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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, 25 Nov 2016 18:17:46 +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/Nov/25/t1480094335q0efxy6z2cchh5t.htm/, Retrieved Sun, 19 May 2024 00:27:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297098, Retrieved Sun, 19 May 2024 00:27:17 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71

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 
7
7
11
11
10
9
9
11
NA
11
6
8
13
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NA
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NA
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13
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NA
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4
9
10
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NA
12
14
12
12
9
9
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11
10
10
7
11
13
11
11
9
9
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9
10
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11
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14
8
10
10
10
9
9
8
9
NA
12
10
11
10
10
13
12
10
10
12
5
11
7
11
10
11
11
14
11
14
12
13
13
10
7
11
9
8
9
8
9
12
9
10
12
10
9
10
13
10
NA
10
9
13
12
NA
11
12
13
NA
10
10
7
9
13
13
11
11
12
13
14
12
9
13
10
8
10
10
NA
10
9
12
10
9
10
9
11
8
10
9
10
Dataseries Y:
Download CSV
Histogram 
9
9
9
12
9
7
7
6
7
10
10
8
13
9
8
5
12
NA
NA
9
NA
8
7
10
6
9
9
6
12
7
5
8
11
7
10
8
6
12
7
8
9
8
NA
10
12
8
6
NA
8
10
11
6
11
10
12
8
5
7
10
10
7
9
11
10
11
6
9
12
12
12
10
9
NA
8
3
9
11
4
6
7
6
7
8
4
5
10
13
9
9
NA
11
14
7
4
9
7
9
8
4
9
NA
9
7
5
NA
5
10
9
11
11
9
12
11
11
7
6
8
10
10
7
7
10
7
7
7
8
11
6
NA
9
6
10
6
12
6
10
12
NA
7
7
5
9
7
NA
8
9
8
10
6
11
9
11
7
10
12
7
NA
8
8
NA
5
8
5
9
11
11
11
9
8

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=297098&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=297098&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297098&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
Mean10.23333333333338.53333333333333
Biased Variance3.818888888888894.98222222222222
Biased Standard Deviation1.954197760946652.23208920570443
Covariance0.411633109619687
Correlation0.0937400650682905
Determination0.00878719979900734
T-Test1.14544082393613
p-value (2 sided)0.25387541676367
p-value (1 sided)0.126937708381835
95% CI of Correlation[-0.0675360502451502, 0.250242220961641]
Degrees of Freedom148
Number of Observations150

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 10.2333333333333 & 8.53333333333333 \tabularnewline
Biased Variance & 3.81888888888889 & 4.98222222222222 \tabularnewline
Biased Standard Deviation & 1.95419776094665 & 2.23208920570443 \tabularnewline
Covariance & 0.411633109619687 \tabularnewline
Correlation & 0.0937400650682905 \tabularnewline
Determination & 0.00878719979900734 \tabularnewline
T-Test & 1.14544082393613 \tabularnewline
p-value (2 sided) & 0.25387541676367 \tabularnewline
p-value (1 sided) & 0.126937708381835 \tabularnewline
95% CI of Correlation & [-0.0675360502451502, 0.250242220961641] \tabularnewline
Degrees of Freedom & 148 \tabularnewline
Number of Observations & 150 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297098&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]10.2333333333333[/C][C]8.53333333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]3.81888888888889[/C][C]4.98222222222222[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.95419776094665[/C][C]2.23208920570443[/C][/ROW]
[ROW][C]Covariance[/C][C]0.411633109619687[/C][/ROW]
[ROW][C]Correlation[/C][C]0.0937400650682905[/C][/ROW]
[ROW][C]Determination[/C][C]0.00878719979900734[/C][/ROW]
[ROW][C]T-Test[/C][C]1.14544082393613[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.25387541676367[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.126937708381835[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][-0.0675360502451502, 0.250242220961641][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]148[/C][/ROW]
[ROW][C]Number of Observations[/C][C]150[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297098&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297098&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
Mean10.23333333333338.53333333333333
Biased Variance3.818888888888894.98222222222222
Biased Standard Deviation1.954197760946652.23208920570443
Covariance0.411633109619687
Correlation0.0937400650682905
Determination0.00878719979900734
T-Test1.14544082393613
p-value (2 sided)0.25387541676367
p-value (1 sided)0.126937708381835
95% CI of Correlation[-0.0675360502451502, 0.250242220961641]
Degrees of Freedom148
Number of Observations150






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.2204, p-value = 0.3295
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.3812, p-value = 0.304
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.182, p-value = 1.455e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4572, p-value = 0.0008867


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.2204, p-value = 0.3295
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.3812, p-value = 0.304
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.182, p-value = 1.455e-05

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4572, p-value = 0.0008867

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297098&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 2.2204, p-value = 0.3295
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.3812, p-value = 0.304
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 2.182, p-value = 1.455e-05

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4572, p-value = 0.0008867

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297098&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297098&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 = 2.2204, p-value = 0.3295
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.3812, p-value = 0.304
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 2.182, p-value = 1.455e-05

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.4572, p-value = 0.0008867


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()