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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 computationWed, 09 Dec 2015 10:32:10 +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/t14496572898bb97nhbvuymoi3.htm/, Retrieved Thu, 16 May 2024 15:10:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285601, Retrieved Thu, 16 May 2024 15:10:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103

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 
0.458
0.714
0.715
0.831
0.521
0.772
0.804
0.724
0.928
0.879
0.743
0.789
0.812
0.549
0.78
0.784
0.88
0.717
0.471
0.471
0.579
0.579
0.729
0.678
0.74
0.846
0.774
0.376
0.384
0.575
0.498
0.9
0.631
0.361
0.365
0.815
0.71
0.71
0.483
0.549
0.758
0.812
0.819
0.85
0.861
0.899
0.461
0.718
0.695
0.695
0.705
0.679
0.657
0.553
0.377
0.836
0.422
0.722
0.879
0.882
0.666
0.436
0.736
0.908
0.566
0.854
0.747
0.62
0.387
0.402
0.632
0.466
0.615
0.817
0.89
0.581
0.678
0.678
0.639
0.9
0.885
0.872
0.872
0.714
0.887
0.744
0.75
0.527
0.599
0.886
0.886
0.81
0.618
0.618
0.804
0.764
0.476
0.402
0.753
0.887
0.828
0.881
0.881
0.495
0.411
0.768
0.692
0.405
0.823
0.823
0.475
0.759
0.752
0.752
0.627
0.656
0.682
0.787
0.612
0.384
0.517
0.616
0.616
0.533
0.914
0.904
0.608
0.328
0.496
0.941
0.781
0.531
0.77
0.679
0.757
0.484
0.672
0.727
0.652
0.83
0.819
0.843
0.843
0.782
0.782
0.463
0.745
0.718
0.69
0.69
0.825
0.483
0.744
0.744
0.749
0.36
0.896
0.827
0.874
0.494
0.646
0.646
0.868
0.74
0.74
0.468
0.701
0.53
0.896
0.914
0.662
0.662
0.6
0.6
0.716
0.467
0.702
0.764
0.716
0.752
0.69
0.477
0.73
0.824
0.891
0.911
0.783
0.653
0.618
0.618
0.632
0.497
0.543
0.473
Dataseries Y:
Download CSV
Histogram 
421
493
515
NA
398
400
598
477
597
573
532
433
384
501
517
556
578
423
464
449
407
474
494
450
554
534
582
433
413
403
442
563
NA
NA
NA
551
592
498
580
438
524
489
483
547
568
545
NA
411
435
NA
468
471
499
NA
355
552
444
448
510
564
395
397
524
565
444
529
367
500
390
NA
468
408
466
583
545
581
516
519
390
563
485
563
453
444
541
433
479
432
NA
NA
579
385
529
404
581
488
483
323
326
NA
557
537
475
533
420
553
NA
405
578
NA
NA
576
499
NA
544
621
469
NA
515
347
441
395
NA
472
540
602
465
344
437
509
323
508
NA
411
453
NA
534
540
525
540
538
431
318
572
556
373
360
448
NA
NA
330
461
NA
509
NA
389
593
570
573
362
474
NA
576
492
427
420
NA
419
515
558
453
538
362
392
495
424
484
488
541
543
481
389
539
376
584
531
589
506
NA
490
518
367
416
493

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=285601&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=285601&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285601&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
Mean0.692369047619048482.375
Biased Variance0.02338995904195015245.79389880952
Biased Standard Deviation0.1529377619881772.4278530595069
Covariance6.09264520958084
Correlation0.546754965272195
Determination0.2989409920498
T-Test8.41336039463679
p-value (2 sided)1.75415237890775e-14
p-value (1 sided)8.77076189453874e-15
95% CI of Correlation[0.431027368554462, 0.644786698033197]
Degrees of Freedom166
Number of Observations168

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 0.692369047619048 & 482.375 \tabularnewline
Biased Variance & 0.0233899590419501 & 5245.79389880952 \tabularnewline
Biased Standard Deviation & 0.15293776198817 & 72.4278530595069 \tabularnewline
Covariance & 6.09264520958084 \tabularnewline
Correlation & 0.546754965272195 \tabularnewline
Determination & 0.2989409920498 \tabularnewline
T-Test & 8.41336039463679 \tabularnewline
p-value (2 sided) & 1.75415237890775e-14 \tabularnewline
p-value (1 sided) & 8.77076189453874e-15 \tabularnewline
95% CI of Correlation & [0.431027368554462, 0.644786698033197] \tabularnewline
Degrees of Freedom & 166 \tabularnewline
Number of Observations & 168 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285601&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]0.692369047619048[/C][C]482.375[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.0233899590419501[/C][C]5245.79389880952[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.15293776198817[/C][C]72.4278530595069[/C][/ROW]
[ROW][C]Covariance[/C][C]6.09264520958084[/C][/ROW]
[ROW][C]Correlation[/C][C]0.546754965272195[/C][/ROW]
[ROW][C]Determination[/C][C]0.2989409920498[/C][/ROW]
[ROW][C]T-Test[/C][C]8.41336039463679[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.75415237890775e-14[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]8.77076189453874e-15[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.431027368554462, 0.644786698033197][/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=285601&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285601&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
Mean0.692369047619048482.375
Biased Variance0.02338995904195015245.79389880952
Biased Standard Deviation0.1529377619881772.4278530595069
Covariance6.09264520958084
Correlation0.546754965272195
Determination0.2989409920498
T-Test8.41336039463679
p-value (2 sided)1.75415237890775e-14
p-value (1 sided)8.77076189453874e-15
95% CI of Correlation[0.431027368554462, 0.644786698033197]
Degrees of Freedom166
Number of Observations168






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 9.8352, p-value = 0.007317
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 7.3522, p-value = 0.02532
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.1535, p-value = 1.722e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.3466, p-value = 0.00167


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 9.8352, p-value = 0.007317
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 7.3522, p-value = 0.02532
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.1535, p-value = 1.722e-05

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.3466, p-value = 0.00167

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285601&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 9.8352, p-value = 0.007317
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 7.3522, p-value = 0.02532
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 2.1535, p-value = 1.722e-05

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.3466, p-value = 0.00167

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285601&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285601&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 = 9.8352, p-value = 0.007317
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 7.3522, p-value = 0.02532
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.1535, p-value = 1.722e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.3466, p-value = 0.00167


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()