.6
7.0
6.0
5.9
5.6
5.5
5.6
5.7
5.3
5.5
5.5
5.4
5.4
5.6
5.6
5.8
5.4
5.1
5.2
5.3
6.0
6.3
6.4

Dataseries Y:

Download CSV

Histogram

8.4
8.9
9.3
9.1
8.6
8.7
8.9
8.8
9.1
9.3
8.9
9.0
9.4
9.8
10.0
9.8
9.0
8.9
9.0
9.1
9.3
9.4
9.3
9.3
9.5
10.2
10.2
10.1
9.0
8.9
9.0
9.5
9.5
9.6
9.3
9.3
9.6
10.9
10.9
10.6
8.4
8.2
8.3
9.6
9.7
9.7
9.1
9.0
9.3
9.4
9.4
9.3
8.1
7.9
8.0
8.8
9.0
9.0
8.5
8.5
8.6
9.2
9.3
9.2
7.8
7.8
7.8
8.8
8.9
9.0
8.3
8.3
8.9
7.4
7.5
7.1
6.9
6.9
7.0
7.0
7.2
7.3
8.4
8.4
8.8
8.9
9.3
8.7
8.1
8.0
8.3
8.2
8.5
8.7

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3233&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3233&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3233&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Pearson Product Moment Correlation - Ungrouped Data
Statistic	Variable X	Variable Y
Mean	6.88723404255319	8.84148936170213
Biased Variance	0.76153915799004	0.692853100950656
Biased Standard Deviation	0.872662109862712	0.832377979616626
Covariance	0.479997712194006
Correlation	0.653773872069974
Determination	0.427420275801366
T-Test	8.28711739850069
p-value (2 sided)	9.07718344933528e-13
p-value (1 sided)	4.53859172466764e-13
Degrees of Freedom	92
Number of Observations	94

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 6.88723404255319 & 8.84148936170213 \tabularnewline
Biased Variance & 0.76153915799004 & 0.692853100950656 \tabularnewline
Biased Standard Deviation & 0.872662109862712 & 0.832377979616626 \tabularnewline
Covariance & 0.479997712194006 \tabularnewline
Correlation & 0.653773872069974 \tabularnewline
Determination & 0.427420275801366 \tabularnewline
T-Test & 8.28711739850069 \tabularnewline
p-value (2 sided) & 9.07718344933528e-13 \tabularnewline
p-value (1 sided) & 4.53859172466764e-13 \tabularnewline
Degrees of Freedom & 92 \tabularnewline
Number of Observations & 94 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3233&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]6.88723404255319[/C][C]8.84148936170213[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.76153915799004[/C][C]0.692853100950656[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.872662109862712[/C][C]0.832377979616626[/C][/ROW]
[ROW][C]Covariance[/C][C]0.479997712194006[/C][/ROW]
[ROW][C]Correlation[/C][C]0.653773872069974[/C][/ROW]
[ROW][C]Determination[/C][C]0.427420275801366[/C][/ROW]
[ROW][C]T-Test[/C][C]8.28711739850069[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]9.07718344933528e-13[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]4.53859172466764e-13[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]92[/C][/ROW]
[ROW][C]Number of Observations[/C][C]94[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3233&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3233&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	6.88723404255319	8.84148936170213
Biased Variance	0.76153915799004	0.692853100950656
Biased Standard Deviation	0.872662109862712	0.832377979616626
Covariance	0.479997712194006
Correlation	0.653773872069974
Determination	0.427420275801366
T-Test	8.28711739850069
p-value (2 sided)	9.07718344933528e-13
p-value (1 sided)	4.53859172466764e-13
Degrees of Freedom	92
Number of Observations	94

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')

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Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code