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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 computationFri, 11 Dec 2015 16:31:26 +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/11/t1449851608n73etp5svr4f62i.htm/, Retrieved Thu, 16 May 2024 11:53:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285993, Retrieved Thu, 16 May 2024 11:53:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66

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 
0.5215052
0.4248284
0.4250311
0.4771938
0.8280212
0.6156186
0.366627
0.4308883
0.2810287
0.4646245
0.2693951
0.5779049
0.5661151
0.5077584
0.7507175
0.6808395
0.7661091
0.4561473
0.4977496
0.4193273
0.6095514
0.457337
0.5705478
0.3478996
0.3874993
0.5824285
0.2391033
0.2367445
0.2626158
0.4240934
0.365275
0.3750758
0.4090056
0.3891676
0.240261
0.1589496
0.4393373
0.5094681
0.3743465
0.4339828
0.4130557
0.3288928
0.5186648
0.5486504
0.5469111
0.4963494
0.5308929
0.5957761
0.5570584
0.5731325
0.5005416
0.5431269
0.5593657
0.6911693
0.4403485
0.5676662
0.5969114
0.4735537
0.5923935
0.5975556
0.6334127
0.6057115
0.7046107
0.4805263
0.702686
0.7009017
0.6030854
0.6980919
0.597656
0.8023421
0.6017109
0.5993127
0.6025625
0.7016625
0.4995714
0.4980918
0.497569
0.600183
0.3339542
0.274437
0.3209428
0.5406671
0.4050209
0.2885961
0.3275942
0.3132606
0.2575562
0.2138386
0.1861856
0.1592713
Dataseries Y:
Download CSV
Histogram 
4.031636
3.702076
3.056176
3.280707
2.984728
3.693712
3.226317
2.190349
2.599515
3.080288
2.929672
2.922548
3.234943
2.983081
3.284389
3.806511
3.784579
2.645654
3.092081
3.204859
3.107225
3.466909
2.984404
3.218072
2.82731
3.182049
2.236319
2.033218
1.644804
1.627971
1.677559
2.330828
2.493615
2.257172
2.655517
2.298655
2.600402
3.04523
2.790583
3.227052
2.967479
2.938817
3.277961
3.423985
3.072646
2.754253
2.910431
3.174369
3.068387
3.089543
2.906654
2.931161
3.02566
2.939551
2.691019
3.19812
3.07639
2.863873
3.013802
3.053364
2.864753
3.057062
2.959365
3.252258
3.602988
3.497704
3.296867
3.602417
3.3001
3.40193
3.502591
3.402348
3.498551
3.199823
2.700064
2.801034
2.898628
2.800854
2.399942
2.402724
2.202331
2.102594
1.798293
1.202484
1.400201
1.200832
1.298083
1.099742
1.001377
0.8361743

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285993&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285993&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285993&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'Herman Ole Andreas Wold' @ wold.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean0.4840349966666672.80444771444444
Biased Variance0.02280849186155170.458304402404026
Biased Standard Deviation0.151024805451130.676981833141796
Covariance0.0727303226801652
Correlation0.703457253559277
Determination0.494852107585161
T-Test9.28474061587881
p-value (2 sided)1.06581410364015e-14
p-value (1 sided)5.32907051820075e-15
95% CI of Correlation[0.581007106898875, 0.794766924129167]
Degrees of Freedom88
Number of Observations90

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 0.484034996666667 & 2.80444771444444 \tabularnewline
Biased Variance & 0.0228084918615517 & 0.458304402404026 \tabularnewline
Biased Standard Deviation & 0.15102480545113 & 0.676981833141796 \tabularnewline
Covariance & 0.0727303226801652 \tabularnewline
Correlation & 0.703457253559277 \tabularnewline
Determination & 0.494852107585161 \tabularnewline
T-Test & 9.28474061587881 \tabularnewline
p-value (2 sided) & 1.06581410364015e-14 \tabularnewline
p-value (1 sided) & 5.32907051820075e-15 \tabularnewline
95% CI of Correlation & [0.581007106898875, 0.794766924129167] \tabularnewline
Degrees of Freedom & 88 \tabularnewline
Number of Observations & 90 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285993&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]0.484034996666667[/C][C]2.80444771444444[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.0228084918615517[/C][C]0.458304402404026[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.15102480545113[/C][C]0.676981833141796[/C][/ROW]
[ROW][C]Covariance[/C][C]0.0727303226801652[/C][/ROW]
[ROW][C]Correlation[/C][C]0.703457253559277[/C][/ROW]
[ROW][C]Determination[/C][C]0.494852107585161[/C][/ROW]
[ROW][C]T-Test[/C][C]9.28474061587881[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.06581410364015e-14[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]5.32907051820075e-15[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.581007106898875, 0.794766924129167][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]88[/C][/ROW]
[ROW][C]Number of Observations[/C][C]90[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285993&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285993&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
Mean0.4840349966666672.80444771444444
Biased Variance0.02280849186155170.458304402404026
Biased Standard Deviation0.151024805451130.676981833141796
Covariance0.0727303226801652
Correlation0.703457253559277
Determination0.494852107585161
T-Test9.28474061587881
p-value (2 sided)1.06581410364015e-14
p-value (1 sided)5.32907051820075e-15
95% CI of Correlation[0.581007106898875, 0.794766924129167]
Degrees of Freedom88
Number of Observations90






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1549, p-value = 0.5613
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 20.726, p-value = 3.159e-05
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.41569, p-value = 0.3266

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.3082, p-value = 2.392e-08


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1549, p-value = 0.5613
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 20.726, p-value = 3.159e-05
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.41569, p-value = 0.3266

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.3082, p-value = 2.392e-08

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285993&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1549, p-value = 0.5613
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 20.726, p-value = 3.159e-05
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.41569, p-value = 0.3266

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 3.3082, p-value = 2.392e-08

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285993&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285993&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 = 1.1549, p-value = 0.5613
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 20.726, p-value = 3.159e-05
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.41569, p-value = 0.3266

> ad.y
	Anderson-Darling normality test
data:  y
A = 3.3082, p-value = 2.392e-08


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()