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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 computationTue, 12 Dec 2017 17:55:13 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/12/t15130977400xsyjn2uxdzo9vn.htm/, Retrieved Wed, 15 May 2024 14:44:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309156, Retrieved Wed, 15 May 2024 14:44:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2017-12-12 16:55:13] [6b1874e4714eefd7b92809f59303eb6f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
58.5
59.8
64.6
62.2
68
64.3
58.9
64.8
67.5
76.2
73.7
70.4
67.7
63.7
72.4
66
70.1
70.4
66.6
72.6
74
79
76.1
72.3
71.6
67.2
73.8
70.8
71.4
70.4
70.7
70.6
75.5
82.1
74.3
76.3
74.5
71.1
73.3
73.8
69
71.1
71.9
69
77.3
82.8
74
77.6
72.3
70.7
81
76.4
72.3
79.5
73.3
74.5
82.7
83.8
81.6
85.5
76.7
71.8
80.2
76.8
76.1
80.7
71.3
80.9
85
84.5
87.7
87.7
80.2
74.4
85.8
77
84.5
83.6
77.7
85.7
87.9
93.7
92.3
87
89.1
81.3
92.7
83.9
87.3
89.1
86.9
91.7
93
105.3
101.6
94.2
100.5
95.8
95.8
102.1
96
96.8
98.9
93.4
105.5
110.9
98.6
102.6
93.5
90.8
99.7
97.8
91.1
98.1
96
93.5
101.2
105.2
98.9
101.3
92.1
90.6
105.4
98.4
92.7
101.2
93.4
98.3
104.3
107
107.7
108.9
99.6
96.1
109
99.5
104.6
99.9
94.1
105.3
110.4
110.5
110
108.5
104.3
101.2
109.2
99.6
105.6
106.2
102.2
107.5
105.8
120.5
113.2
104.3
107.7
99.2
105.1
104.3
106.1
100.8
106.7
101.6
104.4
114.8
105.4
104
102
96.5
102.3
105.3
101.9
102.2
102.8
100.4
110.7
116.4
106
109.2
103
99.8
109.8
107.3
101.2
111.8
106.9
103.5
113.1
119.4
113.3
115
104.7
107.2
116.6
111.3
111.4
115
102.4
111.4
113.2
112.9
114.2
115.6
107.1
102.3
117.9
105.8
114.3
113.1
102.9
112.2
Dataseries Y:
Download CSV
Histogram 
55.5
63
77.2
71.1
90.1
91.5
76.1
87.8
81
77.2
73.8
68.9
68.4
65.2
78.7
77
97.6
88.1
98.7
93.4
68
87.9
75.8
66.3
68.4
71.3
77.4
87.1
88.5
85.9
92.7
88.5
80.2
81.8
70.4
82.2
72.8
69
83
92.4
92.3
100.5
106.9
99.5
85.9
92.6
77.4
84.1
75.3
73.8
100.1
90.7
96.5
111.8
97.4
100.8
93.7
82
86
84.3
73.1
75.4
97.9
97.5
106
112.8
99.5
100.8
102.9
88.8
91.3
88.3
77.4
80.5
96.7
93.8
105
117.1
111.1
105.8
95.7
97.1
91
90.9
83.5
82.3
101.7
108.3
114
118.2
103.4
106.8
95.4
101.8
95.6
94.8
94
82.4
95.8
106.7
114.1
103.9
117.4
105.9
101.7
98.7
91.3
102.3
80.5
86.7
102.6
107.3
108
124.3
117.1
103.9
104.7
95.9
94.2
102.7
70.3
90.2
107.3
104.6
102.7
124.5
117.8
104.2
99.9
91.5
95.7
91.4
86.2
91.5
115.5
113.9
131.9
121.2
105.2
107.5
113.8
100.5
104.8
103.8
93.1
106.2
117.5
109.9
123.6
131.7
111
122
110.9
108
103.6
107.3
94.4
85.2
113.2
111.7
124.3
124
133.4
112.6
115.8
112.3
103.6
111.4
95.1
93.4
117.3
121.5
123.1
139.3
125.8
108.6
121
111.6
99.7
116.7
90.3
90.4
117.3
121.6
114.6
133.3
127.4
115
112.6
108.3
107.6
109
89
102.5
124.5
124.2
130.8
138.7
127.6
130.9
136.9
125.2
131.3
124.1
103.2
118.1
136.5
117.8
145.1
158.8
136.9
132.7

