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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, 15 Dec 2017 13:52:19 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/15/t1513342394pmoztahqi509v99.htm/, Retrieved Thu, 16 May 2024 01:45:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309672, Retrieved Thu, 16 May 2024 01:45:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2017-12-15 12:52:19] [30e08ccf92bdf95f8dcbf6f321363364] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
28,4
33,6
21,4
21,0
31,7
30,8
28,4
38,9
28,0
32,7
31,5
20,1
15,3
37,3
22,3
31,5
41,1
21,0
18,9
35,7
32,0
22,8
18,4
16,4
24,0
18,4
36,0
33,0
40,1
31,7
39,1
44,2
Dataseries Y:
Download CSV
Histogram 
31,8
40,1
33,6
23,4
42,6
24,4
47,5
46,5
30,1
37,5
36,5
25,4
19,8
43,4
40,1
45,3
41,1
27,3
20,2
35,0
29,1
32,6
26,9
17,9
36,7
23,9
49,6
46,7
43,1
46,5
47,5
35,3

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309672&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309672&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309672&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean28.92812535.23125
Biased Variance62.55202148437585.3915234375
Biased Standard Deviation7.90898359363429.24075340205007
Covariance54.9465120967742
Correlation0.728322605079658
Determination0.530453817070019
T-Test5.82163884283595
p-value (2 sided)2.29768741144872e-06
p-value (1 sided)1.14884370572436e-06
95% CI of Correlation[0.508859445053108, 0.858891124502346]
Degrees of Freedom30
Number of Observations32

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 28.928125 & 35.23125 \tabularnewline
Biased Variance & 62.552021484375 & 85.3915234375 \tabularnewline
Biased Standard Deviation & 7.9089835936342 & 9.24075340205007 \tabularnewline
Covariance & 54.9465120967742 \tabularnewline
Correlation & 0.728322605079658 \tabularnewline
Determination & 0.530453817070019 \tabularnewline
T-Test & 5.82163884283595 \tabularnewline
p-value (2 sided) & 2.29768741144872e-06 \tabularnewline
p-value (1 sided) & 1.14884370572436e-06 \tabularnewline
95% CI of Correlation & [0.508859445053108, 0.858891124502346] \tabularnewline
Degrees of Freedom & 30 \tabularnewline
Number of Observations & 32 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309672&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]28.928125[/C][C]35.23125[/C][/ROW]
[ROW][C]Biased Variance[/C][C]62.552021484375[/C][C]85.3915234375[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]7.9089835936342[/C][C]9.24075340205007[/C][/ROW]
[ROW][C]Covariance[/C][C]54.9465120967742[/C][/ROW]
[ROW][C]Correlation[/C][C]0.728322605079658[/C][/ROW]
[ROW][C]Determination[/C][C]0.530453817070019[/C][/ROW]
[ROW][C]T-Test[/C][C]5.82163884283595[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.29768741144872e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.14884370572436e-06[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.508859445053108, 0.858891124502346][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]30[/C][/ROW]
[ROW][C]Number of Observations[/C][C]32[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309672&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309672&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
Mean28.92812535.23125
Biased Variance62.55202148437585.3915234375
Biased Standard Deviation7.90898359363429.24075340205007
Covariance54.9465120967742
Correlation0.728322605079658
Determination0.530453817070019
T-Test5.82163884283595
p-value (2 sided)2.29768741144872e-06
p-value (1 sided)1.14884370572436e-06
95% CI of Correlation[0.508859445053108, 0.858891124502346]
Degrees of Freedom30
Number of Observations32






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.6065, p-value = 0.4479
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.0154, p-value = 0.3651
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.53718, p-value = 0.1559

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.46077, p-value = 0.2435


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.6065, p-value = 0.4479
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.0154, p-value = 0.3651
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.53718, p-value = 0.1559

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.46077, p-value = 0.2435

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309672&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.6065, p-value = 0.4479
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.0154, p-value = 0.3651
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.53718, p-value = 0.1559

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.46077, p-value = 0.2435

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309672&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309672&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 = 1.6065, p-value = 0.4479
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.0154, p-value = 0.3651
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.53718, p-value = 0.1559

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.46077, p-value = 0.2435


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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Variance',header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Standard Deviation',header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Covariance',header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Correlation',header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Determination',header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-Test',header=TRUE)
a<-table.element(a,as.matrix(corxy$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')
qqPlot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qqPlot(y,main='QQplot of variable y')
dev.off()