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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 computationMon, 20 Oct 2008 10:08:26 -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/20/t1224518975laxtz79uqxn5i60.htm/, Retrieved Sun, 19 May 2024 16:32:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17577, Retrieved Sun, 19 May 2024 16:32:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Harrell-Davis Quantiles] [Q7 95% confidence...] [2007-10-20 15:02:46] [b731da8b544846036771bbf9bf2f34ce]
- RMPD    [Pearson Correlation] [Correlatie: Spaar...] [2008-10-20 16:08:26] [e7b118d7688fea522247297d6fc6c452] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
17
19
20
18
19
18
17
15
15
15
14
10
9
5
0
7
9
8
5
7
13
3
12
12
15
17
15
14
12
18
14
16
16
12
11
12
12
15
16
13
7
7
7
8
4
10
9
13
17
16
13
14
16
16
16
16
16
20
19
10
17
Dataseries Y:
Download CSV
Histogram 
14
18
18
12
16
12
19
13
12
13
11
10
16
12
6
8
6
8
8
9
13
8
11
8
10
15
12
13
12
15
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16
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12
15
14
19
16
16
11
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12
11
6
9
6
15
17
13
12
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10
14
13
10
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12
7
11
9

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17577&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17577&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17577&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean12.885245901639312.1475409836066
Biased Variance20.691749529696310.3880677237302
Biased Standard Deviation4.548818476230543.22305254746648
Covariance8.38387978142076
Correlation0.562471426340655
Determination0.316374105449691
T-Test5.22537205769819
p-value (2 sided)2.38490245463296e-06
p-value (1 sided)1.19245122731648e-06
Degrees of Freedom59
Number of Observations61

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 12.8852459016393 & 12.1475409836066 \tabularnewline
Biased Variance & 20.6917495296963 & 10.3880677237302 \tabularnewline
Biased Standard Deviation & 4.54881847623054 & 3.22305254746648 \tabularnewline
Covariance & 8.38387978142076 \tabularnewline
Correlation & 0.562471426340655 \tabularnewline
Determination & 0.316374105449691 \tabularnewline
T-Test & 5.22537205769819 \tabularnewline
p-value (2 sided) & 2.38490245463296e-06 \tabularnewline
p-value (1 sided) & 1.19245122731648e-06 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17577&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]12.8852459016393[/C][C]12.1475409836066[/C][/ROW]
[ROW][C]Biased Variance[/C][C]20.6917495296963[/C][C]10.3880677237302[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4.54881847623054[/C][C]3.22305254746648[/C][/ROW]
[ROW][C]Covariance[/C][C]8.38387978142076[/C][/ROW]
[ROW][C]Correlation[/C][C]0.562471426340655[/C][/ROW]
[ROW][C]Determination[/C][C]0.316374105449691[/C][/ROW]
[ROW][C]T-Test[/C][C]5.22537205769819[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.38490245463296e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.19245122731648e-06[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]59[/C][/ROW]
[ROW][C]Number of Observations[/C][C]61[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17577&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17577&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
Mean12.885245901639312.1475409836066
Biased Variance20.691749529696310.3880677237302
Biased Standard Deviation4.548818476230543.22305254746648
Covariance8.38387978142076
Correlation0.562471426340655
Determination0.316374105449691
T-Test5.22537205769819
p-value (2 sided)2.38490245463296e-06
p-value (1 sided)1.19245122731648e-06
Degrees of Freedom59
Number of Observations61


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')