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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationTue, 16 Dec 2014 16:57:52 +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/2014/Dec/16/t1418749103ghoov3rolxvd5mr.htm/, Retrieved Thu, 31 Oct 2024 23:26:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=269838, Retrieved Thu, 31 Oct 2024 23:26:11 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Paired and Unpaired Two Samples Tests about the Mean] [] [2010-11-01 13:07:12] [b98453cac15ba1066b407e146608df68]
- RMP   [Paired and Unpaired Two Samples Tests about the Mean] [] [2014-10-21 07:47:40] [32b17a345b130fdf5cc88718ed94a974]
- RMPD      [Pearson Correlation] [numeracy total] [2014-12-16 16:57:52] [88f8137dd67cdcd531568536dca46410] [Current]
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Dataseries X:
21
22
22
18
23
12
20
22
21
19
22
15
20
19
18
15
20
21
21
15
16
23
21
18
25
9
30
20
23
16
16
19
25
18
23
21
10
14
22
26
23
23
24
24
18
23
15
19
16
25
23
17
19
21
18
27
21
13
8
29
28
23
21
19
19
20
18
19
17
19
25
19
22
23
14
16
24
20
12
24
22
12
22
20
10
23
17
22
24
18
21
20
20
22
19
20
26
23
24
21
21
19
8
17
20
11
8
15
18
18
19
19
23
22
21
25
30
17
27
23
23
18
18
23
19
15
20
16
24
25
25
19
19
16
19
19
23
21
22
19
20
20
3
23
23
20
15
16
7
24
17
24
24
19
25
20
28
23
27
18
28
21
19
23
27
22
28
25
21
22
28
20
29
25
25
20
20
16
20
20
23
18
25
18
19
25
25
25
24
19
26
10
17
13
17
30
25
4
16
21
23
22
17
20
20
22
16
23
0
18
25
23
12
18
24
11
18
23
24
29
18
15
29
16
19
22
16
23
23
19
4
20
24
20
4
24
22
16
3
15
24
17
20
27
26
23
17
20
22
19
24
19
23
15
27
26
22
22
18
15
22
27
10
20
17
23
19
13
27
23
16
25
2
26
20
23
22
24
Dataseries Y:
12.9
12.2
12.8
7.4
6.7
12.6
14.8
13.3
11.1
8.2
11.4
6.4
10.6
12
6.3
11.3
11.9
9.3
9.6
10
6.4
13.8
10.8
13.8
11.7
10.9
16.1
13.4
9.9
11.5
8.3
11.7
9
9.7
10.8
10.3
10.4
12.7
9.3
11.8
5.9
11.4
13
10.8
12.3
11.3
11.8
7.9
12.7
12.3
11.6
6.7
10.9
12.1
13.3
10.1
5.7
14.3
8
13.3
9.3
12.5
7.6
15.9
9.2
9.1
11.1
13
14.5
12.2
12.3
11.4
8.8
14.6
12.6
13
12.6
13.2
9.9
7.7
10.5
13.4
10.9
4.3
10.3
11.8
11.2
11.4
8.6
13.2
12.6
5.6
9.9
8.8
7.7
9
7.3
11.4
13.6
7.9
10.7
10.3
8.3
9.6
14.2
8.5
13.5
4.9
6.4
9.6
11.6
11.1
4.35
12.7
18.1
17.85
16.6
12.6
17.1
19.1
16.1
13.35
18.4
14.7
10.6
12.6
16.2
13.6
18.9
14.1
14.5
16.15
14.75
14.8
12.45
12.65
17.35
8.6
18.4
16.1
11.6
17.75
15.25
17.65
16.35
17.65
13.6
14.35
14.75
18.25
9.9
16
18.25
16.85
14.6
13.85
18.95
15.6
14.85
11.75
18.45
15.9
17.1
16.1
19.9
10.95
18.45
15.1
15
11.35
15.95
18.1
14.6
15.4
15.4
17.6
13.35
19.1
15.35
7.6
13.4
13.9
19.1
15.25
12.9
16.1
17.35
13.15
12.15
12.6
10.35
15.4
9.6
18.2
13.6
14.85
14.75
14.1
14.9
16.25
19.25
13.6
13.6
15.65
12.75
14.6
9.85
12.65
19.2
16.6
11.2
15.25
11.9
13.2
16.35
12.4
15.85
18.15
11.15
15.65
17.75
7.65
12.35
15.6
19.3
15.2
17.1
15.6
18.4
19.05
18.55
19.1
13.1
12.85
9.5
4.5
11.85
13.6
11.7
12.4
13.35
11.4
14.9
19.9
11.2
14.6
17.6
14.05
16.1
13.35
11.85
11.95
14.75
15.15
13.2
16.85
7.85
7.7
12.6
7.85
10.95
12.35
9.95
14.9
16.65
13.4
13.95
15.7
16.85
10.95
15.35
12.2
15.1
17.75
15.2
14.6
16.65
8.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269838&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]1 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=269838&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269838&T=0

