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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 computationThu, 30 Oct 2008 07:59:14 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/30/t1225375204f7tkmihn14t6zyc.htm/, Retrieved Wed, 11 Feb 2026 04:07:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=20044, Retrieved Wed, 11 Feb 2026 04:07:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact447

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Pearson Correlation] [Q3 Clothing produ...] [2007-10-20 14:22:11] [b731da8b544846036771bbf9bf2f34ce]
-    D  [Pearson Correlation] [Q3 reproduce] [2008-10-20 16:49:56] [deb3c14ac9e4607a6d84fc9d0e0e6cc2]
F    D    [Pearson Correlation] [Pearson correlati...] [2008-10-30 13:52:30] [deb3c14ac9e4607a6d84fc9d0e0e6cc2]
F    D      [Pearson Correlation] [Pearson correlati...] [2008-10-30 13:57:31] [deb3c14ac9e4607a6d84fc9d0e0e6cc2]
-    D          [Pearson Correlation] [Pearson correlati...] [2008-10-30 13:59:14] [5e9e099b83e50415d7642e10d74756e4] [Current]
-    D            [Pearson Correlation] [Pearson correlati...] [2008-10-30 14:00:51] [deb3c14ac9e4607a6d84fc9d0e0e6cc2]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4.8
-4.2
1.6
5.2
9.2
4.6
10.6
Dataseries Y:
Download CSV
Histogram 
0.9
0.85
0.83
0.84
0.85
0.83
0.83

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=20044&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=20044&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=20044&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean4.542857142857140.847142857142857
Biased Variance20.56816326530610.000534693877551021
Biased Standard Deviation4.535213695660450.0231234486517695
Covariance-0.00952380952380953
Correlation-0.0778419219245376
Determination0.00605936480890581
T-Test-0.174589583625608
p-value (2 sided)0.868251453003535
p-value (1 sided)0.434125726501767
Degrees of Freedom5
Number of Observations7

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 4.54285714285714 & 0.847142857142857 \tabularnewline
Biased Variance & 20.5681632653061 & 0.000534693877551021 \tabularnewline
Biased Standard Deviation & 4.53521369566045 & 0.0231234486517695 \tabularnewline
Covariance & -0.00952380952380953 \tabularnewline
Correlation & -0.0778419219245376 \tabularnewline
Determination & 0.00605936480890581 \tabularnewline
T-Test & -0.174589583625608 \tabularnewline
p-value (2 sided) & 0.868251453003535 \tabularnewline
p-value (1 sided) & 0.434125726501767 \tabularnewline
Degrees of Freedom & 5 \tabularnewline
Number of Observations & 7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=20044&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]4.54285714285714[/C][C]0.847142857142857[/C][/ROW]
[ROW][C]Biased Variance[/C][C]20.5681632653061[/C][C]0.000534693877551021[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.53521369566045[/C][C]0.0231234486517695[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.00952380952380953[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.0778419219245376[/C][/ROW]
[ROW][C]Determination[/C][C]0.00605936480890581[/C][/ROW]
[ROW][C]T-Test[/C][C]-0.174589583625608[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.868251453003535[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.434125726501767[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]5[/C][/ROW]
[ROW][C]Number of Observations[/C][C]7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=20044&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=20044&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
Mean4.542857142857140.847142857142857
Biased Variance20.56816326530610.000534693877551021
Biased Standard Deviation4.535213695660450.0231234486517695
Covariance-0.00952380952380953
Correlation-0.0778419219245376
Determination0.00605936480890581
T-Test-0.174589583625608
p-value (2 sided)0.868251453003535
p-value (1 sided)0.434125726501767
Degrees of Freedom5
Number of Observations7


Figures (Output of Computation)

Input Parameters & R Code

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')