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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 computationThu, 18 Dec 2014 07:32:21 +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/18/t1418887991c8xg2nnoayn9q2m.htm/, Retrieved Fri, 17 May 2024 08:10:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270751, Retrieved Fri, 17 May 2024 08:10:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Percentiles] [Intrinsic Motivat...] [2010-10-12 12:10:58] [b98453cac15ba1066b407e146608df68]
- RMPD  [Kernel Density Estimation] [] [2011-10-18 22:42:23] [b98453cac15ba1066b407e146608df68]
- RMPD    [Percentiles] [] [2011-10-18 22:46:45] [b98453cac15ba1066b407e146608df68]
- RMPD      [Notched Boxplots] [] [2011-10-18 22:58:56] [b98453cac15ba1066b407e146608df68]
- RMP         [Notched Boxplots] [] [2014-10-16 18:35:18] [bcf5edf18529a33bd1494456d2c6cb9a]
- RMPD            [Pearson Correlation] [] [2014-12-18 07:32:21] [88f8137dd67cdcd531568536dca46410] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
91
137
92
148
131
59
128
90
83
116
42
155
96
49
104
76
66
74
99
96
108
97
116
106
80
74
114
87
140
127
74
91
98
126
98
95
133
110
70
95
86
130
96
99
68
121
131
71
102
68
89
87
49
96
100
141
102
110
100
146
147
94
52
61
98
60
118
109
68
109
115
78
118
73
162
122
65
100
82
52
115
90
121
101
104
42
96
110
108
113
57
86
88
115
85
111
102
86
114
94
64
77
105
49
95
89
78
110
117
63
131
102
63
117
57
73
77
105
31
112
139
49
56
158
128
224
105
159
167
165
159
48
119
163
153
148
188
149
63
244
150
132
161
105
162
81
97
110
104
166
88
111
145
99
162
163
109
76
109
120
91
148
108
125
119
116
149
138
148
159
164
176
202
214
188
110
48
54
50
124
121
221
150
153
154
94
156
151
157
194
159
39
100
187
105
111
162
99
186
183
138
101
177
126
101
139
114
114
162
111
75
82
159
158
67
121
32
117
165
147
165
150
154
126
149
145
109
120
172
132
169
172
114
156
167
2
113
165
165
118
173
158
155
49
220
122
151
44
141
152
103
107
175
154
110
143
131
167
137
121
168
149
94
51
168
145
140
109
66
119
164
132
126
83
142
93
117
166
Dataseries Y:
Download CSV
Histogram 
11.3
9.6
13.4
16.1
12.7
12.3
5.7
7.9
12.3
11.6
6.7
12.1
13.3
8
12.2
8.8
9.1
9.9
14.6
10.5
12.6
4.3
13.4
11.8
11.2
12.6
5.6
10.9
9.9
10.3
11.4
8.6
7.7
7.3
11.4
13.6
13.2
7.9
10.7
8.8
8.3
9.6
14.2
11.1
12.6
9
18.9
11.6
10.3
14.6
13.85
15.9
10.95
15.1
15.95
14.6
8.5
17.6
13.5
15.35
12.9
4.9
6.4
12.6
9.6
10.35
11.6
15.4
9.6
16.6
14.85
11.75
18.45
14.85
19.9
18.45
13.6
15
11.35
12.65
18.1
13.4
13.9
16.6
15.25
11.2
15.85
16.1
17.35
13.15
11.15
15.6
13.1
12.15
12.4
18.2
14.9
11.2
14.6
14.75
7.85
13.6
7.85
10.95
9.95
14.1
14.9
16.25
15.65
14.6
19.2
14.9
13.4
16.85
10.95
12.2
13.2
15.2
8.1
15.65
12.2
7.65
15.2
7.4
6.7
12.6
13.3
11.1
8.2
11.4
6.4
11.85
10.6
11.9
6.4
13.8
13.8
11.7
11.4
10.9
9.9
9
9.7
10.8
19.9
15.15
10.3
16.85
12.6
9.3
12.35
5.9
11.4
16.65
13
10.8
11.8
13.95
15.7
15.35
15.1
10.9
17.75
13.3
16.65
10.1
12.9
14.3
12.8
14.8
9.3
12
15.9
13
14.5
7.7
4.35
6.3
12.7
9.3
10
10.8
18.1
11.5
17.85
8.3
11.7
10.4
11.8
17.1
16.1
14.7
10.6
11.3
12.7
12.6
12.5
7.6
9.2
11.1
16.2
13.6
12.3
11.4
14.1
12.6
14.5
14.75
13
14.8
12.45
12.65
13.2
19.1
13.35
17.35
8.6
16.1
17.75
18.4
16.15
18.4
15.25
17.65
16.35
17.65
14.35
13.6
18.25
14.75
9.9
16.85
16
18.25
18.95
16.1
15.6
15.4
15.4
13.35
17.1
19.1
19.1
7.6
19.25
12.75
14.75
9.85
13.6
15.25
12.4
11.9
18.15
16.35
12.35
17.75
15.6
19.3
17.1
18.4
12.85
19.05
9.5
4.5
18.55
13.6
19.1
13.35
11.7
14.05
17.6
13.35
16.1
11.95
11.85
7.7
14.6
13.2

