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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, 19 Dec 2008 05:11:42 -0700
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/Dec/19/t1229688744e9pdd7f950rozi4.htm/, Retrieved Wed, 15 May 2024 06:52:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35083, Retrieved Wed, 15 May 2024 06:52:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157

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] [2008-12-19 12:11:42] [6797a1f4a60918966297e9d9220cabc2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
519
517
510
509
501
507
569
580
578
565
547
555
562
561
555
544
537
543
594
611
613
611
594
595
591
589
584
573
567
569
621
629
628
612
595
597
593
590
580
574
573
573
620
626
620
588
566
557
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
Dataseries Y:
Download CSV
Histogram 
100.03
100.49
108.76
105.28
104.55
108.91
105.83
82.12
113.71
117.53
104.75
104.3
102.82
106.86
123.1
112.02
103.66
121.78
107.81
93.54
119.41
117.99
116.82
112.62
105.76
107.86
122.06
114.29
109.95
119.99
103.77
96.02
120.83
110.14
119.77
113.61
106.83
108
126.39
105.09
118.95
120.6
106.07
96.59
118.74
121.88
120.89
105.66
113.76
111.92
127.19
109.19
118.05
123.23
114.68
104.57
115.73
129.87
120.31
104.23
123.92
124.1
125.61
133.91
124.47
129.64
128.58
103.55
129.57

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=35083&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=35083&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35083&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
Mean558.231884057971113.195797101449
Biased Variance1615.13463558076100.052456248687
Biased Standard Deviation40.188737670904310.0026224685673
Covariance-132.921805200341
Correlation-0.325865069893437
Determination0.106188043776654
T-Test-2.82131859694191
p-value (2 sided)0.00628745022535685
p-value (1 sided)0.00314372511267843
Degrees of Freedom67
Number of Observations69

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 558.231884057971 & 113.195797101449 \tabularnewline
Biased Variance & 1615.13463558076 & 100.052456248687 \tabularnewline
Biased Standard Deviation & 40.1887376709043 & 10.0026224685673 \tabularnewline
Covariance & -132.921805200341 \tabularnewline
Correlation & -0.325865069893437 \tabularnewline
Determination & 0.106188043776654 \tabularnewline
T-Test & -2.82131859694191 \tabularnewline
p-value (2 sided) & 0.00628745022535685 \tabularnewline
p-value (1 sided) & 0.00314372511267843 \tabularnewline
Degrees of Freedom & 67 \tabularnewline
Number of Observations & 69 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35083&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]558.231884057971[/C][C]113.195797101449[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1615.13463558076[/C][C]100.052456248687[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]40.1887376709043[/C][C]10.0026224685673[/C][/ROW]
[ROW][C]Covariance[/C][C]-132.921805200341[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.325865069893437[/C][/ROW]
[ROW][C]Determination[/C][C]0.106188043776654[/C][/ROW]
[ROW][C]T-Test[/C][C]-2.82131859694191[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00628745022535685[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00314372511267843[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]67[/C][/ROW]
[ROW][C]Number of Observations[/C][C]69[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35083&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35083&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
Mean558.231884057971113.195797101449
Biased Variance1615.13463558076100.052456248687
Biased Standard Deviation40.188737670904310.0026224685673
Covariance-132.921805200341
Correlation-0.325865069893437
Determination0.106188043776654
T-Test-2.82131859694191
p-value (2 sided)0.00628745022535685
p-value (1 sided)0.00314372511267843
Degrees of Freedom67
Number of Observations69


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')