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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 computationWed, 22 Dec 2010 20:28:19 +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/22/t12930496056prhmpvxb92q8eo.htm/, Retrieved Mon, 06 May 2024 10:35:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114564, Retrieved Mon, 06 May 2024 10:35:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [sleep] [2010-12-22 19:34:33] [960f506a46b790b06fab7ca57984a121]
-    D    [Pearson Correlation] [] [2010-12-22 20:28:19] [e7b77eb06cdf8868fc9cf2043e42b3da] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-999.000
6.300
-999.000
-999.000
2.100
9.100
15.800
5.200
10.900
8.300
11.000
3.200
7.600
-999.000
6.300
8.600
6.600
9.500
4.800
12.000
-999.000
3.300
11.000
-999.000
4.700
-999.000
10.400
7.400
2.100
-999.000
-999.000
7.700
17.900
6.100
8.200
8.400
11.900
10.800
13.800
14.300
-999.000
15.200
10.000
11.900
6.500
7.500
-999.000
10.600
7.400
8.400
5.700
4.900
-999.000
3.200
-999.000
8.100
11.000
4.900
13.200
9.700
12.800
-999.000
Dataseries Y:
Download CSV
Histogram 
-999.000
2.000
-999.000
-999.000
1.8
0.700
3.900
1.000
3.600
1.400
1.500
0.700
2.700
-999.000
2.100
0.000
4.100
1.200
1.300
6.100
0.300
0.500
3.400
-999.000
1.500
-999.000
3.400
0.800
0.800
-999.000
-999.000
1.400
2.000
1.900
2.400
2.800
1.300
2.000
5.600
3.100
1.000
1.800
0.900
1.800
1.900
0.900
-999.000
2.600
2.400
1.200
0.900
0.500
-999.000
0.600
-999.000
2.200
2.300
0.500
2.600
0.600
6.600
-999.000

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=114564&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=114564&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114564&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
Mean-218.866129032258-191.764516129032
Biased Variance177521.107078564156392.635192508
Biased Standard Deviation421.332537407882395.465087197982
Covariance153663.90566367
Correlation0.907354224061972
Determination0.823291687923102
T-Test16.7195275519602
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom60
Number of Observations62

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & -218.866129032258 & -191.764516129032 \tabularnewline
Biased Variance & 177521.107078564 & 156392.635192508 \tabularnewline
Biased Standard Deviation & 421.332537407882 & 395.465087197982 \tabularnewline
Covariance & 153663.90566367 \tabularnewline
Correlation & 0.907354224061972 \tabularnewline
Determination & 0.823291687923102 \tabularnewline
T-Test & 16.7195275519602 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 60 \tabularnewline
Number of Observations & 62 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114564&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]-218.866129032258[/C][C]-191.764516129032[/C][/ROW]
[ROW][C]Biased Variance[/C][C]177521.107078564[/C][C]156392.635192508[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]421.332537407882[/C][C]395.465087197982[/C][/ROW]
[ROW][C]Covariance[/C][C]153663.90566367[/C][/ROW]
[ROW][C]Correlation[/C][C]0.907354224061972[/C][/ROW]
[ROW][C]Determination[/C][C]0.823291687923102[/C][/ROW]
[ROW][C]T-Test[/C][C]16.7195275519602[/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]60[/C][/ROW]
[ROW][C]Number of Observations[/C][C]62[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114564&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114564&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
Mean-218.866129032258-191.764516129032
Biased Variance177521.107078564156392.635192508
Biased Standard Deviation421.332537407882395.465087197982
Covariance153663.90566367
Correlation0.907354224061972
Determination0.823291687923102
T-Test16.7195275519602
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom60
Number of Observations62


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')