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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationTue, 14 Dec 2010 21:39:04 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/14/t1292362634nygudbljusorbwu.htm/, Retrieved Fri, 13 Feb 2026 01:29:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110224, Retrieved Fri, 13 Feb 2026 01:29:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact360

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Competence to learn] [2010-11-17 07:43:53] [b98453cac15ba1066b407e146608df68]
- R PD  [Multiple Regression] [Workshop 7 - Firs...] [2010-11-19 10:36:36] [8b017ffbf7b0eded54d8efebfb3e4cfa]
-   P     [Multiple Regression] [Workshop 7 - Firs...] [2010-11-19 10:41:24] [8b017ffbf7b0eded54d8efebfb3e4cfa]
- R PD      [Multiple Regression] [] [2010-11-23 16:27:22] [1ad9dd03b6c5806e9fe90049663fcef1]
- RMPD          [Pearson Correlation] [correlatie SWS - ...] [2010-12-14 21:39:04] [5f761c4a622da19727fd2adf71158b48] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6.3
2.1
9.1
15.8
5.2
10.9
8.3
11
3.2
6.3
8.6
6.6
9.5
3.3
11
4.7
10.4
7.4
2.1
7.7
17.9
6.1
11.9
10.8
13.8
14.3
15.2
10
11.9
6.5
7.5
10.6
7.4
8.4
5.7
4.9
3.2
11
4.9
13.2
9.7
12.8
Dataseries Y:
Download CSV
Histogram 
4,5
69
27
19
30,4
28
50
7
30
3,5
50
6
10,4
20
3,9
41
9
7,6
46
2,6
24
100
3,2
2
5
6,5
12
20,2
13
27
18
4,7
9,8
29
7
6
20
4,5
7,5
2,3
24
3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110224&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110224&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110224&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean8.7428571428571419.3714285714286
Biased Variance14.3753061224490400.581088435374
Biased Standard Deviation3.7914780920439220.0145219387168
Covariance-28.935818815331
Correlation-0.372234455510252
Determination0.138558489869014
T-Test-2.53649300366088
p-value (2 sided)0.0152033516740617
p-value (1 sided)0.00760167583703083
Degrees of Freedom40
Number of Observations42

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 8.74285714285714 & 19.3714285714286 \tabularnewline
Biased Variance & 14.3753061224490 & 400.581088435374 \tabularnewline
Biased Standard Deviation & 3.79147809204392 & 20.0145219387168 \tabularnewline
Covariance & -28.935818815331 \tabularnewline
Correlation & -0.372234455510252 \tabularnewline
Determination & 0.138558489869014 \tabularnewline
T-Test & -2.53649300366088 \tabularnewline
p-value (2 sided) & 0.0152033516740617 \tabularnewline
p-value (1 sided) & 0.00760167583703083 \tabularnewline
Degrees of Freedom & 40 \tabularnewline
Number of Observations & 42 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110224&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]8.74285714285714[/C][C]19.3714285714286[/C][/ROW]
[ROW][C]Biased Variance[/C][C]14.3753061224490[/C][C]400.581088435374[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]3.79147809204392[/C][C]20.0145219387168[/C][/ROW]
[ROW][C]Covariance[/C][C]-28.935818815331[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.372234455510252[/C][/ROW]
[ROW][C]Determination[/C][C]0.138558489869014[/C][/ROW]
[ROW][C]T-Test[/C][C]-2.53649300366088[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0152033516740617[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00760167583703083[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]40[/C][/ROW]
[ROW][C]Number of Observations[/C][C]42[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110224&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110224&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean8.7428571428571419.3714285714286
Biased Variance14.3753061224490400.581088435374
Biased Standard Deviation3.7914780920439220.0145219387168
Covariance-28.935818815331
Correlation-0.372234455510252
Determination0.138558489869014
T-Test-2.53649300366088
p-value (2 sided)0.0152033516740617
p-value (1 sided)0.00760167583703083
Degrees of Freedom40
Number of Observations42


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = pearson ;
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')