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309156&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309156&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309156&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean92.0816037735849100.866509433962
Biased Variance248.463576673193331.864491589534
Biased Standard Deviation15.762727450323918.2171482836786
Covariance208.185779084324
Correlation0.721582338250543
Determination0.520681070875122
T-Test15.1036965601848
p-value (2 sided)2.21688133955835e-35
p-value (1 sided)1.10844066977918e-35
95% CI of Correlation[0.650038183985693, 0.780446561716617]
Degrees of Freedom210
Number of Observations212

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 92.0816037735849 & 100.866509433962 \tabularnewline
Biased Variance & 248.463576673193 & 331.864491589534 \tabularnewline
Biased Standard Deviation & 15.7627274503239 & 18.2171482836786 \tabularnewline
Covariance & 208.185779084324 \tabularnewline
Correlation & 0.721582338250543 \tabularnewline
Determination & 0.520681070875122 \tabularnewline
T-Test & 15.1036965601848 \tabularnewline
p-value (2 sided) & 2.21688133955835e-35 \tabularnewline
p-value (1 sided) & 1.10844066977918e-35 \tabularnewline
95% CI of Correlation & [0.650038183985693, 0.780446561716617] \tabularnewline
Degrees of Freedom & 210 \tabularnewline
Number of Observations & 212 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309156&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]92.0816037735849[/C][C]100.866509433962[/C][/ROW]
[ROW][C]Biased Variance[/C][C]248.463576673193[/C][C]331.864491589534[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]15.7627274503239[/C][C]18.2171482836786[/C][/ROW]
[ROW][C]Covariance[/C][C]208.185779084324[/C][/ROW]
[ROW][C]Correlation[/C][C]0.721582338250543[/C][/ROW]
[ROW][C]Determination[/C][C]0.520681070875122[/C][/ROW]
[ROW][C]T-Test[/C][C]15.1036965601848[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.21688133955835e-35[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.10844066977918e-35[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.650038183985693, 0.780446561716617][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]210[/C][/ROW]
[ROW][C]Number of Observations[/C][C]212[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309156&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309156&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
Mean92.0816037735849100.866509433962
Biased Variance248.463576673193331.864491589534
Biased Standard Deviation15.762727450323918.2171482836786
Covariance208.185779084324
Correlation0.721582338250543
Determination0.520681070875122
T-Test15.1036965601848
p-value (2 sided)2.21688133955835e-35
p-value (1 sided)1.10844066977918e-35
95% CI of Correlation[0.650038183985693, 0.780446561716617]
Degrees of Freedom210
Number of Observations212






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 14.919, p-value = 0.0005758
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.2588, p-value = 0.5329
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 4.5398, p-value = 2.711e-11

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.19207, p-value = 0.8949


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 14.919, p-value = 0.0005758
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.2588, p-value = 0.5329
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 4.5398, p-value = 2.711e-11

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.19207, p-value = 0.8949

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309156&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 14.919, p-value = 0.0005758
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.2588, p-value = 0.5329
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 4.5398, p-value = 2.711e-11

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 0.19207, p-value = 0.8949

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309156&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309156&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 = 14.919, p-value = 0.0005758
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 1.2588, p-value = 0.5329
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 4.5398, p-value = 2.711e-11

> ad.y
	Anderson-Darling normality test
data:  y
A = 0.19207, p-value = 0.8949


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
library(psychometric)
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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Variance',header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Standard Deviation',header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Covariance',header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Correlation',header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Determination',header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-Test',header=TRUE)
a<-table.element(a,as.matrix(corxy$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,'95% CI of Correlation',header=TRUE)
a<-table.element(a,paste('[',CIr(r=cxy, n = lx, level = .95)[1],', ', CIr(r=cxy, n = lx, level = .95)[2],']',sep=''),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')
qqPlot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qqPlot(y,main='QQplot of variable y')
dev.off()