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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270751&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270751&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270751&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'George Udny Yule' @ yule.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean116.40287769784212.975
Biased Variance1581.0679053879211.4802293165468
Biased Standard Deviation39.76264459751043.3882487093699
Covariance40.9247292418773
Correlation0.302670605058516
Determination0.0916094951664883
T-Test5.27580205818605
p-value (2 sided)2.67562768385687e-07
p-value (1 sided)1.33781384192844e-07
Degrees of Freedom276
Number of Observations278

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 116.402877697842 & 12.975 \tabularnewline
Biased Variance & 1581.06790538792 & 11.4802293165468 \tabularnewline
Biased Standard Deviation & 39.7626445975104 & 3.3882487093699 \tabularnewline
Covariance & 40.9247292418773 \tabularnewline
Correlation & 0.302670605058516 \tabularnewline
Determination & 0.0916094951664883 \tabularnewline
T-Test & 5.27580205818605 \tabularnewline
p-value (2 sided) & 2.67562768385687e-07 \tabularnewline
p-value (1 sided) & 1.33781384192844e-07 \tabularnewline
Degrees of Freedom & 276 \tabularnewline
Number of Observations & 278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270751&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]116.402877697842[/C][C]12.975[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1581.06790538792[/C][C]11.4802293165468[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]39.7626445975104[/C][C]3.3882487093699[/C][/ROW]
[ROW][C]Covariance[/C][C]40.9247292418773[/C][/ROW]
[ROW][C]Correlation[/C][C]0.302670605058516[/C][/ROW]
[ROW][C]Determination[/C][C]0.0916094951664883[/C][/ROW]
[ROW][C]T-Test[/C][C]5.27580205818605[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.67562768385687e-07[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.33781384192844e-07[/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=270751&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270751&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
Mean116.40287769784212.975
Biased Variance1581.0679053879211.4802293165468
Biased Standard Deviation39.76264459751043.3882487093699
Covariance40.9247292418773
Correlation0.302670605058516
Determination0.0916094951664883
T-Test5.27580205818605
p-value (2 sided)2.67562768385687e-07
p-value (1 sided)1.33781384192844e-07
Degrees of Freedom276
Number of Observations278






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1364, p-value = 0.5666
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 = 0.8152, p-value = 0.03473

> 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 = 1.1364, p-value = 0.5666
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 = 0.8152, p-value = 0.03473

 \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=270751&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.1364, p-value = 0.5666
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 = 0.8152, p-value = 0.03473

[/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=270751&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270751&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 = 1.1364, p-value = 0.5666
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 = 0.8152, p-value = 0.03473

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.4263, p-value = 0.3124


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()