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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 computationSat, 27 Nov 2010 09:00:00 +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/Nov/27/t129084832818v571tbib0uthv.htm/, Retrieved Sat, 18 Apr 2026 23:47:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102320, Retrieved Sat, 18 Apr 2026 23:47:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact419

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
- RMPD    [Pearson Correlation] [paper - lineaire ...] [2010-11-25 18:40:11] [58c953249d32df2a8d41ff3671d3073f]
-    D        [Pearson Correlation] [mini tutorial] [2010-11-27 09:00:00] [75888b09f354cf7130ae5528df429303] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Dataseries Y:
Download CSV
Histogram 
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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'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=102320&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=102320&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102320&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1.623456790123463.60493827160494
Biased Variance0.2347584209724130.646395366559976
Biased Standard Deviation0.4845187519306270.803987168156293
Covariance-0.0378805306341538
Correlation-0.0966422891135652
Determination0.00933973204510992
T-Test-1.22818793552642
p-value (2 sided)0.221180044323049
p-value (1 sided)0.110590022161524
Degrees of Freedom160
Number of Observations162

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1.62345679012346 & 3.60493827160494 \tabularnewline
Biased Variance & 0.234758420972413 & 0.646395366559976 \tabularnewline
Biased Standard Deviation & 0.484518751930627 & 0.803987168156293 \tabularnewline
Covariance & -0.0378805306341538 \tabularnewline
Correlation & -0.0966422891135652 \tabularnewline
Determination & 0.00933973204510992 \tabularnewline
T-Test & -1.22818793552642 \tabularnewline
p-value (2 sided) & 0.221180044323049 \tabularnewline
p-value (1 sided) & 0.110590022161524 \tabularnewline
Degrees of Freedom & 160 \tabularnewline
Number of Observations & 162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102320&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]1.62345679012346[/C][C]3.60493827160494[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.234758420972413[/C][C]0.646395366559976[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.484518751930627[/C][C]0.803987168156293[/C][/ROW]
[ROW][C]Covariance[/C][C]-0.0378805306341538[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.0966422891135652[/C][/ROW]
[ROW][C]Determination[/C][C]0.00933973204510992[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.22818793552642[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.221180044323049[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.110590022161524[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]160[/C][/ROW]
[ROW][C]Number of Observations[/C][C]162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102320&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102320&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
Mean1.623456790123463.60493827160494
Biased Variance0.2347584209724130.646395366559976
Biased Standard Deviation0.4845187519306270.803987168156293
Covariance-0.0378805306341538
Correlation-0.0966422891135652
Determination0.00933973204510992
T-Test-1.22818793552642
p-value (2 sided)0.221180044323049
p-value (1 sided)0.110590022161524
Degrees of Freedom160
Number of Observations162


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')