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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, 12 Dec 2014 13:30:37 +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/t14183910446rx3xrx2hnckgw3.htm/, Retrieved Thu, 16 May 2024 09:38:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266672, Retrieved Thu, 16 May 2024 09:38:02 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80

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 13:30:37] [d33b7eb92cfcc384850e3711242e8bfe] [Current]
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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 
41
146
182
192
263
35
439
214
341
58
292
85
200
158
199
297
227
108
86
302
148
178
120
207
157
128
296
323
79
70
146
246
196
199
127
153
299
228
190
180
212
269
130
179
243
190
299
121
137
305
157
96
183
52
238
40
226
190
214
145
119
222
222
159
165
249
125
122
186
148
274
172
84
168
102
106
2
139
95
130
72
141
113
206
268
175
77
125
255
111
132
211
92
76
171
83
266
186
50
117
219
246
279
148
137
181
98
226
234
138
85
66
236
106
135
122
218
199
112
278
94
113
84
86
62
222
167
82
207
184
83
183
89
225
237
102
221
128
91
198
204
158
138
226
44
196
83
79
52
105
116
83
196
153
157
75
106
58
75
74
185
265
131
139
196

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=266672&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=266672&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266672&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
Mean10.8969696969697161.769696969697
Biased Variance4.783324150596885417.38938475666
Biased Standard Deviation2.1870811943311373.6029169582066
Covariance0.781005173688101
Correlation0.00482229619557281
Determination2.3254540597836e-05
T-Test0.0615676722444777
p-value (2 sided)0.950982549207192
p-value (1 sided)0.475491274603596
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 & 161.769696969697 \tabularnewline
Biased Variance & 4.78332415059688 & 5417.38938475666 \tabularnewline
Biased Standard Deviation & 2.18708119433113 & 73.6029169582066 \tabularnewline
Covariance & 0.781005173688101 \tabularnewline
Correlation & 0.00482229619557281 \tabularnewline
Determination & 2.3254540597836e-05 \tabularnewline
T-Test & 0.0615676722444777 \tabularnewline
p-value (2 sided) & 0.950982549207192 \tabularnewline
p-value (1 sided) & 0.475491274603596 \tabularnewline
Degrees of Freedom & 163 \tabularnewline
Number of Observations & 165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266672&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]161.769696969697[/C][/ROW]
[ROW][C]Biased Variance[/C][C]4.78332415059688[/C][C]5417.38938475666[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.18708119433113[/C][C]73.6029169582066[/C][/ROW]
[ROW][C]Covariance[/C][C]0.781005173688101[/C][/ROW]
[ROW][C]Correlation[/C][C]0.00482229619557281[/C][/ROW]
[ROW][C]Determination[/C][C]2.3254540597836e-05[/C][/ROW]
[ROW][C]T-Test[/C][C]0.0615676722444777[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.950982549207192[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.475491274603596[/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=266672&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266672&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
Mean10.8969696969697161.769696969697
Biased Variance4.783324150596885417.38938475666
Biased Standard Deviation2.1870811943311373.6029169582066
Covariance0.781005173688101
Correlation0.00482229619557281
Determination2.3254540597836e-05
T-Test0.0615676722444777
p-value (2 sided)0.950982549207192
p-value (1 sided)0.475491274603596
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 = 7.2556, p-value = 0.02657
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 = 0.8665, p-value = 0.02568


\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 = 7.2556, p-value = 0.02657
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 = 0.8665, p-value = 0.02568

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266672&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 = 7.2556, p-value = 0.02657
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 = 0.8665, p-value = 0.02568

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266672&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266672&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 = 7.2556, p-value = 0.02657
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 = 0.8665, p-value = 0.02568


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()