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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, 13 Dec 2010 13:22:15 +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/13/t1292246503yewe05yylpvqsh3.htm/, Retrieved Mon, 06 May 2024 11:56:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108902, Retrieved Mon, 06 May 2024 11:56:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13
12
15
12
10
12
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9
12
11
11
11
15
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8
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11
4
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7
19
12
12
13
15
8
12
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8
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15
16
13
16
9
14
14
12
Dataseries Y:
Download CSV
Histogram 
5
3
0
7
4
1
6
3
12
0
5
6
6
6
2
1
5
7
3
3
3
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3
5
5
10
2
6
4
6
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4
5
10
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7
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10
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3
3
3
7
15
0
0
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5
5
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9
2
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0
0
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1
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6
11
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8
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9
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2
12
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5
9
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3
0
2
8
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0
5
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9
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0
7
0
5
0
14
5
2
8
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2
6
3
5
9
3
3
0
10
4
2
3
10
7
0
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10
5

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'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108902&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108902&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108902&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'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean12.04487179487185.01282051282051
Biased Variance8.56849934253789.62804076265615
Biased Standard Deviation2.927199915027643.10290843607351
Covariance2.65748552522746
Correlation0.290707785925906
Determination0.0845110167979426
T-Test3.77042635693978
p-value (2 sided)0.000231799575226566
p-value (1 sided)0.000115899787613283
Degrees of Freedom154
Number of Observations156

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 12.0448717948718 & 5.01282051282051 \tabularnewline
Biased Variance & 8.5684993425378 & 9.62804076265615 \tabularnewline
Biased Standard Deviation & 2.92719991502764 & 3.10290843607351 \tabularnewline
Covariance & 2.65748552522746 \tabularnewline
Correlation & 0.290707785925906 \tabularnewline
Determination & 0.0845110167979426 \tabularnewline
T-Test & 3.77042635693978 \tabularnewline
p-value (2 sided) & 0.000231799575226566 \tabularnewline
p-value (1 sided) & 0.000115899787613283 \tabularnewline
Degrees of Freedom & 154 \tabularnewline
Number of Observations & 156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108902&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]12.0448717948718[/C][C]5.01282051282051[/C][/ROW]
[ROW][C]Biased Variance[/C][C]8.5684993425378[/C][C]9.62804076265615[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.92719991502764[/C][C]3.10290843607351[/C][/ROW]
[ROW][C]Covariance[/C][C]2.65748552522746[/C][/ROW]
[ROW][C]Correlation[/C][C]0.290707785925906[/C][/ROW]
[ROW][C]Determination[/C][C]0.0845110167979426[/C][/ROW]
[ROW][C]T-Test[/C][C]3.77042635693978[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000231799575226566[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000115899787613283[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]154[/C][/ROW]
[ROW][C]Number of Observations[/C][C]156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108902&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108902&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
Mean12.04487179487185.01282051282051
Biased Variance8.56849934253789.62804076265615
Biased Standard Deviation2.927199915027643.10290843607351
Covariance2.65748552522746
Correlation0.290707785925906
Determination0.0845110167979426
T-Test3.77042635693978
p-value (2 sided)0.000231799575226566
p-value (1 sided)0.000115899787613283
Degrees of Freedom154
Number of Observations156


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')