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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 computationSat, 10 Dec 2016 12:01:10 +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/2016/Dec/10/t14813677179k3vby5lbjuroyq.htm/, Retrieved Mon, 06 May 2024 02:29:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298640, Retrieved Mon, 06 May 2024 02:29:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pearson Correlatie] [2016-12-10 11:01:10] [6fe662842930c5949e61d44eeb8a265b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
22
24
26
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26
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24
27
28
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NA
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NA
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NA
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27
22
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23
28
NA
24
26
22
25
25
24
24
26
21
25
25
26
25
26
27
25
NA
20
24
26
25
25
24
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25
28
27
25
26
26
26
NA
28
NA
21
25
25
24
24
24
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23
24
24
25
28
23
24
23
24
25
24
23
23
25
21
22
19
24
25
21
22
23
27
NA
26
29
28
24
25
25
22
25
26
26
24
25
19
25
23
25
25
26
27
24
22
25
24
23
27
24
24
21
25
25
23
Dataseries Y:
Download CSV
Histogram 
13
16
17
NA
NA
16
NA
NA
NA
17
17
15
16
14
16
17
NA
NA
NA
NA
16
NA
16
NA
NA
NA
16
15
16
16
13
15
17
NA
13
17
NA
14
14
18
NA
17
13
16
15
15
NA
15
13
NA
17
NA
NA
11
14
13
NA
17
16
NA
17
16
16
16
15
12
17
14
14
16
NA
NA
NA
NA
NA
15
16
14
15
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NA
10
NA
17
NA
20
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18
NA
17
14
NA
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NA
17
NA
16
18
18
16
NA
NA
15
13
NA
NA
NA
NA
NA
16
NA
NA
NA
12
NA
16
16
NA
16
14
15
14
NA
15
NA
15
16
NA
NA
NA
11
NA
18
NA
11
NA
18
NA
15
19
17
NA
14
NA
13
17
14
19
14
NA
NA
16
16
15
12
NA
17
NA
NA
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18
15
NA
NA
NA
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NA
16

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298640&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]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298640&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298640&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 time3 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean24.627450980392215.4607843137255
Biased Variance3.449442522106883.48375624759708
Biased Standard Deviation1.857267488033671.86648231912255
Covariance1.65851291011454
Correlation0.473741817484153
Determination0.224431309633189
T-Test5.37937211874121
p-value (2 sided)4.92798817366795e-07
p-value (1 sided)2.46399408683397e-07
95% CI of Correlation[0.307607030418164, 0.61184672992439]
Degrees of Freedom100
Number of Observations102

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 24.6274509803922 & 15.4607843137255 \tabularnewline
Biased Variance & 3.44944252210688 & 3.48375624759708 \tabularnewline
Biased Standard Deviation & 1.85726748803367 & 1.86648231912255 \tabularnewline
Covariance & 1.65851291011454 \tabularnewline
Correlation & 0.473741817484153 \tabularnewline
Determination & 0.224431309633189 \tabularnewline
T-Test & 5.37937211874121 \tabularnewline
p-value (2 sided) & 4.92798817366795e-07 \tabularnewline
p-value (1 sided) & 2.46399408683397e-07 \tabularnewline
95% CI of Correlation & [0.307607030418164, 0.61184672992439] \tabularnewline
Degrees of Freedom & 100 \tabularnewline
Number of Observations & 102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298640&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]24.6274509803922[/C][C]15.4607843137255[/C][/ROW]
[ROW][C]Biased Variance[/C][C]3.44944252210688[/C][C]3.48375624759708[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.85726748803367[/C][C]1.86648231912255[/C][/ROW]
[ROW][C]Covariance[/C][C]1.65851291011454[/C][/ROW]
[ROW][C]Correlation[/C][C]0.473741817484153[/C][/ROW]
[ROW][C]Determination[/C][C]0.224431309633189[/C][/ROW]
[ROW][C]T-Test[/C][C]5.37937211874121[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]4.92798817366795e-07[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.46399408683397e-07[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.307607030418164, 0.61184672992439][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]100[/C][/ROW]
[ROW][C]Number of Observations[/C][C]102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298640&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298640&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
Mean24.627450980392215.4607843137255
Biased Variance3.449442522106883.48375624759708
Biased Standard Deviation1.857267488033671.86648231912255
Covariance1.65851291011454
Correlation0.473741817484153
Determination0.224431309633189
T-Test5.37937211874121
p-value (2 sided)4.92798817366795e-07
p-value (1 sided)2.46399408683397e-07
95% CI of Correlation[0.307607030418164, 0.61184672992439]
Degrees of Freedom100
Number of Observations102






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.45935, p-value = 0.7948
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.4587, p-value = 0.1076
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4172, p-value = 0.001092

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.8991, p-value = 7.032e-05


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.45935, p-value = 0.7948
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.4587, p-value = 0.1076
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4172, p-value = 0.001092

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.8991, p-value = 7.032e-05

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298640&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.45935, p-value = 0.7948
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.4587, p-value = 0.1076
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4172, p-value = 0.001092

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.8991, p-value = 7.032e-05

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298640&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298640&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 = 0.45935, p-value = 0.7948
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 4.4587, p-value = 0.1076
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 1.4172, p-value = 0.001092

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.8991, p-value = 7.032e-05


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()