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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 computationSun, 14 Dec 2014 18:10:49 +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/14/t14185811426onfoiqzky9d02d.htm/, Retrieved Thu, 16 May 2024 06:29:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267797, Retrieved Thu, 16 May 2024 06:29:03 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [correlatie] [2014-12-14 18:10:49] [26b3f07cb5f54f7efd4618e9d9764016] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
149
148
158
128
224
159
105
159
167
165
159
176
54
91
163
124
121
148
221
149
244
148
150
153
94
156
132
105
151
131
157
162
163
59
187
116
148
155
125
116
138
164
162
99
186
188
177
139
162
108
159
110
96
87
97
127
74
114
95
121
130
52
118
48
50
150
154
109
68
194
158
159
67
147
39
100
111
138
101
131
101
114
165
114
111
75
82
121
32
150
117
71
165
154
126
149
145
120
109
132
172
169
114
156
172
68
89
167
113
115
78
118
87
173
2
162
49
122
96
100
82
100
115
141
165
165
110
118
158
146
49
90
121
155
104
147
110
108
113
115
61
60
109
68
111
77
73
151
89
78
110
220
65
141
117
122
63
44
52
131
101
42
152
107
77
154
103
96
175
57
112
143
49
110
131
167
56
137
86
121
149
168
140
88
168
94
51
48
145
66
85
109
63
102
162
86
114
164
119
126
132
142
83
94
81
166
110
64
93
104
105
49
88
95
102
99
63
76
109
117
57
120
73
91
108
105
117
119
31
Dataseries Y:
Download CSV
Histogram 
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
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1
0
0
1
0
0
1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267797&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267797&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267797&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean117.432314410480.550218340611354
Biased Variance1632.690833508130.247478118266242
Biased Standard Deviation40.40656918754840.497471726097315
Covariance-1.37926147245844
Correlation-0.068316497084082
Determination0.00466714377383939
T-Test-1.03170218004568
p-value (2 sided)0.303309605299689
p-value (1 sided)0.151654802649845
Degrees of Freedom227
Number of Observations229

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 117.43231441048 & 0.550218340611354 \tabularnewline
Biased Variance & 1632.69083350813 & 0.247478118266242 \tabularnewline
Biased Standard Deviation & 40.4065691875484 & 0.497471726097315 \tabularnewline
Covariance & -1.37926147245844 \tabularnewline
Correlation & -0.068316497084082 \tabularnewline
Determination & 0.00466714377383939 \tabularnewline
T-Test & -1.03170218004568 \tabularnewline
p-value (2 sided) & 0.303309605299689 \tabularnewline
p-value (1 sided) & 0.151654802649845 \tabularnewline
Degrees of Freedom & 227 \tabularnewline
Number of Observations & 229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267797&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]117.43231441048[/C][C]0.550218340611354[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1632.69083350813[/C][C]0.247478118266242[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]40.4065691875484[/C][C]0.497471726097315[/C][/ROW]
[ROW][C]Covariance[/C][C]-1.37926147245844[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.068316497084082[/C][/ROW]
[ROW][C]Determination[/C][C]0.00466714377383939[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.03170218004568[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.303309605299689[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.151654802649845[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]227[/C][/ROW]
[ROW][C]Number of Observations[/C][C]229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267797&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267797&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
Mean117.432314410480.550218340611354
Biased Variance1632.690833508130.247478118266242
Biased Standard Deviation40.40656918754840.497471726097315
Covariance-1.37926147245844
Correlation-0.068316497084082
Determination0.00466714377383939
T-Test-1.03170218004568
p-value (2 sided)0.303309605299689
p-value (1 sided)0.151654802649845
Degrees of Freedom227
Number of Observations229






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.1613, p-value = 0.9225
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 38.1825, p-value = 5.114e-09
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.9157, p-value = 0.01953

> ad.y
	Anderson-Darling normality test
data:  y
A = 41.5281, p-value < 2.2e-16


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.1613, p-value = 0.9225
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 38.1825, p-value = 5.114e-09
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.9157, p-value = 0.01953

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 41.5281, p-value < 2.2e-16

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267797&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 0.1613, p-value = 0.9225
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 38.1825, p-value = 5.114e-09
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.9157, p-value = 0.01953

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 41.5281, p-value < 2.2e-16

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267797&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267797&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 = 0.1613, p-value = 0.9225
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 38.1825, p-value = 5.114e-09
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.9157, p-value = 0.01953

> ad.y
	Anderson-Darling normality test
data:  y
A = 41.5281, p-value < 2.2e-16


Figures (Output of Computation)

Input Parameters & R Code

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()