As an alternative you can also use a 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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean19.996402877697812.975
Biased Variance26.104303607473711.4802293165468
Biased Standard Deviation5.109237086637673.3882487093699
Covariance2.13113718411552
Correlation0.122663412428338
Determination0.0150463127485646
T-Test2.05334383307683
p-value (2 sided)0.040981554757118
p-value (1 sided)0.020490777378559
Degrees of Freedom276
Number of Observations278

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 19.9964028776978 & 12.975 \tabularnewline
Biased Variance & 26.1043036074737 & 11.4802293165468 \tabularnewline
Biased Standard Deviation & 5.10923708663767 & 3.3882487093699 \tabularnewline
Covariance & 2.13113718411552 \tabularnewline
Correlation & 0.122663412428338 \tabularnewline
Determination & 0.0150463127485646 \tabularnewline
T-Test & 2.05334383307683 \tabularnewline
p-value (2 sided) & 0.040981554757118 \tabularnewline
p-value (1 sided) & 0.020490777378559 \tabularnewline
Degrees of Freedom & 276 \tabularnewline
Number of Observations & 278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269838&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]19.9964028776978[/C][C]12.975[/C][/ROW]
[ROW][C]Biased Variance[/C][C]26.1043036074737[/C][C]11.4802293165468[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]5.10923708663767[/C][C]3.3882487093699[/C][/ROW]
[ROW][C]Covariance[/C][C]2.13113718411552[/C][/ROW]
[ROW][C]Correlation[/C][C]0.122663412428338[/C][/ROW]
[ROW][C]Determination[/C][C]0.0150463127485646[/C][/ROW]
[ROW][C]T-Test[/C][C]2.05334383307683[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.040981554757118[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.020490777378559[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]276[/C][/ROW]
[ROW][C]Number of Observations[/C][C]278[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269838&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269838&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean19.996402877697812.975
Biased Variance26.104303607473711.4802293165468
Biased Standard Deviation5.109237086637673.3882487093699
Covariance2.13113718411552
Correlation0.122663412428338
Determination0.0150463127485646
T-Test2.05334383307683
p-value (2 sided)0.040981554757118
p-value (1 sided)0.020490777378559
Degrees of Freedom276
Number of Observations278







Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 98.6694, p-value < 2.2e-16
alternative hypothesis: greater
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2947, p-value = 0.1926
alternative hypothesis: greater
> ad.x
	Anderson-Darling normality test
data:  x
A = 4.2713, p-value = 1.233e-10
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4263, p-value = 0.3124

\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 98.6694, p-value < 2.2e-16
alternative hypothesis: greater
\tabularnewline
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2947, p-value = 0.1926
alternative hypothesis: greater
\tabularnewline
> ad.x
	Anderson-Darling normality test
data:  x
A = 4.2713, p-value = 1.233e-10
\tabularnewline
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4263, p-value = 0.3124
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=269838&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 98.6694, p-value < 2.2e-16
alternative hypothesis: greater
[/C][/ROW] [ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2947, p-value = 0.1926
alternative hypothesis: greater
[/C][/ROW] [ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 4.2713, p-value = 1.233e-10
[/C][/ROW] [ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4263, p-value = 0.3124
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=269838&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269838&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 98.6694, p-value < 2.2e-16
alternative hypothesis: greater
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2947, p-value = 0.1926
alternative hypothesis: greater
> ad.x
	Anderson-Darling normality test
data:  x
A = 4.2713, p-value = 1.233e-10
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4263, p-value = 0.3124



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
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,'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()