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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 computationFri, 24 Dec 2010 10:44:24 +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/24/t1293187401881j2pt8n2sdhxd.htm/, Retrieved Tue, 30 Apr 2024 05:45:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114733, Retrieved Tue, 30 Apr 2024 05:45:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pearson Correlation] [2010-12-24 10:44:24] [fba9c6aa004af59d8497d682e70ddad5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3.4
3.4
3.4
-3.5
-3.5
-3.5
-8.3
-8.3
-8.3
-16.7
-16.7
-16.7
-11.6
-11.6
-11.6
-8.4
-8.4
-8.4
-8.6
-8.6
-8.6
0.6
0.6
0.6
-1.5
-1.5
-1.5
9.3
9.3
9.3
2.0
2.0
2.0
-5.5
-5.5
-5.5
4.0
4.0
4.0
-0.5
-0.5
-0.5
10.9
10.9
10.9
19.4
19.4
19.4
13.9
13.9
13.9
10.6
10.6
10.6
4.8
4.8
4.8
4.7
4.7
4.7
-3.9
-3.9
-3.9
-0.2
-0.2
-0.2
Dataseries Y:
Download CSV
Histogram 
13.7
13.7
13.7
1.3
1.3
1.3
-7.4
-7.4
-7.4
-12.9
-12.9
-12.9
-9.6
-9.6
-9.6
-11.1
-11.1
-11.1
-8.3
-8.3
-8.3
-2.7
-2.7
-2.7
5.1
5.1
5.1
4.6
4.6
4.6
5.6
5.6
5.6
5.1
5.1
5.1
0.8
0.8
0.8
6
6
6
9.3
9.3
9.3
8.7
8.7
8.7
11
11
11
8.5
8.5
8.5
4.4
4.4
4.4
2.5
2.5
2.5
0.3
0.3
0.3
-3
-3
-3

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=114733&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=114733&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114733&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
Mean0.6772727272727271.45
Biased Variance74.604483471074453.9615909090909
Biased Standard Deviation8.637388695148237.34585535585141
Covariance52.4106923076923
Correlation0.813512969399595
Determination0.661803351381346
T-Test11.1910237711224
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom64
Number of Observations66

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 0.677272727272727 & 1.45 \tabularnewline
Biased Variance & 74.6044834710744 & 53.9615909090909 \tabularnewline
Biased Standard Deviation & 8.63738869514823 & 7.34585535585141 \tabularnewline
Covariance & 52.4106923076923 \tabularnewline
Correlation & 0.813512969399595 \tabularnewline
Determination & 0.661803351381346 \tabularnewline
T-Test & 11.1910237711224 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 64 \tabularnewline
Number of Observations & 66 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114733&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]0.677272727272727[/C][C]1.45[/C][/ROW]
[ROW][C]Biased Variance[/C][C]74.6044834710744[/C][C]53.9615909090909[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]8.63738869514823[/C][C]7.34585535585141[/C][/ROW]
[ROW][C]Covariance[/C][C]52.4106923076923[/C][/ROW]
[ROW][C]Correlation[/C][C]0.813512969399595[/C][/ROW]
[ROW][C]Determination[/C][C]0.661803351381346[/C][/ROW]
[ROW][C]T-Test[/C][C]11.1910237711224[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]64[/C][/ROW]
[ROW][C]Number of Observations[/C][C]66[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114733&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114733&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
Mean0.6772727272727271.45
Biased Variance74.604483471074453.9615909090909
Biased Standard Deviation8.637388695148237.34585535585141
Covariance52.4106923076923
Correlation0.813512969399595
Determination0.661803351381346
T-Test11.1910237711224
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom64
Number of Observations66


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')