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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 computationSun, 07 Dec 2008 12:14:51 -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/07/t1228677319xeqm8qwf7t9g4h5.htm/, Retrieved Sat, 18 May 2024 21:27:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30260, Retrieved Sat, 18 May 2024 21:27:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean versus Median] [Totale Invoer naa...] [2008-12-07 18:21:05] [299afd6311e4c20059ea2f05c8dd029d]
- RM D  [Variability] [Totale Invoer naa...] [2008-12-07 18:28:38] [299afd6311e4c20059ea2f05c8dd029d]
- RMP     [Stem-and-leaf Plot] [Totale Invoer naa...] [2008-12-07 18:32:41] [299afd6311e4c20059ea2f05c8dd029d]
- RMPD      [Quartiles] [Totale Invoer naa...] [2008-12-07 18:52:56] [299afd6311e4c20059ea2f05c8dd029d]
- RM D        [Harrell-Davis Quantiles] [Totale Invoer naa...] [2008-12-07 19:02:20] [299afd6311e4c20059ea2f05c8dd029d]
- RM D            [Pearson Correlation] [Totale Invoer vs ...] [2008-12-07 19:14:51] [5e2b1e7aa808f9f0d23fd35605d4968f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13429,9
13470,1
14785,8
14292
14308,8
14013
13240,9
12153,4
14289,7
15669,2
14169,5
14569,8
14469,1
14264,9
15320,9
14433,5
13691,5
14194,1
13519,2
11857,9
14616
15643,4
14077,2
14887,5
14159,9
14643
17192,5
15386,1
14287,1
17526,6
14497
14398,3
16629,6
16670,7
16614,8
16869,2
15663,9
16359,9
18447,7
16889
16505
18320,9
15052,1
15699,8
18135,3
16768,7
18883
19021
18101,9
17776,1
21489,9
17065,3
18690
18953,1
16398,9
16895,7
18553
19270
19422,1
17579,4
18637,3
18076,7
20438,6
18075,2
19563
19899,2
19227,5
17789,6
19220,8
21968,9
21131,5
19484,6
Dataseries Y:
Download CSV
Histogram 
476
475
470
461
455
456
517
525
523
519
509
512
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

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 & 0 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30260&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]0 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=30260&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30260&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 time0 seconds
R Server'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean16495.7875553.902777777778
Biased Variance5392838.780260421967.00443672840
Biased Standard Deviation2322.2486473804744.3509237415456
Covariance27540.6213028169
Correlation0.263686683196421
Determination0.0695306668951296
T-Test2.28710543244863
p-value (2 sided)0.0252166827594964
p-value (1 sided)0.0126083413797482
Degrees of Freedom70
Number of Observations72

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 16495.7875 & 553.902777777778 \tabularnewline
Biased Variance & 5392838.78026042 & 1967.00443672840 \tabularnewline
Biased Standard Deviation & 2322.24864738047 & 44.3509237415456 \tabularnewline
Covariance & 27540.6213028169 \tabularnewline
Correlation & 0.263686683196421 \tabularnewline
Determination & 0.0695306668951296 \tabularnewline
T-Test & 2.28710543244863 \tabularnewline
p-value (2 sided) & 0.0252166827594964 \tabularnewline
p-value (1 sided) & 0.0126083413797482 \tabularnewline
Degrees of Freedom & 70 \tabularnewline
Number of Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30260&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]16495.7875[/C][C]553.902777777778[/C][/ROW]
[ROW][C]Biased Variance[/C][C]5392838.78026042[/C][C]1967.00443672840[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2322.24864738047[/C][C]44.3509237415456[/C][/ROW]
[ROW][C]Covariance[/C][C]27540.6213028169[/C][/ROW]
[ROW][C]Correlation[/C][C]0.263686683196421[/C][/ROW]
[ROW][C]Determination[/C][C]0.0695306668951296[/C][/ROW]
[ROW][C]T-Test[/C][C]2.28710543244863[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0252166827594964[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0126083413797482[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]70[/C][/ROW]
[ROW][C]Number of Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30260&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30260&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
Mean16495.7875553.902777777778
Biased Variance5392838.780260421967.00443672840
Biased Standard Deviation2322.2486473804744.3509237415456
Covariance27540.6213028169
Correlation0.263686683196421
Determination0.0695306668951296
T-Test2.28710543244863
p-value (2 sided)0.0252166827594964
p-value (1 sided)0.0126083413797482
Degrees of Freedom70
Number of Observations72


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')