FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 09 Dec 2015 10:37:56 +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/2015/Dec/09/t1449657504oycc7iulu4k7unr.htm/, Retrieved Thu, 16 May 2024 14:30:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285605, Retrieved Thu, 16 May 2024 14:30:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117

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 Correlati...] [2015-12-09 10:37:56] [b6628d6ea1d7803ffc2dc825d38ead4a] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.466
0.714
0.715
0.83
0.524
0.773
0.806
0.728
0.931
0.88
0.745
0.788
0.813
0.554
0.776
0.785
0.88
0.731
0.473
0.473
0.58
0.58
0.729
0.681
0.742
0.852
0.776
0.385
0.386
0.579
0.501
0.901
0.635
0.365
0.37
0.819
0.715
0.708
0.486
0.561
0.761
0.812
0.813
0.848
0.861
0.9
0.465
0.716
0.698
0.698
0.708
0.681
0.66
0.556
0.38
0.839
0.429
0.722
0.879
0.884
0.67
0.438
0.741
0.911
0.571
0.854
0.743
0.626
0.391
0.396
0.635
0.469
0.616
0.817
0.893
0.583
0.681
0.681
0.641
0.901
0.886
0.872
0.872
0.715
0.888
0.744
0.755
0.531
0.606
0.888
0.888
0.813
0.621
0.621
0.808
0.764
0.481
0.407
0.789
0.888
0.831
0.88
0.88
0.496
0.411
0.77
0.695
0.406
0.827
0.827
0.485
0.769
0.755
0.755
0.629
0.657
0.692
0.787
0.614
0.389
0.52
0.62
0.62
0.537
0.915
0.908
0.611
0.335
0.5
0.943
0.781
0.535
0.773
0.683
0.761
0.49
0.67
0.734
0.656
0.833
0.822
0.85
0.85
0.782
0.782
0.502
0.749
0.715
0.693
0.693
0.833
0.484
0.743
0.743
0.755
0.368
0.899
0.829
0.874
0.489
0.654
0.654
0.869
0.745
0.745
0.472
0.702
0.529
0.897
0.916
0.662
0.662
0.603
0.603
0.72
0.47
0.704
0.765
0.719
0.756
0.693
0.48
0.733
0.825
0.89
0.912
0.787
0.657
0.617
0.617
0.635
0.499
0.554
0.484
Dataseries Y:
Download CSV
Histogram 
382
512
463
538
370
422
595
496
598
581
517
402
431
487
489
566
597
495
467
490
457
502
460
445
556
491
582
415
458
351
439
566
NA
NA
NA
567
588
505
NA
418
495
491
470
521
570
556
NA
450
446
NA
476
475
482
NA
371
563
434
444
517
555
457
464
571
570
427
533
366
496
386
NA
457
407
417
585
534
582
511
517
357
552
488
563
445
433
544
457
499
438
NA
NA
586
378
514
350
570
498
401
306
432
561
548
559
507
447
387
540
563
382
615
NA
420
528
504
NA
545
NA
470
NA
515
330
492
368
NA
461
540
584
454
401
440
519
381
512
NA
400
485
NA
457
539
539
554
549
397
375
570
557
356
389
413
NA
NA
301
421
NA
528
NA
345
595
576
522
433
475
NA
573
490
458
438
NA
499
503
577
458
546
474
388
498
428
NA
499
507
549
424
381
540
390
587
533
591
532
NA
483
535
378
428
489

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285605&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285605&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285605&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean0.697461538461538483.01775147929
Biased Variance0.02324976331360955047.02335352404
Biased Standard Deviation0.15247873069254471.0424053191053
Covariance6.56598580586081
Correlation0.602553469531076
Determination0.363070683643938
T-Test9.75681808328735
p-value (2 sided)0
p-value (1 sided)0
95% CI of Correlation[0.496781418238339, 0.690687531961296]
Degrees of Freedom167
Number of Observations169

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 0.697461538461538 & 483.01775147929 \tabularnewline
Biased Variance & 0.0232497633136095 & 5047.02335352404 \tabularnewline
Biased Standard Deviation & 0.152478730692544 & 71.0424053191053 \tabularnewline
Covariance & 6.56598580586081 \tabularnewline
Correlation & 0.602553469531076 \tabularnewline
Determination & 0.363070683643938 \tabularnewline
T-Test & 9.75681808328735 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
95% CI of Correlation & [0.496781418238339, 0.690687531961296] \tabularnewline
Degrees of Freedom & 167 \tabularnewline
Number of Observations & 169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285605&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]0.697461538461538[/C][C]483.01775147929[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.0232497633136095[/C][C]5047.02335352404[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.152478730692544[/C][C]71.0424053191053[/C][/ROW]
[ROW][C]Covariance[/C][C]6.56598580586081[/C][/ROW]
[ROW][C]Correlation[/C][C]0.602553469531076[/C][/ROW]
[ROW][C]Determination[/C][C]0.363070683643938[/C][/ROW]
[ROW][C]T-Test[/C][C]9.75681808328735[/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]95% CI of Correlation[/C][C][0.496781418238339, 0.690687531961296][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]167[/C][/ROW]
[ROW][C]Number of Observations[/C][C]169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285605&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285605&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
Mean0.697461538461538483.01775147929
Biased Variance0.02324976331360955047.02335352404
Biased Standard Deviation0.15247873069254471.0424053191053
Covariance6.56598580586081
Correlation0.602553469531076
Determination0.363070683643938
T-Test9.75681808328735
p-value (2 sided)0
p-value (1 sided)0
95% CI of Correlation[0.496781418238339, 0.690687531961296]
Degrees of Freedom167
Number of Observations169






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 10.402, p-value = 0.00551
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.5019, p-value = 0.03874
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.3203, p-value = 6.713e-06

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1313, p-value = 0.005685


\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 10.402, p-value = 0.00551
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.5019, p-value = 0.03874
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.3203, p-value = 6.713e-06

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1313, p-value = 0.005685

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285605&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 10.402, p-value = 0.00551
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.5019, p-value = 0.03874
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 2.3203, p-value = 6.713e-06

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1313, p-value = 0.005685

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285605&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285605&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 10.402, p-value = 0.00551
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.5019, p-value = 0.03874
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.3203, p-value = 6.713e-06

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1313, p-value = 0.005685


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
library(psychometric)
x <- x[!is.na(y)]
y <- y[!is.na(y)]
y <- y[!is.na(x)]
x <- x[!is.na(x)]
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, sub=main)
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', na.rm = T)
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,'95% CI of Correlation',header=TRUE)
a<-table.element(a,paste('[',CIr(r=cxy, n = lx, level = .95)[1],', ', CIr(r=cxy, n = lx, level = .95)[2],']',sep=''),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')
library(moments)
library(nortest)
jarque.x <- jarque.test(x)
jarque.y <- jarque.test(y)
if(lx>7) {
ad.x <- ad.test(x)
ad.y <- ad.test(y)
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Normality Tests',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('jarque.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('jarque.y'),'
',sep=''))
a<-table.row.end(a)
if(lx>7) {
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('ad.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('ad.y'),'
',sep=''))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
library(car)
bitmap(file='test2.png')
qq.plot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qq.plot(y,main='QQplot of variable y')
dev.off()