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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationMon, 20 Oct 2008 16:38:23 -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/21/t1224542419txnshg5g4bppvfq.htm/, Retrieved Fri, 17 May 2024 04:13:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18273, Retrieved Fri, 17 May 2024 04:13:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Brussel vs Belgie...] [2008-10-20 22:38:23] [2cd04a6a1efa7ed8c62c55b6a1308fc1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
680,2
668,9
611,4
640,8
549,8
541,8
628,6
686,5
611,8
588,4
566,9
563,7
569,9
635,4
590,8
634,3
576,1
351,6
507,5
586,2
666,4
693,6
650,6
654,8
733,5
648,1
678,1
816,2
591
563,5
742,5
694,4
728,6
749
538,9
568,5
692,8
580,5
506,9
612,8
442,9
523,3
596,7
533,7
523,1
559,2
430,7
538,2
612,4
428
522,4
531,1
425,9
410,3
551
555,6
460,2
288,9
392,3
400,5
399
354,9
337,6
379,2
334,1
321,6
449,8
486,3
421,9
405,6
420
432,4
418,1
Dataseries Y:
Download CSV
Histogram 
15859.4
15258.9
15498.6
15106.5
15023.6
12083
15761.3
16942.6
15070.3
13659.6
14768.9
14725.1
15998.1
15370.6
14956.9
15469.7
15101.8
11703.7
16283.6
16726.5
14968.9
14861
14583.3
15305.8
17903.9
16379.4
15420.3
17870.5
15912.8
13866.5
17823.2
17872
17422
16704.5
15991.2
16583.6
19123.5
17838.7
17209.4
18586.5
16258.1
15141.6
19202.1
17746.5
19090.1
18040.3
17515.5
17751.8
21072.4
17170
19439.5
19795.4
17574.9
16165.4
19464.6
19932.1
19961.2
17343.4
18924.2
18574.1
21350.6
18594.6
19823.1
20844.4
19640.2
17735.4
19813.6
22238.5
20682.2
17818.6
21872.1
22117
21865.9

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=18273&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=18273&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18273&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
Mean545.04383561643817317.1931506849
Biased Variance13942.54246200045413537.37296678
Biased Standard Deviation118.0785436139882326.70096337428
Covariance-98435.4374733638
Correlation-0.353386174388342
Determination0.124881788248828
T-Test-3.18306397879478
p-value (2 sided)0.00216345308432527
p-value (1 sided)0.00108172654216263
Degrees of Freedom71
Number of Observations73

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 545.043835616438 & 17317.1931506849 \tabularnewline
Biased Variance & 13942.5424620004 & 5413537.37296678 \tabularnewline
Biased Standard Deviation & 118.078543613988 & 2326.70096337428 \tabularnewline
Covariance & -98435.4374733638 \tabularnewline
Correlation & -0.353386174388342 \tabularnewline
Determination & 0.124881788248828 \tabularnewline
T-Test & -3.18306397879478 \tabularnewline
p-value (2 sided) & 0.00216345308432527 \tabularnewline
p-value (1 sided) & 0.00108172654216263 \tabularnewline
Degrees of Freedom & 71 \tabularnewline
Number of Observations & 73 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18273&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]545.043835616438[/C][C]17317.1931506849[/C][/ROW]
[ROW][C]Biased Variance[/C][C]13942.5424620004[/C][C]5413537.37296678[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]118.078543613988[/C][C]2326.70096337428[/C][/ROW]
[ROW][C]Covariance[/C][C]-98435.4374733638[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.353386174388342[/C][/ROW]
[ROW][C]Determination[/C][C]0.124881788248828[/C][/ROW]
[ROW][C]T-Test[/C][C]-3.18306397879478[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00216345308432527[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00108172654216263[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]71[/C][/ROW]
[ROW][C]Number of Observations[/C][C]73[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18273&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18273&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
Mean545.04383561643817317.1931506849
Biased Variance13942.54246200045413537.37296678
Biased Standard Deviation118.0785436139882326.70096337428
Covariance-98435.4374733638
Correlation-0.353386174388342
Determination0.124881788248828
T-Test-3.18306397879478
p-value (2 sided)0.00216345308432527
p-value (1 sided)0.00108172654216263
Degrees of Freedom71
Number of Observations73


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')