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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 10:40:39 +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/t1449657682tiyu0tectrnxxzr.htm/, Retrieved Thu, 16 May 2024 20:59:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285606, Retrieved Thu, 16 May 2024 20:59:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107

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 
0.468
0.716
0.717
0.83
0.526
0.774
0.808
0.73
0.933
0.881
0.747
0.789
0.815
0.558
0.776
0.786
0.881
0.732
0.476
0.476
0.584
0.584
0.731
0.683
0.744
0.852
0.777
0.388
0.389
0.584
0.504
0.902
0.636
0.341
0.372
0.822
0.719
0.711
0.488
0.564
0.763
0.812
0.815
0.845
0.861
0.9
0.467
0.717
0.7
0.7
0.711
0.682
0.662
0.556
0.381
0.84
0.435
0.724
0.879
0.884
0.674
0.441
0.744
0.911
0.573
0.853
0.744
0.628
0.392
0.396
0.638
0.471
0.617
0.818
0.895
0.586
0.684
0.684
0.642
0.899
0.888
0.872
0.872
0.715
0.89
0.745
0.757
0.535
0.607
0.891
0.891
0.814
0.628
0.628
0.81
0.765
0.486
0.412
0.784
0.889
0.834
0.881
0.881
0.498
0.414
0.773
0.698
0.407
0.829
0.829
0.487
0.771
0.756
0.756
0.63
0.663
0.698
0.789
0.617
0.393
0.524
0.624
0.624
0.54
0.915
0.91
0.614
0.337
0.504
0.944
0.783
0.537
0.775
0.686
0.765
0.491
0.676
0.737
0.66
0.834
0.822
0.851
0.851
0.785
0.785
0.506
0.75
0.714
0.694
0.694
0.836
0.485
0.745
0.745
0.756
0.374
0.901
0.83
0.874
0.491
0.658
0.658
0.869
0.75
0.75
0.473
0.705
0.53
0.898
0.917
0.658
0.658
0.607
0.607
0.722
0.473
0.705
0.766
0.721
0.759
0.698
0.484
0.734
0.827
0.892
0.914
0.79
0.661
0.616
0.616
0.638
0.5
0.561
0.492
Dataseries Y:
Download CSV
Histogram 
307
487
471
NA
370
353
591
554
590
591
514
424
427
488
484
575
591
447
459
558
461
451
442
444
560
441
572
406
412
338
445
565
NA
NA
NA
574
582
499
NA
397
521
521
386
523
571
550
NA
383
429
NA
457
463
450
NA
389
564
427
NA
522
559
468
464
527
570
419
526
NA
490
382
NA
417
403
462
580
506
577
509
520
360
562
484
561
448
428
542
440
501
427
NA
NA
581
344
536
383
562
492
490
314
355
556
550
558
558
468
399
549
400
433
547
NA
354
557
496
NA
528
NA
474
477
505
369
462
347
NA
478
536
608
463
408
418
540
405
497
NA
389
480
NA
508
543
516
565
559
441
312
576
553
396
368
420
NA
NA
311
452
551
NA
NA
341
605
527
557
398
475
NA
578
477
NA
435
403
446
510
580
470
548
437
368
498
428
NA
479
497
550
472
407
542
385
590
532
587
521
NA
496
542
395
417
488

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=285606&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=285606&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285606&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
Mean0.698616766467066479.497005988024
Biased Variance0.0231932543296645502.41765570655
Biased Standard Deviation0.15229331675967974.178282911554
Covariance6.43704703845321
Correlation0.566396653162602
Determination0.320805168713797
T-Test8.82806382649138
p-value (2 sided)1.33226762955019e-15
p-value (1 sided)6.66133814775094e-16
95% CI of Correlation[0.453544722178516, 0.661372289356257]
Degrees of Freedom165
Number of Observations167

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 0.698616766467066 & 479.497005988024 \tabularnewline
Biased Variance & 0.023193254329664 & 5502.41765570655 \tabularnewline
Biased Standard Deviation & 0.152293316759679 & 74.178282911554 \tabularnewline
Covariance & 6.43704703845321 \tabularnewline
Correlation & 0.566396653162602 \tabularnewline
Determination & 0.320805168713797 \tabularnewline
T-Test & 8.82806382649138 \tabularnewline
p-value (2 sided) & 1.33226762955019e-15 \tabularnewline
p-value (1 sided) & 6.66133814775094e-16 \tabularnewline
95% CI of Correlation & [0.453544722178516, 0.661372289356257] \tabularnewline
Degrees of Freedom & 165 \tabularnewline
Number of Observations & 167 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285606&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]0.698616766467066[/C][C]479.497005988024[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.023193254329664[/C][C]5502.41765570655[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.152293316759679[/C][C]74.178282911554[/C][/ROW]
[ROW][C]Covariance[/C][C]6.43704703845321[/C][/ROW]
[ROW][C]Correlation[/C][C]0.566396653162602[/C][/ROW]
[ROW][C]Determination[/C][C]0.320805168713797[/C][/ROW]
[ROW][C]T-Test[/C][C]8.82806382649138[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.33226762955019e-15[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]6.66133814775094e-16[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.453544722178516, 0.661372289356257][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]165[/C][/ROW]
[ROW][C]Number of Observations[/C][C]167[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285606&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285606&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
Mean0.698616766467066479.497005988024
Biased Variance0.0231932543296645502.41765570655
Biased Standard Deviation0.15229331675967974.178282911554
Covariance6.43704703845321
Correlation0.566396653162602
Determination0.320805168713797
T-Test8.82806382649138
p-value (2 sided)1.33226762955019e-15
p-value (1 sided)6.66133814775094e-16
95% CI of Correlation[0.453544722178516, 0.661372289356257]
Degrees of Freedom165
Number of Observations167






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 10.167, p-value = 0.006198
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 7.5174, p-value = 0.02331
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.2356, p-value = 1.082e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.5083, p-value = 0.0006663


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 10.167, p-value = 0.006198
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 7.5174, p-value = 0.02331
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.2356, p-value = 1.082e-05

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.5083, p-value = 0.0006663

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285606&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 10.167, p-value = 0.006198
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 7.5174, p-value = 0.02331
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 2.2356, p-value = 1.082e-05

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.5083, p-value = 0.0006663

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285606&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285606&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 = 10.167, p-value = 0.006198
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 7.5174, p-value = 0.02331
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.2356, p-value = 1.082e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.5083, p-value = 0.0006663


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()