FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 12 Dec 2014 13:03:48 +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/12/t141838954630w5t60czrdnfru.htm/, Retrieved Thu, 16 May 2024 20:04:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266637, Retrieved Thu, 16 May 2024 20:04:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2014-12-12 13:03:48] [fe6a3e2d5def86ae31dbd813f23b564f] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9
11
12
12
7
12
12
12
10
15
10
15
10
15
9
15
12
13
12
12
8
9
15
12
12
15
11
12
6
14
12
12
12
11
12
12
12
12
8
8
12
12
11
10
11
12
13
12
12
10
10
11
8
12
9
12
9
11
15
8
8
11
11
11
13
7
12
8
8
4
11
10
7
12
11
9
10
8
8
11
12
10
10
12
8
11
8
10
14
9
9
10
13
12
13
8
3
8
12
11
9
12
12
12
10
13
9
12
11
14
11
9
12
8
15
12
14
12
9
9
13
13
15
11
7
10
11
14
14
13
12
8
13
9
12
13
11
11
13
12
12
10
9
10
13
13
9
11
12
8
12
12
12
9
12
12
11
12
6
7
10
12
10
12
9
Dataseries Y:
Download CSV
Histogram 
34
95
96
122
162
38
175
89
142
42
135
29
121
86
79
161
129
66
55
149
115
92
60
76
110
63
148
127
50
24
112
115
174
103
77
100
79
102
128
95
114
97
87
129
142
91
168
88
69
55
103
27
149
40
99
73
102
82
117
88
85
135
135
90
70
118
56
20
122
95
150
59
39
62
97
64
22
79
83
64
26
63
85
80
129
78
45
93
143
85
81
105
52
92
95
53
81
102
26
78
97
85
148
41
75
109
45
110
141
67
81
39
112
47
48
86
129
122
88
155
67
123
56
59
38
68
86
25
96
77
28
149
74
128
124
83
100
104
59
86
93
98
74
95
30
73
74
44
40
93
46
28
106
83
53
22
103
64
40
26
100
122
67
108
103

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266637&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266637&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266637&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean10.896969696969786.9818181818182
Biased Variance4.783324150596881298.56330578512
Biased Standard Deviation2.1870811943311336.03558388295
Covariance-2.23359201773836
Correlation-0.0281687310409002
Determination0.000793477408454572
T-Test-0.359777048902341
p-value (2 sided)0.719479571449972
p-value (1 sided)0.359739785724986
Degrees of Freedom163
Number of Observations165

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 10.8969696969697 & 86.9818181818182 \tabularnewline
Biased Variance & 4.78332415059688 & 1298.56330578512 \tabularnewline
Biased Standard Deviation & 2.18708119433113 & 36.03558388295 \tabularnewline
Covariance & -2.23359201773836 \tabularnewline
Correlation & -0.0281687310409002 \tabularnewline
Determination & 0.000793477408454572 \tabularnewline
T-Test & -0.359777048902341 \tabularnewline
p-value (2 sided) & 0.719479571449972 \tabularnewline
p-value (1 sided) & 0.359739785724986 \tabularnewline
Degrees of Freedom & 163 \tabularnewline
Number of Observations & 165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266637&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]10.8969696969697[/C][C]86.9818181818182[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4.78332415059688[/C][C]1298.56330578512[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.18708119433113[/C][C]36.03558388295[/C][/ROW]
[ROW][C]Covariance[/C][C]-2.23359201773836[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.0281687310409002[/C][/ROW]
[ROW][C]Determination[/C][C]0.000793477408454572[/C][/ROW]
[ROW][C]T-Test[/C][C]-0.359777048902341[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.719479571449972[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.359739785724986[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]163[/C][/ROW]
[ROW][C]Number of Observations[/C][C]165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266637&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266637&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
Mean10.896969696969786.9818181818182
Biased Variance4.783324150596881298.56330578512
Biased Standard Deviation2.1870811943311336.03558388295
Covariance-2.23359201773836
Correlation-0.0281687310409002
Determination0.000793477408454572
T-Test-0.359777048902341
p-value (2 sided)0.719479571449972
p-value (1 sided)0.359739785724986
Degrees of Freedom163
Number of Observations165






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 9.4737, p-value = 0.008766
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.6721, p-value = 0.2629
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4676, p-value = 1.054e-08

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.439, p-value = 0.2901


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 9.4737, p-value = 0.008766
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.6721, p-value = 0.2629
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4676, p-value = 1.054e-08

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.439, p-value = 0.2901

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266637&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 9.4737, p-value = 0.008766
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.6721, p-value = 0.2629
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4676, p-value = 1.054e-08

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.439, p-value = 0.2901

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266637&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266637&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 = 9.4737, p-value = 0.008766
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 2.6721, p-value = 0.2629
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 3.4676, p-value = 1.054e-08

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.439, p-value = 0.2901


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par3 = FALSE ;
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()