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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, 06 Dec 2015 13:01:05 +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/06/t1449406941ddh6my7mp8zt5na.htm/, Retrieved Thu, 16 May 2024 11:30:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285272, Retrieved Thu, 16 May 2024 11:30:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.453
0.708
0.709
0.832
0.504
0.778
0.799
0.72
0.926
0.877
0.743
0.788
0.812
0.539
0.779
0.779
0.877
0.714
0.467
0.467
0.569
0.569
0.726
0.672
0.739
0.844
0.773
0.367
0.381
0.571
0.493
0.896
0.622
0.355
0.349
0.808
0.701
0.706
0.479
0.565
0.75
0.806
0.824
0.848
0.858
0.898
0.452
0.717
0.691
0.691
0.701
0.678
0.652
0.559
0.373
0.83
0.409
0.721
0.877
0.879
0.662
0.44
0.733
0.904
0.556
0.856
0.746
0.613
0.38
0.401
0.626
0.462
0.612
0.817
0.886
0.57
0.671
0.671
0.638
0.899
0.881
0.869
0.869
0.712
0.884
0.744
0.747
0.522
0.599
0.882
0.882
0.807
0.614
0.614
0.809
0.759
0.472
0.393
0.799
0.882
0.829
0.881
0.881
0.494
0.406
0.766
0.688
0.398
0.821
0.821
0.475
0.753
0.748
0.748
0.627
0.652
0.671
0.784
0.603
0.38
0.514
0.61
0.61
0.527
0.904
0.903
0.604
0.323
0.492
0.939
0.78
0.526
0.768
0.671
0.759
0.479
0.669
0.722
0.651
0.826
0.816
0.847
0.847
0.779
0.779
0.453
0.747
0.717
0.688
0.688
0.815
0.483
0.743
0.743
0.763
0.353
0.894
0.826
0.873
0.489
0.638
0.638
0.864
0.736
0.736
0.463
0.698
0.527
0.895
0.915
0.662
0.662
0.596
0.596
0.715
0.46
0.701
0.764
0.715
0.738
0.687
0.472
0.726
0.824
0.895
0.908
0.779
0.648
0.617
0.617
0.629
0.484
0.53
0.459
Dataseries Y:
Download CSV
Histogram 
439
488
517
569
353
416
587
464
596
576
505
445
433
487
511
583
581
468
417
NA
484
500
497
427
554
439
591
421
419
461
435
568
NA
NA
NA
575
596
505
NA
402
529
504
457
527
562
558
NA
433
438
NA
470
468
524
NA
445
567
436
524
510
556
417
412
525
568
450
521
402
508
395
NA
429
417
458
568
549
578
517
518
393
561
483
555
439
444
545
447
481
434
NA
NA
576
388
539
372
557
466
NA
332
337
NA
562
561
498
489
469
536
507
386
498
NA
463
550
502
NA
531
515
476
NA
507
399
477
371
NA
462
524
604
477
390
456
529
421
503
NA
415
456
NA
459
543
534
541
538
439
476
578
553
351
420
409
NA
NA
355
462
NA
529
NA
395
595
547
552
483
473
NA
579
518
438
395
412
460
532
560
457
534
416
403
498
429
NA
478
509
547
485
411
535
387
585
533
567
523
NA
500
519
381
417
495

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=285272&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=285272&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285272&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
Mean0.692470238095238486.113095238095
Biased Variance0.02344580863803864113.13601899093
Biased Standard Deviation0.15312024241764664.133735420533
Covariance5.83182075135443
Correlation0.590326409204974
Determination0.348485269404838
T-Test9.42289033606084
p-value (2 sided)0
p-value (1 sided)0
95% CI of Correlation[0.481998195280279, 0.680878466333262]
Degrees of Freedom166
Number of Observations168

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 0.692470238095238 & 486.113095238095 \tabularnewline
Biased Variance & 0.0234458086380386 & 4113.13601899093 \tabularnewline
Biased Standard Deviation & 0.153120242417646 & 64.133735420533 \tabularnewline
Covariance & 5.83182075135443 \tabularnewline
Correlation & 0.590326409204974 \tabularnewline
Determination & 0.348485269404838 \tabularnewline
T-Test & 9.42289033606084 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
95% CI of Correlation & [0.481998195280279, 0.680878466333262] \tabularnewline
Degrees of Freedom & 166 \tabularnewline
Number of Observations & 168 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285272&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]0.692470238095238[/C][C]486.113095238095[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.0234458086380386[/C][C]4113.13601899093[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.153120242417646[/C][C]64.133735420533[/C][/ROW]
[ROW][C]Covariance[/C][C]5.83182075135443[/C][/ROW]
[ROW][C]Correlation[/C][C]0.590326409204974[/C][/ROW]
[ROW][C]Determination[/C][C]0.348485269404838[/C][/ROW]
[ROW][C]T-Test[/C][C]9.42289033606084[/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][0.481998195280279, 0.680878466333262][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]166[/C][/ROW]
[ROW][C]Number of Observations[/C][C]168[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285272&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285272&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
Mean0.692470238095238486.113095238095
Biased Variance0.02344580863803864113.13601899093
Biased Standard Deviation0.15312024241764664.133735420533
Covariance5.83182075135443
Correlation0.590326409204974
Determination0.348485269404838
T-Test9.42289033606084
p-value (2 sided)0
p-value (1 sided)0
95% CI of Correlation[0.481998195280279, 0.680878466333262]
Degrees of Freedom166
Number of Observations168






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 10.266, p-value = 0.005899
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.2675, p-value = 0.04355
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.191, p-value = 1.393e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1037, p-value = 0.006649


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 10.266, p-value = 0.005899
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.2675, p-value = 0.04355
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.191, p-value = 1.393e-05

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1037, p-value = 0.006649

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285272&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 10.266, p-value = 0.005899
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.2675, p-value = 0.04355
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 2.191, p-value = 1.393e-05

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1037, p-value = 0.006649

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285272&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285272&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 = 10.266, p-value = 0.005899
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 6.2675, p-value = 0.04355
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.191, p-value = 1.393e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.1037, p-value = 0.006649


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()